This document summarizes a talk about higher-order link prediction in networks. It discusses organizational principles of systems with higher-order interactions, how they evolve over time through simplicial closure events, and how insights can be used to create effective higher-order link prediction methods. Key points include that simplicial closure depends on the structure and strength of ties in the projected graph, and this closure process is similar for 3 and 4 nodes.
1. The document discusses sequences of sets, which is a common data structure where each item in a sequence can be a set of elements rather than a single element. Examples of data that can be modeled as sequences of sets include email recipients, tags on questions, academic coauthors, and contacts.
2. The authors provide a generative model to capture important characteristics of sequences of sets, such as subsets and supersets of prior sets being common and recency bias in repeat behavior.
3. Applications of the model include predicting new sets, anomaly detection, understanding user behaviors, and simulation.
This document discusses research on modeling and predicting higher-order interactions in networks beyond pairwise connections. The researchers collected datasets containing time-stamped groups or "simplices" of nodes and analyzed properties like triangle closure. They propose "higher-order link prediction" to predict which new simplices will form based on structural features like edge weights between nodes. Scoring functions were tested and averages of edge weights often performed well, differing from classical link prediction methods.
Simplicial closure & higher-order link predictionAustin Benson
The document discusses higher-order link prediction in networks. It summarizes previous work representing higher-order interactions as tensors, hypergraphs, etc. It then proposes evaluating models of higher-order data using "higher-order link prediction" to predict which groups of more than two nodes will interact based on past data. The authors analyze dynamics of triadic closure in several real-world networks and propose methods to predict closure based on structural properties like edge weights.
Sampling methods for counting temporal motifsAustin Benson
The document summarizes research on developing scalable algorithms for counting temporal network motifs in real-time from high-throughput temporal network data streams. It discusses existing methods being insufficient and the problem of not having algorithms that can analyze modern temporal network datasets at fine time scales and high frequencies. It also briefly introduces the idea of using parallel sampling to speed up motif counting algorithms and enable analysis of very large temporal networks.
Link prediction in networks with core-fringe structureAustin Benson
1. The document discusses link prediction in networks with a core-fringe structure. It examines how including connections from fringe nodes affects the performance of link prediction algorithms on the core nodes.
2. An experiment was conducted where a link prediction algorithm was run multiple times, each time including more fringe nodes and connections in order to measure the effect on link prediction accuracy for the core nodes.
3. The results showed that including more information from the fringe helped improve the link prediction performance on the core nodes.
The document discusses different models for how social networks grow over time, including preferential attachment and fitness models. It proposes using discrete choice theory as a way to model network growth, which allows incorporating covariates and flexible modeling. The approach is statistically rigorous and allows easy incorporation of new models and effects compared to traditional static network models.
1. The document discusses sequences of sets, which is a common data structure where each item in a sequence can be a set of elements rather than a single element. Examples of data that can be modeled as sequences of sets include email recipients, tags on questions, academic coauthors, and contacts.
2. The authors provide a generative model to capture important characteristics of sequences of sets, such as subsets and supersets of prior sets being common and recency bias in repeat behavior.
3. Applications of the model include predicting new sets, anomaly detection, understanding user behaviors, and simulation.
This document discusses research on modeling and predicting higher-order interactions in networks beyond pairwise connections. The researchers collected datasets containing time-stamped groups or "simplices" of nodes and analyzed properties like triangle closure. They propose "higher-order link prediction" to predict which new simplices will form based on structural features like edge weights between nodes. Scoring functions were tested and averages of edge weights often performed well, differing from classical link prediction methods.
Simplicial closure & higher-order link predictionAustin Benson
The document discusses higher-order link prediction in networks. It summarizes previous work representing higher-order interactions as tensors, hypergraphs, etc. It then proposes evaluating models of higher-order data using "higher-order link prediction" to predict which groups of more than two nodes will interact based on past data. The authors analyze dynamics of triadic closure in several real-world networks and propose methods to predict closure based on structural properties like edge weights.
Sampling methods for counting temporal motifsAustin Benson
The document summarizes research on developing scalable algorithms for counting temporal network motifs in real-time from high-throughput temporal network data streams. It discusses existing methods being insufficient and the problem of not having algorithms that can analyze modern temporal network datasets at fine time scales and high frequencies. It also briefly introduces the idea of using parallel sampling to speed up motif counting algorithms and enable analysis of very large temporal networks.
Link prediction in networks with core-fringe structureAustin Benson
1. The document discusses link prediction in networks with a core-fringe structure. It examines how including connections from fringe nodes affects the performance of link prediction algorithms on the core nodes.
2. An experiment was conducted where a link prediction algorithm was run multiple times, each time including more fringe nodes and connections in order to measure the effect on link prediction accuracy for the core nodes.
3. The results showed that including more information from the fringe helped improve the link prediction performance on the core nodes.
The document discusses different models for how social networks grow over time, including preferential attachment and fitness models. It proposes using discrete choice theory as a way to model network growth, which allows incorporating covariates and flexible modeling. The approach is statistically rigorous and allows easy incorporation of new models and effects compared to traditional static network models.
The document discusses three perspectives on predicting sets of items rather than single items. It describes how sets are common in data such as team formations, medical codes, and online purchases. It then discusses three specific approaches to set prediction: (1) predicting which sets an individual will interact with based on their history, (2) modeling sequences of sets using a generative model, and (3) understanding characteristics of set-based data like subsets and repeats. Applications include prediction, analysis, and simulation.
Simplicial closure and higher-order link predictionAustin Benson
This document summarizes research on simplicial closure and higher-order link prediction in network science. It finds that groups of nodes often interact through complex trajectories before reaching "simplicial closure" where all nodes are jointly present in a simplex. Predicting these closed simplices is framed as a higher-order link prediction problem. Various score functions are proposed based on edge weights, node neighborhoods, and similarity measures. Scores combining local edge weight information consistently perform well, outperforming classical link prediction approaches. The results provide insights into higher-order structure and a framework for evaluating models of complex relational data.
Three hypergraph eigenvector centralitiesAustin Benson
Three hypergraph eigenvector centralities are proposed to measure the importance of nodes in complex systems modeled as hypergraphs. Hypergraphs generalize graphs by allowing edges to connect any number of nodes. The proposed centralities are adaptations of the standard graph eigenvector centrality to hypergraphs. They measure a node's centrality based on 1) the centralities of its neighbors, 2) being positive values, and 3) being the principal eigenvector of the hypergraph adjacency matrix.
Simplicial closure and higher-order link prediction --- SIAMNS18Austin Benson
The document discusses higher-order link prediction, which aims to predict the formation of new groups or "simplices" containing more than two nodes, based on structural properties in timestamped simplex data from various domains. It finds that predicting the closure of open triangles (where a pair of nodes have interacted but not with the third) performs well, and that simply averaging the edge weights in a triangle is often a good predictor. Predicting new structures in communication, collaboration and proximity networks can provide insights beyond classical link prediction.
Simplicial closure and higher-order link prediction (SIAMNS18)Austin Benson
This document summarizes research on modeling and predicting the formation of higher-order relationships or interactions between nodes in network datasets. It introduces the concept of "simplicial closure" to describe how groups of nodes interact over time until forming a simplex or higher-order relationship. The researchers propose "higher-order link prediction" as a framework to evaluate models for predicting the formation of new simplices. They test various methods for scoring open triangles based on edge weights and other structural properties to predict which will become closed triangles. The results show these approaches can significantly outperform random prediction, with simply averaging edge weights often performing well.
The study about the analysis of responsiveness pair clustering tosocial netwo...acijjournal
In this study, regional (cities, towns and villages
) data and tweet data are obtained from Twitter, an
d
extract information of "purchase information (Where
and what bought)" from the tweet data by
morphological analysis and rule-based dependency an
alysis. Then, the "The regional information" and th
e
"Theinformation of purchase history (Where and wha
t bought information)" are captured as bipartite
graph, and Responsiveness Pair Clustering analysis
(a clustering using correspondence analysis as
similarity measure) is conducted. In this study, si
nce it was found to be difficult to analyze a netwo
rk such
as bipartite graph having limitations in links by u
sing modularity Q, responsiveness is used instead o
f
modularity Q as similarity measure. As a result of
this analysis, "regional information cluster" which
refers
to similar "Theinformation of purchase history" nod
es group is generated. Finally, similar regions are
visualized by mapping the regional information clus
ter on the map. This visualization system is expect
ed to
contribute as an analytical tool for customers’ pur
chasing behaviour and so on.
FUZZY STATISTICAL DATABASE AND ITS PHYSICAL ORGANIZATIONijdms
This document discusses fuzzy statistical databases and their physical organization. It introduces the concept of fuzzy cardinality for counting elements in a fuzzy set or fuzzy relation. A fuzzy statistical database is proposed to store fuzzy statistics generated from fuzzy relational databases. This fuzzy statistical database contains fuzzy statistical tables, which can be type-1 or type-2 depending on the complexity of the fuzzy attributes. The physical organization of these fuzzy statistical tables is discussed to facilitate efficient storage and retrieval of the imprecise statistical data.
K-means and bayesian networks to determine building damage levelsTELKOMNIKA JOURNAL
Many troubles in life require decision-making with convoluted processes because they are caused by uncertainty about the process of relationships that appear in the system. This problem leads to the creation of a model called the Bayesian Network. Bayesian Network is a Bayesian supported development supported by computing advancements. The Bayesian network has also been developed in various fields. At this time, information can implement Bayesian Networks in determining the extent of damage to buildings using individual building data. In practice, there is mixed data which is a combination of continuous and discrete variables. Therefore, to simplify the study it is assumed that all variables are discrete in order to solve practical problems in the implementation of theory. Discretization method used is the K-Means clustering because the percentage of validity obtained by this method is greater than the binning method.
Computational Frameworks for Higher-order Network Data AnalysisAustin Benson
1. The document discusses computational frameworks for analyzing higher-order network data, where interactions can involve more than two nodes. Real-world systems often involve higher-order interactions that are reduced to pairwise connections.
2. The author presents several datasets involving higher-order interactions and shows that predicting the formation of new higher-order connections is similar to link prediction but considers groups of nodes rather than individual links. Structural properties like edge density and tie strength influence the likelihood of simplicial closure.
3. Models are proposed to score open simplices based on structural features and predict which will transition to closed simplices. Accounting for higher-order structure provides new insights beyond traditional network analysis of pairwise connections.
Simplicial closure and higher-order link prediction LA/OPTAustin Benson
- The speaker proposes a framework called "higher-order link prediction" to evaluate models of higher-order network data. This extends classical link prediction to predict new groups of nodes that will form simplices.
- Analysis of datasets shows that many have many "open triangles" of nodes connected by edges but not in a simplex. A simple probabilistic model can account for variation in open triangles.
- Simplicial closure probability depends on edge density and tie strength between nodes, both for 3 and 4-node groups.
- For higher-order link prediction, the speaker evaluates score functions based on edge weights, structural properties, whole-network similarities, and machine learning to predict which open triangles will close.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
This document summarizes an empirical study comparing several supervised machine learning approaches for word sense disambiguation: Naive Bayes, decision tree, decision list, and support vector machine (SVM). The study used a dataset of 15 words annotated with senses from WordNet and Senseval-3. Each approach was implemented and evaluated based on its accuracy in identifying the correct sense of each word. The results showed that the decision list approach achieved the highest overall accuracy of 69.12%, followed by SVM at 56.11%, naive Bayes at 58.32%, and decision tree at 45.14%. Thus, the study concluded that decision list performed best on this dataset for the task of word sense disambiguation.
Higher-order link prediction and other hypergraph modelingAustin Benson
Higher-order link prediction and other hypergraph modeling can better model real-world systems composed of higher-order interactions that are often reduced to pairwise ones. Hypergraphs allow the modeling of interactions between more than two nodes, like groups of people collaborating, multiple recipients of emails, students gathering in groups, and drug compounds made of several substances.
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Bat-Cluster: A Bat Algorithm-based Automated Graph Clustering Approach IJECEIAES
The document presents a new approach called Bat-Cluster (BC) for automated graph clustering. BC combines the Fast Fourier Domain Positioning (FFDP) algorithm and the Bat Algorithm. FFDP positions graph nodes, then Bat Algorithm optimizes clustering by finding configurations that minimize the Davies-Bouldin Index. BC is tested on four benchmark graphs and outperforms Particle Swarm Optimization, Ant Colony Optimization, and Differential Evolution in providing higher clustering precision.
This document compares different supervised learning approaches for word sense disambiguation (WSD), including Naive Bayes, Decision Tree, and Decision List classifiers. An experiment is conducted using a dataset of 15 words and their senses from WordNet. The Decision List approach achieves the highest accuracy at 69.12%, followed by Naive Bayes at 58.32% and Decision Tree at 45.14%. While no single approach performed best for all words, overall Decision List provided the most accurate WSD and is presented as the best performing method for this problem among the three approaches studied.
This paper analyzes networks of scientific collaborations and dolphin social relationships. It establishes co-author and dolphin networks from data, then analyzes properties like degree distribution, information entropy, and influential nodes. Four indicators of cooperation, degree, quadratic correlation, and betweenness are used to calculate a Marshall Entropy Index (MEI) for the co-author network. A modified PageRank algorithm applied to a quotation network identifies the most influential paper. Analysis finds the dolphin network exhibits small world properties more than scale-free properties, with the dolphin SN100 as most influential.
In a distributed medical system, building cross-site records while maintaining appropriate patients anonymity is essential. The distributed databases contain information about the same individuals, often described by using the same variables, which do not fit quite frequently due to accidental distortions. In such cases, the record linkage methods are used to find records that correspond to the same individuals in order to create a consistent database.
Our goal was to find a solution for this problem. In this paper, we propose an anonymous identifier, based on combinations of first two letters from the surname, name, date of birth and gender, which can allow a deidentifying merged dataset from multiple databases of a distributed medical system.
A HYBRID MODEL FOR MINING MULTI DIMENSIONAL DATA SETSEditor IJCATR
This paper presents a hybrid data mining approach based on supervised learning and unsupervised learning to identify the closest data patterns in the data base. This technique enables to achieve the maximum accuracy rate with minimal complexity. The proposed algorithm is compared with traditional clustering and classification algorithm and it is also implemented with multidimensional datasets. The implementation results show better prediction accuracy and reliability.
Simplicial closure and simplicial diffusionsAustin Benson
This document summarizes research on modeling higher-order interactions in network data using simplicial complexes. It finds that most real-world network datasets exhibit a mixture of closed and open triangles, with the fraction varying by domain. A simple probabilistic model can account for this variation. The document proposes that groups of nodes go through trajectories of interactions until reaching a "simplicial closure event" where a new simplex is formed, analogous to triangle closure. It evaluates models' ability to predict such closures using a framework of "higher-order link prediction". Key indicators of closure are edge density and tie strength between nodes.
Simplicial closure & higher-order link predictionAustin Benson
This document discusses higher-order link prediction and simplicial closure as ways to analyze and model higher-order interactions in network data. It summarizes that networks can be viewed as weighted projected graphs where simplices "fill in" structures, and that new simplices and closed triangles tend to form through trajectories of nodes reaching "simplicial closure events". It proposes evaluating models of higher-order structure through higher-order link prediction, predicting the formation of new simplices.
The document discusses three perspectives on predicting sets of items rather than single items. It describes how sets are common in data such as team formations, medical codes, and online purchases. It then discusses three specific approaches to set prediction: (1) predicting which sets an individual will interact with based on their history, (2) modeling sequences of sets using a generative model, and (3) understanding characteristics of set-based data like subsets and repeats. Applications include prediction, analysis, and simulation.
Simplicial closure and higher-order link predictionAustin Benson
This document summarizes research on simplicial closure and higher-order link prediction in network science. It finds that groups of nodes often interact through complex trajectories before reaching "simplicial closure" where all nodes are jointly present in a simplex. Predicting these closed simplices is framed as a higher-order link prediction problem. Various score functions are proposed based on edge weights, node neighborhoods, and similarity measures. Scores combining local edge weight information consistently perform well, outperforming classical link prediction approaches. The results provide insights into higher-order structure and a framework for evaluating models of complex relational data.
Three hypergraph eigenvector centralitiesAustin Benson
Three hypergraph eigenvector centralities are proposed to measure the importance of nodes in complex systems modeled as hypergraphs. Hypergraphs generalize graphs by allowing edges to connect any number of nodes. The proposed centralities are adaptations of the standard graph eigenvector centrality to hypergraphs. They measure a node's centrality based on 1) the centralities of its neighbors, 2) being positive values, and 3) being the principal eigenvector of the hypergraph adjacency matrix.
Simplicial closure and higher-order link prediction --- SIAMNS18Austin Benson
The document discusses higher-order link prediction, which aims to predict the formation of new groups or "simplices" containing more than two nodes, based on structural properties in timestamped simplex data from various domains. It finds that predicting the closure of open triangles (where a pair of nodes have interacted but not with the third) performs well, and that simply averaging the edge weights in a triangle is often a good predictor. Predicting new structures in communication, collaboration and proximity networks can provide insights beyond classical link prediction.
Simplicial closure and higher-order link prediction (SIAMNS18)Austin Benson
This document summarizes research on modeling and predicting the formation of higher-order relationships or interactions between nodes in network datasets. It introduces the concept of "simplicial closure" to describe how groups of nodes interact over time until forming a simplex or higher-order relationship. The researchers propose "higher-order link prediction" as a framework to evaluate models for predicting the formation of new simplices. They test various methods for scoring open triangles based on edge weights and other structural properties to predict which will become closed triangles. The results show these approaches can significantly outperform random prediction, with simply averaging edge weights often performing well.
The study about the analysis of responsiveness pair clustering tosocial netwo...acijjournal
In this study, regional (cities, towns and villages
) data and tweet data are obtained from Twitter, an
d
extract information of "purchase information (Where
and what bought)" from the tweet data by
morphological analysis and rule-based dependency an
alysis. Then, the "The regional information" and th
e
"Theinformation of purchase history (Where and wha
t bought information)" are captured as bipartite
graph, and Responsiveness Pair Clustering analysis
(a clustering using correspondence analysis as
similarity measure) is conducted. In this study, si
nce it was found to be difficult to analyze a netwo
rk such
as bipartite graph having limitations in links by u
sing modularity Q, responsiveness is used instead o
f
modularity Q as similarity measure. As a result of
this analysis, "regional information cluster" which
refers
to similar "Theinformation of purchase history" nod
es group is generated. Finally, similar regions are
visualized by mapping the regional information clus
ter on the map. This visualization system is expect
ed to
contribute as an analytical tool for customers’ pur
chasing behaviour and so on.
FUZZY STATISTICAL DATABASE AND ITS PHYSICAL ORGANIZATIONijdms
This document discusses fuzzy statistical databases and their physical organization. It introduces the concept of fuzzy cardinality for counting elements in a fuzzy set or fuzzy relation. A fuzzy statistical database is proposed to store fuzzy statistics generated from fuzzy relational databases. This fuzzy statistical database contains fuzzy statistical tables, which can be type-1 or type-2 depending on the complexity of the fuzzy attributes. The physical organization of these fuzzy statistical tables is discussed to facilitate efficient storage and retrieval of the imprecise statistical data.
K-means and bayesian networks to determine building damage levelsTELKOMNIKA JOURNAL
Many troubles in life require decision-making with convoluted processes because they are caused by uncertainty about the process of relationships that appear in the system. This problem leads to the creation of a model called the Bayesian Network. Bayesian Network is a Bayesian supported development supported by computing advancements. The Bayesian network has also been developed in various fields. At this time, information can implement Bayesian Networks in determining the extent of damage to buildings using individual building data. In practice, there is mixed data which is a combination of continuous and discrete variables. Therefore, to simplify the study it is assumed that all variables are discrete in order to solve practical problems in the implementation of theory. Discretization method used is the K-Means clustering because the percentage of validity obtained by this method is greater than the binning method.
Computational Frameworks for Higher-order Network Data AnalysisAustin Benson
1. The document discusses computational frameworks for analyzing higher-order network data, where interactions can involve more than two nodes. Real-world systems often involve higher-order interactions that are reduced to pairwise connections.
2. The author presents several datasets involving higher-order interactions and shows that predicting the formation of new higher-order connections is similar to link prediction but considers groups of nodes rather than individual links. Structural properties like edge density and tie strength influence the likelihood of simplicial closure.
3. Models are proposed to score open simplices based on structural features and predict which will transition to closed simplices. Accounting for higher-order structure provides new insights beyond traditional network analysis of pairwise connections.
Simplicial closure and higher-order link prediction LA/OPTAustin Benson
- The speaker proposes a framework called "higher-order link prediction" to evaluate models of higher-order network data. This extends classical link prediction to predict new groups of nodes that will form simplices.
- Analysis of datasets shows that many have many "open triangles" of nodes connected by edges but not in a simplex. A simple probabilistic model can account for variation in open triangles.
- Simplicial closure probability depends on edge density and tie strength between nodes, both for 3 and 4-node groups.
- For higher-order link prediction, the speaker evaluates score functions based on edge weights, structural properties, whole-network similarities, and machine learning to predict which open triangles will close.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
This document summarizes an empirical study comparing several supervised machine learning approaches for word sense disambiguation: Naive Bayes, decision tree, decision list, and support vector machine (SVM). The study used a dataset of 15 words annotated with senses from WordNet and Senseval-3. Each approach was implemented and evaluated based on its accuracy in identifying the correct sense of each word. The results showed that the decision list approach achieved the highest overall accuracy of 69.12%, followed by SVM at 56.11%, naive Bayes at 58.32%, and decision tree at 45.14%. Thus, the study concluded that decision list performed best on this dataset for the task of word sense disambiguation.
Higher-order link prediction and other hypergraph modelingAustin Benson
Higher-order link prediction and other hypergraph modeling can better model real-world systems composed of higher-order interactions that are often reduced to pairwise ones. Hypergraphs allow the modeling of interactions between more than two nodes, like groups of people collaborating, multiple recipients of emails, students gathering in groups, and drug compounds made of several substances.
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Bat-Cluster: A Bat Algorithm-based Automated Graph Clustering Approach IJECEIAES
The document presents a new approach called Bat-Cluster (BC) for automated graph clustering. BC combines the Fast Fourier Domain Positioning (FFDP) algorithm and the Bat Algorithm. FFDP positions graph nodes, then Bat Algorithm optimizes clustering by finding configurations that minimize the Davies-Bouldin Index. BC is tested on four benchmark graphs and outperforms Particle Swarm Optimization, Ant Colony Optimization, and Differential Evolution in providing higher clustering precision.
This document compares different supervised learning approaches for word sense disambiguation (WSD), including Naive Bayes, Decision Tree, and Decision List classifiers. An experiment is conducted using a dataset of 15 words and their senses from WordNet. The Decision List approach achieves the highest accuracy at 69.12%, followed by Naive Bayes at 58.32% and Decision Tree at 45.14%. While no single approach performed best for all words, overall Decision List provided the most accurate WSD and is presented as the best performing method for this problem among the three approaches studied.
This paper analyzes networks of scientific collaborations and dolphin social relationships. It establishes co-author and dolphin networks from data, then analyzes properties like degree distribution, information entropy, and influential nodes. Four indicators of cooperation, degree, quadratic correlation, and betweenness are used to calculate a Marshall Entropy Index (MEI) for the co-author network. A modified PageRank algorithm applied to a quotation network identifies the most influential paper. Analysis finds the dolphin network exhibits small world properties more than scale-free properties, with the dolphin SN100 as most influential.
In a distributed medical system, building cross-site records while maintaining appropriate patients anonymity is essential. The distributed databases contain information about the same individuals, often described by using the same variables, which do not fit quite frequently due to accidental distortions. In such cases, the record linkage methods are used to find records that correspond to the same individuals in order to create a consistent database.
Our goal was to find a solution for this problem. In this paper, we propose an anonymous identifier, based on combinations of first two letters from the surname, name, date of birth and gender, which can allow a deidentifying merged dataset from multiple databases of a distributed medical system.
A HYBRID MODEL FOR MINING MULTI DIMENSIONAL DATA SETSEditor IJCATR
This paper presents a hybrid data mining approach based on supervised learning and unsupervised learning to identify the closest data patterns in the data base. This technique enables to achieve the maximum accuracy rate with minimal complexity. The proposed algorithm is compared with traditional clustering and classification algorithm and it is also implemented with multidimensional datasets. The implementation results show better prediction accuracy and reliability.
Simplicial closure and simplicial diffusionsAustin Benson
This document summarizes research on modeling higher-order interactions in network data using simplicial complexes. It finds that most real-world network datasets exhibit a mixture of closed and open triangles, with the fraction varying by domain. A simple probabilistic model can account for this variation. The document proposes that groups of nodes go through trajectories of interactions until reaching a "simplicial closure event" where a new simplex is formed, analogous to triangle closure. It evaluates models' ability to predict such closures using a framework of "higher-order link prediction". Key indicators of closure are edge density and tie strength between nodes.
Simplicial closure & higher-order link predictionAustin Benson
This document discusses higher-order link prediction and simplicial closure as ways to analyze and model higher-order interactions in network data. It summarizes that networks can be viewed as weighted projected graphs where simplices "fill in" structures, and that new simplices and closed triangles tend to form through trajectories of nodes reaching "simplicial closure events". It proposes evaluating models of higher-order structure through higher-order link prediction, predicting the formation of new simplices.
This document discusses community detection in networks. It begins by emphasizing the importance of defining what constitutes a community based on the goals and data of the specific network being analyzed. It then briefly describes four common community detection techniques: hierarchical clustering, k-means clustering, spectral clustering, and modularity maximization. Hierarchical and k-means clustering partition networks based on node similarity, while spectral clustering and modularity maximization detect communities as groups of densely connected nodes.
Foundation and Synchronization of the Dynamic Output Dual Systemsijtsrd
In this paper, the synchronization problem of the dynamic output dual systems is firstly introduced and investigated. Based on the time domain approach, the state variables synchronization of such dual systems can be verified. Meanwhile, the guaranteed exponential convergence rate can be accurately estimated. Finally, some numerical simulations are provided to illustrate the feasibility and effectiveness of the obtained result. Yeong-Jeu Sun "Foundation and Synchronization of the Dynamic Output Dual Systems" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-6 , October 2019, URL: https://www.ijtsrd.com/papers/ijtsrd29256.pdf Paper URL: https://www.ijtsrd.com/engineering/electrical-engineering/29256/foundation-and-synchronization-of-the-dynamic-output-dual-systems/yeong-jeu-sun
The document provides an overview of the topics that will be covered in a bioinformatics course over 11 lessons from September to December. It includes brief descriptions of the topics to be covered in each lesson such as biological databases, sequence alignments, database searching, phylogenetics, and protein structure. The document also notes that there will be no class on two specified dates in October and November.
Using Local Spectral Methods to Robustify Graph-Based LearningDavid Gleich
This is my KDD2015 talk on robustness in semi-supervised learning. The paper is already on Michael Mahoney's website: http://www.stat.berkeley.edu/~mmahoney/pubs/robustifying-kdd15.pdf See the KDD paper for all the details, which this talk is a bit light on.
PEC - AN ALTERNATE AND MORE EFFICIENT PUBLIC KEY CRYPTOSYSTEMijcisjournal
In an increasingly connected world, security is a top concern for Internet of Things (IoT). These IoT devices have to
be inexpensive implying that they will be constrained in storage and computing resources. In order to secure such
devices, highly efficient public key cryptosystems (PKC) are critical. Elliptic Curve Cryptography (ECC) is the most
commonly implemented PKC in use today. In this paper, an alternate and a more efficient PKC, called the PEC (Pells
Equation Cryptography) has been proposed based on Pells equation: x
2 − D ∗ y
2 ≡ 1 (mod p). It is shown that scalar
multiplication in PEC is significantly more efficient compared to ECC. It is also shown that the Discrete Logarithm
Problem - computing the private key from the public key - in PEC is at least as hard as that of ECC.
Gaining Confidence in Signalling and Regulatory NetworksMichael Stumpf
Mathematical models of signalling and gene regulatory systems are abstractions of much more complicated processes. Even as more and larger data sets are becoming available we are not be able to dispense entirely with mechanistic models of real-world processes; nor should we. However, trying to develop informative and realistic models of such systems typically involves suitable statistical inference methods, domain expertise and a modicum of luck. Except
for cases where physical principles provide sucient guidance it will also be generally possible to come up with a large number of potential models that are compatible with a given biological system and any finite amount of data generated from experiments on that system.
Here I will discuss how we can systematically evaluate
potentially vast sets of mechanistic candidate models in light
of experimental and prior knowledge about biological systems. This enables us to evaluate quantitatively
the dependence of model inferences and predictions on the assumed model structures. Failure to consider the impact of structural uncertainty introduces biases into the analysis and potentially gives rise to misleading conclusions.
The document summarizes different methods for predicting global warming trends, including extrapolation methods, linear regression, and artificial neural networks. It analyzes ice core and lake temperature data and finds 80 very different predictions from various methods. The conclusion is that taking the median of the 80 predictions provides a better estimate than any single method. The median prediction for the current season is 91 days before thaw. The document closes by noting uncertainties around causes and impacts of global warming.
Some key models of social network generation are discussed, including random graph models, Watts-Strogatz models, and scale-free networks. Scale-free networks can generate networks with few components, small diameters, and heavy-tailed degree distributions, but do not capture high clustering. Biological networks like metabolic and protein interaction networks also tend to be scale-free.
Higher-order clustering coefficients generalize the traditional clustering coefficient to account for clique closure beyond triangles. This allows analyzing relationships between clustering at different orders, insights into real-world networks that may only cluster up to a certain order, and applications in finding higher-order communities. If a network exhibits non-trivial higher-order clustering, then it should contain local clusters that can be found efficiently.
An information-theoretic, all-scales approach to comparing networksJim Bagrow
My presentation at NetSci 2018 on Portrait Divergence, a new approach to comparing networks that is simple, general-purpose, and easy to interpret.
The preprint: https://arxiv.org/abs/1804.03665
The code: https://github.com/bagrow/portrait-divergence
Here are the responses to the questions:
1. A statistical population is the entire set of individuals or objects of interest. A sample is a subset of the population selected to represent the population. The sample infers information about the characteristics, attributes, and properties of the entire population.
2. Variance is the average of the squared deviations from the mean. It is calculated as the sum of the squared deviations from the mean divided by the number of values in the data set minus 1. Standard deviation is the square root of the variance. It measures how far data values spread out from the mean.
3. No data was provided to create graphs. Additional data on the number of fish in each age group would be needed.
IntroductionFor this assignment, you will examine the role of thTatianaMajor22
Introduction
For this assignment, you will examine the role of the nurse in caring for clients with cognitive issues. You will identify your target audience (such as staff nurses, pre-licensure nursing students, etc.) and create an orientation PowerPoint presentation (instructions below). This final assignment will reflect ability and achievement in the following areas:
· Intentional Learning, Reflection, and Clinical Judgment
· Decision Making and Evidence Based Practice
· Organization and Presentation
· Writing and APA Formatting
Objectives
· Demonstrate collaborative standardization of safe practices through health promotion.
· Integrate course concepts within management of a cognitive alteration.
Instructions
A nurse educator is preparing an orientation on cognitive illness and the workplace. There is a need to address the many clients with cognitive issues that seek healthcare services and how to better understand the needs. Choose a cognitive illness that you feel less knowledgeable about and address the following prompts by including two to three examples of each bullet point:
· Compare and contrast this illness with a physical illness (one that can be “seen”).
· Provide examples of the historical, socioeconomic, political, educational, and topographical aspects of this disease.
· Report the appropriate interdisciplinary interventions for high-risk health behaviors associated with this disease.
· Determine the influences of their value systems on management of this disease.
· Outline health-care practices, including acute versus preventive care; barriers to health care; the meaning of pain and the sick role; and cultural practices that can impact this disease.
· Identify cultural issues related to learning styles, autonomy, and educational preparation and any impact on disease management.
Your presentation should be 15-20 slides (not including title, objectives, and references slides) with detailed notes for each slide. Include at least two scholarly sources. Follow best practices for PowerPoint presentations related to text size, color, images, effects, wordiness, and multimedia enhancements. Review the rubric criteria for this assignment. No audio recording is required. Be sure to completely answer all the points/questions. Use clear headings that allow your professor to know which bullet you are addressing on the slides in your presentation. Support your content with citations throughout your presentation. Make sure to reference the citations using the APA writing style for the presentation. Include a slide for your references at the end.
Assignment Expectations
· Length: 15-20 slides; answers must thoroughly address the questions in a clear, concise manner. Include at least four scholarly sources.
· Title: 1 slide
· Compare and contrast illness: at least 3 slides
· Provide examples of the historical, socioeconomic, political, educational, and topographical aspects of culture: at least 2 slides
· Report interdisciplinary in ...
Interpretation of the biological knowledge using networks approachElena Sügis
This document discusses using biological networks to analyze and interpret biological knowledge. It begins with an overview of networks as tools to reduce complexity and integrate data. Key properties of networks are described, including nodes, edges, degree distribution, clustering coefficient, and centrality measures. Methods for analyzing networks like community detection and network motifs are also covered. The document emphasizes that biological networks must be analyzed and interpreted based on their properties and by mapping relevant biological data to provide meaningful insights.
ICPSR - Complex Systems Models in the Social Sciences - Lecture 3 - Professor...Daniel Katz
This document provides a summary of Stanley Milgram's small world experiment and discussion of complex network models. It discusses how Milgram found that the average path length between individuals in society is around 6 degrees of separation. Later work by Watts and Strogatz showed that networks with a small amount of randomness can display both clustering and small world properties. Degree distributions and other network measures like clustering coefficients and connected components are discussed. Preferential attachment models that generate power law degree distributions are presented.
Similar to Higher-order Link Prediction Syracuse (20)
Spectral embeddings and evolving networksAustin Benson
Spectral embeddings provide a fundamental approach for many machine learning tasks but are challenging for dynamic networks that change over time. The authors develop improved methods for maintaining spectral embeddings on evolving networks by (1) incrementally updating embeddings with small perturbations, (2) measuring convergence to speed computations, and (3) proposing a new dynamic graph model to test algorithms. They formalize these ideas with perturbation theory and algorithms that warm-start iterative solvers using the previous embedding.
Hypergraph Cuts with General Splitting FunctionsAustin Benson
The document discusses joint work on hypergraph cuts with Cornell researchers Nate Veldt and Jon Kleinberg. It presents at the SIAM MDS 2020 conference on Pattern Analysis for Networks and Network Generalizations. The work aims to generalize graph minimum s-t cuts to hypergraphs by minimizing a cut function subject to constraints.
Random spatial network models for core-periphery structureAustin Benson
The document proposes a random spatial network model for generating networks with core-periphery structure. The model assigns each node u a weight e^θu and the probability of an edge between nodes u and v is proportional to e^θu + e^θv. This generates networks where high-weight nodes in the "core" have many connections and low-weight "periphery" nodes have few connections.
Random spatial network models for core-periphery structure.Austin Benson
The document proposes a random spatial network model for generating networks with core-periphery structure. The model assigns each node u a weight e^θu and the probability of an edge between nodes u and v is proportional to e^θu + e^θv. This leads to dense connections between high-weight core nodes and sparser connections between core and low-weight peripheral nodes.
Higher-order clustering coefficients generalize the clustering coefficient to capture clustering with respect to larger cliques (denser subgraphs) beyond triangles. The speaker defines higher-order clustering coefficients as the fraction of (r-1)-cliques paired with an adjacent edge that induce an r-clique. These coefficients reveal that real-world networks exhibit clustering to different orders and provide additional insights into network structure compared to only considering triangles. The coefficients also vary across networks such as neural, social, and collaboration networks in ways not explained by random graph models.
New perspectives on measuring network clusteringAustin Benson
This document summarizes a talk on mining and modeling network data given at SIAM DM'18. The talk introduces two new classes of network clustering measures: higher-order clustering coefficients and closure coefficients. Higher-order clustering coefficients measure the probability that cliques of different orders close to form larger cliques. Closure coefficients measure the probability that the friend of a friend becomes a friend. These new measures provide insights into real-world network structure beyond what can be seen from traditional clustering coefficients. They also have applications in data mining tasks like community detection, anomaly detection, and predictive modeling.
Tensor Eigenvectors and Stochastic ProcessesAustin Benson
This document provides an overview of a tutorial on tensor eigenvectors and stochastic processes. The tutorial consists of 6 acts that cover basic tensor notation and operations, motivating applications involving tensors, a review of stochastic processes and Markov chains, introducing spacey random walks as stochastic processes, the theory of spacey random walks, and applications of spacey random walks. The goal is to interpret tensor objects from a stochastic perspective using concepts like random walks on graphs and higher-order Markov chains.
The document summarizes research on spacey random walks, which are a type of stochastic process that can model higher-order Markov chains. Key points:
1. Spacey random walks generalize higher-order Markov chains by forgetting history but pretending to remember a random previous state, with the stationary distribution given by a tensor eigenvector of the transition tensor.
2. This connects higher-order Markov chains to tensor eigenvectors and provides a stochastic interpretation of tensor eigenvectors as stationary distributions.
3. The dynamics of spacey random walks can be modeled as an ordinary differential equation, allowing tensor eigenvectors to be computed by numerically integrating the dynamical system.
1. The document discusses spacey random walks, which are a type of stochastic process that can be used to model higher-order Markov chains.
2. A spacey random walk is defined based on the transition probabilities of a higher-order Markov chain, but "forgets" its history and pretends to come from a random previous state.
3. The stationary distributions of spacey random walks are given by tensor eigenvectors of the transition tensor for the higher-order Markov chain. This provides a connection between higher-order Markov chains and tensor eigenvectors.
06-20-2024-AI Camp Meetup-Unstructured Data and Vector DatabasesTimothy Spann
Tech Talk: Unstructured Data and Vector Databases
Speaker: Tim Spann (Zilliz)
Abstract: In this session, I will discuss the unstructured data and the world of vector databases, we will see how they different from traditional databases. In which cases you need one and in which you probably don’t. I will also go over Similarity Search, where do you get vectors from and an example of a Vector Database Architecture. Wrapping up with an overview of Milvus.
Introduction
Unstructured data, vector databases, traditional databases, similarity search
Vectors
Where, What, How, Why Vectors? We’ll cover a Vector Database Architecture
Introducing Milvus
What drives Milvus' Emergence as the most widely adopted vector database
Hi Unstructured Data Friends!
I hope this video had all the unstructured data processing, AI and Vector Database demo you needed for now. If not, there’s a ton more linked below.
My source code is available here
https://github.com/tspannhw/
Let me know in the comments if you liked what you saw, how I can improve and what should I show next? Thanks, hope to see you soon at a Meetup in Princeton, Philadelphia, New York City or here in the Youtube Matrix.
Get Milvused!
https://milvus.io/
Read my Newsletter every week!
https://github.com/tspannhw/FLiPStackWeekly/blob/main/141-10June2024.md
For more cool Unstructured Data, AI and Vector Database videos check out the Milvus vector database videos here
https://www.youtube.com/@MilvusVectorDatabase/videos
Unstructured Data Meetups -
https://www.meetup.com/unstructured-data-meetup-new-york/
https://lu.ma/calendar/manage/cal-VNT79trvj0jS8S7
https://www.meetup.com/pro/unstructureddata/
https://zilliz.com/community/unstructured-data-meetup
https://zilliz.com/event
Twitter/X: https://x.com/milvusio https://x.com/paasdev
LinkedIn: https://www.linkedin.com/company/zilliz/ https://www.linkedin.com/in/timothyspann/
GitHub: https://github.com/milvus-io/milvus https://github.com/tspannhw
Invitation to join Discord: https://discord.com/invite/FjCMmaJng6
Blogs: https://milvusio.medium.com/ https://www.opensourcevectordb.cloud/ https://medium.com/@tspann
https://www.meetup.com/unstructured-data-meetup-new-york/events/301383476/?slug=unstructured-data-meetup-new-york&eventId=301383476
https://www.aicamp.ai/event/eventdetails/W2024062014
We are pleased to share with you the latest VCOSA statistical report on the cotton and yarn industry for the month of May 2024.
Starting from January 2024, the full weekly and monthly reports will only be available for free to VCOSA members. To access the complete weekly report with figures, charts, and detailed analysis of the cotton fiber market in the past week, interested parties are kindly requested to contact VCOSA to subscribe to the newsletter.
We are pleased to share with you the latest VCOSA statistical report on the cotton and yarn industry for the month of March 2024.
Starting from January 2024, the full weekly and monthly reports will only be available for free to VCOSA members. To access the complete weekly report with figures, charts, and detailed analysis of the cotton fiber market in the past week, interested parties are kindly requested to contact VCOSA to subscribe to the newsletter.
Discover the cutting-edge telemetry solution implemented for Alan Wake 2 by Remedy Entertainment in collaboration with AWS. This comprehensive presentation dives into our objectives, detailing how we utilized advanced analytics to drive gameplay improvements and player engagement.
Key highlights include:
Primary Goals: Implementing gameplay and technical telemetry to capture detailed player behavior and game performance data, fostering data-driven decision-making.
Tech Stack: Leveraging AWS services such as EKS for hosting, WAF for security, Karpenter for instance optimization, S3 for data storage, and OpenTelemetry Collector for data collection. EventBridge and Lambda were used for data compression, while Glue ETL and Athena facilitated data transformation and preparation.
Data Utilization: Transforming raw data into actionable insights with technologies like Glue ETL (PySpark scripts), Glue Crawler, and Athena, culminating in detailed visualizations with Tableau.
Achievements: Successfully managing 700 million to 1 billion events per month at a cost-effective rate, with significant savings compared to commercial solutions. This approach has enabled simplified scaling and substantial improvements in game design, reducing player churn through targeted adjustments.
Community Engagement: Enhanced ability to engage with player communities by leveraging precise data insights, despite having a small community management team.
This presentation is an invaluable resource for professionals in game development, data analytics, and cloud computing, offering insights into how telemetry and analytics can revolutionize player experience and game performance optimization.
1. 1
Joint work with
Rediet Abebe & Jon Kleinberg (Cornell)
Michael Schaub & Ali Jadbabaie (MIT)
Simplicial closure &
higher-order link prediction
Austin R. Benson · Cornell
Syracuse University
April 19, 2019
Slides. bit.ly/arb-syracuse-19
bit.ly/combos-CC
2. Networks are sets of nodes and edges (graphs) that
model real-world systems.
2
Collaboration
nodes are people/groups
edges link entities
working together
Communications
nodes are people/accounts
edges show info.exchange
Social group activity
nodes are people/animals
edges link those that interact
in close proximity
Drug compounds
nodes are substances
edge between substances that
appear in the same drug
3. Real-world systems are composed of“higher-order”
interactions that we often reduce to pairwise ones.
3
Collaboration
nodes are people/groups
teams are made up of
small groups
Communications
nodes are people/accounts
emails often have several
recipients,not just one
Social group activity
nodes are people/animals
people often gather in
small groups
Drug compounds
nodes are substances
drugs are made up of
several substances
4. There are many ways to mathematically represent the
higher-order structure present in relational data.
4
• Hypergraphs [Berge 89]
• Set systems [Frankl 95]
• Tensors [Kolda-Bader 09]
• Affiliation networks [Feld 81,Newman-Watts-Strogatz 02]
• Multipartite networks [Lambiotte-Ausloos 05,Lind-Herrmann 07]
• Abstract simplicial complexes [Lim 15,Osting-Palande-Wang 17]
• Multilayer networks [Kivelä+ 14,Boccaletti+ 14,many others…]
• Meta-paths [Sun-Han 12]
• Motif-based representations [Benson-Gleich-Leskovec 15,17]
• …
Data representation is not the problem. But…
1. Researchers and practitioners often don’t use it.
Graphs are easier and we already have lots of graph analysis tools.
2. We don’t have good frameworks for evaluating them
(especially for what they can do beyond graphs).
5. Link prediction is a classical machine learning problem
in network science,which is used to evaluate models.
5
We observe data which is a list of edges in a graph up to some point t.
We want to predict which new edges will form in the future.
Shows up in a variety of applications
• Predicting new social relationships and friend recommendation.
[Backstrom-Leskovec 11; Wang+ 15]
• Inferring new links between genes and diseases.
[Wang-Gulbahce-Yu 11; Moreau-Tranchevent 12]
• Suggesting novel connections in the scientific community.
[Liben-Nowell-Kleinberg 07; Tang-Wu-Sun-Su 12]
Also useful as a framework to evaluate new methods!
[Liben-Nowell-Kleinberg 07; Lü-Zhau 11]
6. We propose“higher-order link prediction”as a similar
framework for evaluation of higher-order models.
6
t1 : {1, 2, 3, 4}
t2 : {1, 3, 5}
t3 : {1, 6}
t4 : {2, 6}
t5 : {1, 7, 8}
t6 : {3, 9}
t7 : {5, 8}
t8 : {1, 2, 6}
Data.
Observe simplices up to some
time t. Using this data, want to
predict what groups of > 2
nodes will appear in a simplex
in the future.
t
1
2
3
4
5
6
7
8
9
We predict structure that classical link
prediction would not even consider!
Possible applications
• Novel combinations of drugs for treatments.
• Group chat recommendation in social networks.
• Team formation.
7. 7
This talk.
1. What are the basic organizational principles of
systems with higher-order interactions?
2. How do the systems evolve over time (dynamics)?
3. How can we use insights to create effective
higher-order link prediction methods?
Let’s understand higher-order interaction data to build
up to effective higher-order link prediction tasks.
8. 8
What are the basic organizational
principles of systems with
higher-order interactions?
9. We collected a bunch of data…
9
1. Coauthorship in different domains.
2. Emails with multiple recipients.
3. Tags on Q&A forums.
4. Threads on Q&A forums.
5. Contact/proximity measurements.
6. Musical artist collaboration.
7. Substance makeup and
classification codes applied to
drugs the FDA examines.
8. U.S. Congress committee
memberships and bill sponsorship.
9. Combinations of drugs seen in
patients in ER visits.
https://math.stackexchange.com/q/80181
bit.ly/sc-holp-data
10. Thinking of higher-order data as a weighted projected
graph with“filled-in”structures is a convenient viewpoint.
10
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
t1 : {1, 2, 3, 4}
t2 : {1, 3, 5}
t3 : {1, 6}
t4 : {2, 6}
t5 : {1, 7, 8}
t6 : {3, 9}
t7 : {5, 8}
t8 : {1, 2, 6}
Data. Pictures to have in mind.
Projected graph W.
Wij = # of simplices containing nodes i and j.
12. 12
i
j k
i
j k
Warm-up. What’s more common in data?
or
“Open triangle”
each pair has been in a simplex
together but all 3 nodes have
never been in the same simplex
“Closed triangle”
there is some simplex that
contains all 3 nodes
14. Dataset domain separation also occurs at the local level.
14
• Randomly sample 100 egonets per dataset and measure
log of average degree and fraction of open triangles.
• Logistic regression model to predict domain
(coauthorship, tags, threads, email, contact).
• 75% model accuracy vs. 21% with random guessing.
15. Most open triangles do not come from asynchronous
temporal behavior.
15
i
j k
In 61.1% to 97.4% of open triangles,
all three pairs of edges have an
overlapping period of activity.
⟶ there is an overlapping period of
activity between all 3 edges
(Helly’s theorem).
# overlaps
Dataset # open triangles 0 1 2 3
coauth-DBLP 1,295,214 0.012 0.143 0.123 0.722
coauth-MAG-history 96,420 0.002 0.055 0.059 0.884
coauth-MAG-geology 2,494,960 0.010 0.128 0.109 0.753
tags-stack-overflow 300,646,440 0.002 0.067 0.071 0.860
tags-math-sx 2,666,353 0.001 0.040 0.049 0.910
tags-ask-ubuntu 3,288,058 0.002 0.088 0.085 0.825
threads-stack-overflow 99,027,304 0.001 0.034 0.037 0.929
threads-math-sx 11,294,665 0.001 0.038 0.039 0.922
threads-ask-ubuntu 136,374 0.000 0.020 0.023 0.957
NDC-substances 1,136,357 0.020 0.196 0.151 0.633
NDC-classes 9,064 0.022 0.191 0.136 0.652
DAWN 5,682,552 0.027 0.216 0.155 0.602
congress-committees 190,054 0.001 0.046 0.058 0.895
congress-bills 44,857,465 0.003 0.063 0.113 0.821
email-Enron 3,317 0.008 0.130 0.151 0.711
email-Eu 234,600 0.010 0.131 0.132 0.727
contact-high-school 31,850 0.000 0.015 0.019 0.966
contact-primary-school 98,621 0.000 0.012 0.014 0.974
music-rap-genius 70,057 0.028 0.221 0.141 0.611
16. A simple model can account for open triangle variation.
16
• n nodes; only 3-node simplices; {i, j, k} included with prob. p = 1 / nb i.i.d.
• ⟶ always get ϴ(pn3) = ϴ(n3 - b) closed triangles in expectation.
b = 0.8, 0.82, 0.84, ..., 1.8
Larger b is darker marker.
Proposition (sketch).
• b < 1 ⟶ ϴ(n3) open triangles in
expectation for large n.
• b > 1 ⟶ ϴ(n3(2-b)) open triangles
in expectation for large n.
• The number of open triangles
grows faster for b < 3/2.
10 1
100
Edge density in projected graph
0.00
0.25
0.50
0.75
1.00
Fractionoftrianglesopen
Exactly 3 nodes per simplex (simulated)
n = 200
n = 100
n = 50
n = 25
20. Groups of nodes go through trajectories until finally
reaching a“simplicial closure event.”
20
Substances in marketed drugs recorded in the National Drug Code directory.
HIV protease
inhibitors
UGT1A1
inhibitors
Breast cancer
resistance protein inhibitors
1
2+
2+
1
2+
1
1
2+
2+
1
2+
2+
2+
Reyataz
RedPharm
2003
Reyataz
Squibb & Sons
2003
Kaletra
Physicians
Total Care
2006
Promacta
GSK (25mg)
2008
Promacta
GSK (50mg)
2008
Kaletra
DOH Central
Pharmacy
2009
Evotaz
Squibb & Sons
2015
We bin weighted edges into “weak” and “strong ties” in the projected graph W.
Wij = # of simplices containing nodes i and j.
• Weak ties. Wij = 1 (one simplex contains i and j)
• Strong ties. Wij > 2 (at least two simplices contain i and j)
21. Groups of nodes go through trajectories until finally
reaching a“simplicial closure event.”
21
• Weak ties. Wij = 1 (one simplex contains i and j)
• Strong ties. Wij > 2 (at least two simplices contain i and j)
icons
colors 16.04
1
2+
2+
1
2+
2+
How can I change
the icon colors, ap-
pearance, etc. at
the top panel?
2011
How do I change
the icon and text
color?
2012
Ubuntu 15.10
/ 16.04 theme
doesn’t change
2016
Ubuntu 16.04
Eclipse launcher
icon problems
2016
Set desktop icons background
color Kubuntu 16.04
2016
Tags on askubuntu.com forum questions.
23. Simplicial closure depends on structure in projected graph.
23
• First 80% of the data (in time) ⟶ record configurations of triplets not in closed triangle.
• Remainder of data ⟶ find fraction that are now closed triangles.
Increased edge density
increases closure probability.
Increased tie strength
increases closure probability.
Tension between edge
density and tie strength.
Left and middle observations are consistent with theory and empirical studies of social networks.
[Granovetter 73; Leskovec+ 08; Backstrom+ 06; Kossinets-Watts 06]
Closure probability Closure probability Closure probability
coauth-DBLP
coauth-MAG-geology
coauth-MAG-history
congress-bills
congress-committees
email-Eu
email-Enron
threads-stack-overflow
threads-math-sx
threads-ask-ubuntu
music-rap-genius
DAWNtags-stack-overflow
tags-math-sx
tags-ask-ubuntu NDC-substances
NDC-classes
contact-high-school
contact-primary-school
25. 25
How can we compare and evaluate
models for higher-order structure?
26. Link prediction is a classical machine learning problem
in network science that is used to evaluate models.
26
We observe data which is a list of edges in a graph up to some point t.
We want to predict which new edges will form in the future.
Shows up in a variety of applications
• Predicting new social relationships and friend recommendation.
[Backstrom-Leskovec 11; Wang+ 15]
• Inferring new links between genes and diseases.
[Wang-Gulbahce-Yu 11; Moreau-Tranchevent 12]
• Suggesting novel connections in the scientific community.
[Liben-Nowell-Kleinberg 07; Tang-Wu-Sun-Su 12]
Link prediction is also used as a framework to compare models/algorithms.
[Liben-Nowell-Kleinberg 03,07; Lü-Zhau 11]
27. We propose“higher-order link prediction”as a similar
framework for evaluation of higher-order models.
27
t1 : {1, 2, 3, 4}
t2 : {1, 3, 5}
t3 : {1, 6}
t4 : {2, 6}
t5 : {1, 7, 8}
t6 : {3, 9}
t7 : {5, 8}
t8 : {1, 2, 6}
Data.
Observe simplices up to some
time t. Using this data, want to
predict what groups of > 2
nodes will appear in a simplex
in the future.
t
1
2
3
4
5
6
7
8
9
We predict structure that classical link
prediction would not even consider!
Possible applications
• Novel combinations of drugs for treatments.
• Group chat recommendation in social networks.
• Team formation.
28. 28
Our structural analysis tells us what we should be
looking at for prediction.
1. Edge density is a positive indicator.
⟶ focus our attention on predicting which open
triangles become closed triangles.
2. Tie strength is a positive indicator.
⟶ various ways of incorporating this information
i
j k
Wij
Wjk
Wjk
29. 29
For every open triangle,we assign a score function (model)
on first 80% of data based on structural properties.
Four broad classes of score functions for an open triangle.
Score s(i, j, k)…
1. is a function of Wij, Wjk, Wjk
arithmetic mean, geometric mean, etc.
2. looks at common neighbors of the three nodes
generalized Jaccard, Adamic-Adar, etc.
3. uses “whole-network” similarity scores on projected graph
sum of PageRank or Katz scores amongst edges
4. is learned from data
train a logistic regression model with features
i
j k
Wij
Wjk
Wjk
After computing scores, predict that open triangles with highest
scores will be closed triangles in final 20% of data.
Wij = #(simplices
containing i and j)<latexit 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30. 30
1. s(i,j,k) is a function of Wij,Wjk,and Wjk
i
j k
Wij
Wjk
Wjk
1. Arithmetic mean
2. Geometric mean
3. Harmonic mean
4. Generalized mean
s(i, j, k) = 3/(W 1
ij + W 1
ik + W 1
jk )
s(i, j, k) = (WijWikWjk)1/3
s(i, j, k) = (Wij + Wik + Wjk)/3
s(i, j, k) = mp(Wij, Wjk, Wik) = (Wp
ij + Wp
jk + Wp
ik)1/p
Wij = #(simplices
containing i and j)<latexit 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31. 1. Number of common neighbors of all 3 nodes
2. Generalized Jaccard coefficient
3. Preferential attachment
31
2. s(i,j,k) is a function of is a function of neighbors
s(i, j, k) =
|N(i) N(j) N(k)|
|N(i) [ N(j) [ N(k)|<latexit 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s(i, j, k) = |N(i) N(j) N(k)|<latexit 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s(i, j, k) = |N(i)| · |N(j)| · |N(k)|<latexit 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i
j k
l
m
x
y
r
z
N(i) = {j, k, l, m, x, y, z}
N(j) = {i, k, l, m, r}
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32. 32
3. s(i,j,k) is is built from“whole-network”similarity
scores on edges: s(i,j,k) = Sij + Sji + Sjk + Skj + Sik + Ski
i
j k
Wij
Wjk
Wjk
1. PageRank (unweighted or weighted)
2. Katz (unweighted or weighted)
S = (I ↵WD 1
W ) 1
S = (I ↵AD 1
A ) 1
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S = (I W) 1
I
S = (I A) 1
I<latexit 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Wij = #(simplices
containing i and j)
A = min(W, 1)
DW = diag(W1)
DA = diag(A1)<latexit 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33. 33
4. s(i,j,k) is learned from data.
1. Split data into training and validation sets.
2. Compute features of (i, j, k) from previous ideas using training data.
3. Throw features + validation labels into machine learning blender
→ learn model.
4. Re-compute features on combined training + validation
→ apply model on the data.
35. 35
A few lessons learned from applying all of these ideas.
1. We can predict pretty well on all datasets using some method.
→ 4x to 107x better than random w/r/t mean average precision
depending on the dataset/method
2. Thread co-participation and co-tagging on stack exchange are
consistently easy to predict.
3. Simply averaging Wij, Wjk, and Wik consistently performs well.
i
j k
Wij
Wjk
Wjk
36. Generalized means of edges weights are often good
predictors of new 3-node simplices appearing.
36
music-rap-genius
NDC-substances
NDC-classes
DAWN
coauth-DBLP
coauth-MAG-geology
coauth-MAG-history
congress-bills
congress-committees
tags-stack-overflow
tags-math-sx
tags-ask-ubuntu
email-Eu
email-Enron
threads-stack-overflow
threads-math-sx
threads-ask-ubuntu
contact-high-school
contact-primary-school
harmonic geometric arithmetic
p
4 3 2 1 0 1 2 3 4
0
20
40
60
80
Relativeperformance
4 3 2 1 0 1 2 3 4
p
2.5
5.0
7.5
10.0
12.5
Relativeperformance
4 3 2 1 0 1 2 3 4
p
1.0
1.5
2.0
2.5
3.0
3.5
Relativeperformance
Good performance from this local information is a deviation from classical link prediction,where
methods that use long paths (e.g.,PageRank,Katz) perform well [Liben-Nowell & Kleinberg 07].
For structures on k nodes,the subsets of size k-1 contain rich information only when k > 2.
i
j k
Wij
Wjk
Wjk
i
j k
?
scorep(i, j, k)
= (Wp
ij + Wp
jk + Wp
ik)1/p
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37. There are lots of opportunities in studying this data.
37
1. Higher-order data is pervasive!
We have ways to represent data, and higher-order link prediction is a
general framework for comparing comparing models and methods.
2. There is rich static and temporal structure in the datasets we collected.
3. We only briefly looked at 4-node patterns.
Computation becomes much more challenging for 4-node patterns.
bit.ly/sc-holp-data
38. 38
THANKS! Austin R. Benson
Slides. bit.ly/arb-syracuse-19
http://cs.cornell.edu/~arb
@austinbenson
arb@cs.cornell.edu
Simplicial closure &
higher-order
link prediction
Simplicial closure and higher-order link prediction.
Benson, Abebe, Schaub, Jadbabaie, & Kleinberg.
Proceedings of the National Academy of Sciences, 2018.
github.com/arbenson/ScHoLP-Tutorial
bit.ly/sc-holp-data
39. 39
How do we actually solve the systems?
Want to reduce
memory cost (only
need scores on
open triangles).
For each node i that participates in an open triangle
1. Solve
2. Store ith column
using iterative solver with low tolerance
s(i, j, k) = Sij + Sji + Sjk + Skj + Sik + SkiBi,s = Ind[i in sth simplex]
W = BBT
diag(BBT
)
A = spones(W)
First compute = 1/(2 1(W))
to guarantee solution.
S = [(I W) 1
I ] A
(I W)si = ei
(si ei) A:,i