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 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.
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.
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.
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.
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.
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.
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.
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 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.
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 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.
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.
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.
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.
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.
IRJET - Random Data Perturbation Techniques in Privacy Preserving Data Mi...IRJET Journal
This document discusses techniques for privacy-preserving data mining, specifically geometric data perturbation techniques. It begins with an introduction to the need for privacy in data mining due to increased data collection. It then discusses different categories of data perturbation techniques, including additive noise perturbation, condensation-based perturbation, random projection perturbation, and geometric data perturbation. Geometric perturbation consists of random rotation, translation, and distance perturbations of data to preserve privacy while maintaining important geometric properties. The document concludes that geometric perturbation introduces challenges in evaluating privacy but can preserve data quality for classification models.
A statistical data fusion technique in virtual data integration environmentIJDKP
Data fusion in the virtual data integration environment starts after detecting and clustering duplicated
records from the different integrated data sources. It refers to the process of selecting or fusing attribute
values from the clustered duplicates into a single record representing the real world object. In this paper, a
statistical technique for data fusion is introduced based on some probabilistic scores from both data
sources and clustered duplicates
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.
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.
ROLE OF CERTAINTY FACTOR IN GENERATING ROUGH-FUZZY RULEIJCSEA Journal
The generation of effective feature-based rules is essential to the development of any intelligent system. This paper presents an approach that integrates a powerful fuzzy rule generation algorithm with a rough set-assisted feature reduction method to generate diagnostic rule with a certainty factor. Certainty factor of each rule is calculated by considering both the membership value of each linguistic term introduced at time of fuzzyfication of data as well as possibility values, due to inconsistent data, generated by rough set theory at time of rule generation. In time of knowledge inferencing in an intelligent system, certainty factor of each rule will play an important role to find out the appropriate rule to be selected. Experimental results demonstrate the superiority of our approach.
This document summarizes and compares different perturbation techniques for privacy-preserving data mining. It begins by describing value-based perturbation techniques like random noise addition and randomized responses, which aim to preserve statistical characteristics of data. It then covers data mining task-based techniques like condensation and random rotation perturbation that modify data to preserve properties important for specific mining tasks. Dimension reduction techniques like random projection that reduce dimensionality while maintaining privacy are also discussed. The document evaluates these techniques based on criteria like privacy loss, information loss, and ability to perform mining tasks on perturbed data. It concludes that perturbation is a popular privacy-preserving technique but achieving the right balance between privacy and utility remains a challenge.
Applied SPSS for Data Forecasting of Flowers Species Nameijtsrd
SPSS is powerful to analyze data clustering and forecasting. This paper intends to support people who are interesting the species of flowers the benefits of data forecasting with applied SPSS. It showed the species value forecasting based on sepal length and sepal width. As SPSS's background algorithms, it showed the KNN algorithm for data clustering and data forecasting. It includes one sample data was downloaded from Google and was analyzed and viewed. It used IBM SPSS statistics version 23 and PYTHON version 3.7 Aung Cho | Aung Si Thu | Aye Mon Win "Applied SPSS for Data Forecasting of Flowers Species Name" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26665.pdfPaper URL: https://www.ijtsrd.com/computer-science/data-miining/26665/applied-spss-for-data-forecasting-of-flowers-species-name/aung-cho
This document summarizes a research paper that proposes a method for mining association rules from geographical points of interest data. It describes experiments conducted on point of interest data from Luoyang, China. The experiments involved (1) generating transactional data by spatially clustering the points of interest and converting each cluster to a transaction, (2) applying a novel FP-Growth algorithm called FP-GCID to generate frequent itemsets from the transaction data, and (3) ranking the association rules by mean product of probabilities to identify interesting rules. The top rules showed relationships between types of points of interest that should be considered together for deployment, such as banks and entertainment being related to catering establishments.
The document discusses database design, including the goals of database design such as data availability, reliability, currency, consistency and flexibility. It describes the key components of database design - entities, attributes, and relationships. Entities are things about which data is gathered, attributes are properties of entities, and relationships describe how entities relate to each other. The document also covers logical data modeling, normalization, and the three forms of normalization - first, second and third normal form. The goal of normalization is to organize data to eliminate redundancy and inconsistent dependency.
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.
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 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.
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.
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.
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.
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.
IRJET - Random Data Perturbation Techniques in Privacy Preserving Data Mi...IRJET Journal
This document discusses techniques for privacy-preserving data mining, specifically geometric data perturbation techniques. It begins with an introduction to the need for privacy in data mining due to increased data collection. It then discusses different categories of data perturbation techniques, including additive noise perturbation, condensation-based perturbation, random projection perturbation, and geometric data perturbation. Geometric perturbation consists of random rotation, translation, and distance perturbations of data to preserve privacy while maintaining important geometric properties. The document concludes that geometric perturbation introduces challenges in evaluating privacy but can preserve data quality for classification models.
A statistical data fusion technique in virtual data integration environmentIJDKP
Data fusion in the virtual data integration environment starts after detecting and clustering duplicated
records from the different integrated data sources. It refers to the process of selecting or fusing attribute
values from the clustered duplicates into a single record representing the real world object. In this paper, a
statistical technique for data fusion is introduced based on some probabilistic scores from both data
sources and clustered duplicates
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.
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.
ROLE OF CERTAINTY FACTOR IN GENERATING ROUGH-FUZZY RULEIJCSEA Journal
The generation of effective feature-based rules is essential to the development of any intelligent system. This paper presents an approach that integrates a powerful fuzzy rule generation algorithm with a rough set-assisted feature reduction method to generate diagnostic rule with a certainty factor. Certainty factor of each rule is calculated by considering both the membership value of each linguistic term introduced at time of fuzzyfication of data as well as possibility values, due to inconsistent data, generated by rough set theory at time of rule generation. In time of knowledge inferencing in an intelligent system, certainty factor of each rule will play an important role to find out the appropriate rule to be selected. Experimental results demonstrate the superiority of our approach.
This document summarizes and compares different perturbation techniques for privacy-preserving data mining. It begins by describing value-based perturbation techniques like random noise addition and randomized responses, which aim to preserve statistical characteristics of data. It then covers data mining task-based techniques like condensation and random rotation perturbation that modify data to preserve properties important for specific mining tasks. Dimension reduction techniques like random projection that reduce dimensionality while maintaining privacy are also discussed. The document evaluates these techniques based on criteria like privacy loss, information loss, and ability to perform mining tasks on perturbed data. It concludes that perturbation is a popular privacy-preserving technique but achieving the right balance between privacy and utility remains a challenge.
Applied SPSS for Data Forecasting of Flowers Species Nameijtsrd
SPSS is powerful to analyze data clustering and forecasting. This paper intends to support people who are interesting the species of flowers the benefits of data forecasting with applied SPSS. It showed the species value forecasting based on sepal length and sepal width. As SPSS's background algorithms, it showed the KNN algorithm for data clustering and data forecasting. It includes one sample data was downloaded from Google and was analyzed and viewed. It used IBM SPSS statistics version 23 and PYTHON version 3.7 Aung Cho | Aung Si Thu | Aye Mon Win "Applied SPSS for Data Forecasting of Flowers Species Name" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26665.pdfPaper URL: https://www.ijtsrd.com/computer-science/data-miining/26665/applied-spss-for-data-forecasting-of-flowers-species-name/aung-cho
This document summarizes a research paper that proposes a method for mining association rules from geographical points of interest data. It describes experiments conducted on point of interest data from Luoyang, China. The experiments involved (1) generating transactional data by spatially clustering the points of interest and converting each cluster to a transaction, (2) applying a novel FP-Growth algorithm called FP-GCID to generate frequent itemsets from the transaction data, and (3) ranking the association rules by mean product of probabilities to identify interesting rules. The top rules showed relationships between types of points of interest that should be considered together for deployment, such as banks and entertainment being related to catering establishments.
The document discusses database design, including the goals of database design such as data availability, reliability, currency, consistency and flexibility. It describes the key components of database design - entities, attributes, and relationships. Entities are things about which data is gathered, attributes are properties of entities, and relationships describe how entities relate to each other. The document also covers logical data modeling, normalization, and the three forms of normalization - first, second and third normal form. The goal of normalization is to organize data to eliminate redundancy and inconsistent dependency.
The document discusses database design, including the goals of database design such as data availability, reliability, currency, consistency and flexibility. It describes the key components of database design - entities, attributes, and relationships. Entities are things about which data is gathered, attributes are properties of entities, and relationships describe how entities relate to each other. The document also covers logical data modeling, normalization, and the three forms of normalization - first, second and third normal form. The goal of normalization is to organize data to eliminate redundancy and inconsistent dependency.
Data Clustering in Education for StudentsIRJET Journal
This document discusses using k-means clustering to analyze student behavior and performance based on factors like exam scores, assignments, tests, and attendance. The goal is to evaluate students accurately and help professors reduce failure rates and improve performance. It provides background on data clustering and how it can be applied in education. A proposed model is described that uses students' previous grades, quiz scores, assignment completion, lab performance, class test scores and attendance to predict their final grades. The k-means clustering algorithm is explained and results are presented showing how students were clustered into groups based on GPA and whether they passed or failed. The clustering aims to identify weaker students before exams to help improve their performance.
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CIS 336 Final Exam
Question 1. 1. (TCO 1) A DBMS performs several important functions that guarantee the integrity and consistency of the data in the database. Which of the following is NOT one of those functions?
This document discusses advanced concepts in association analysis, including handling continuous and categorical attributes, multi-level association rules, and sequential patterns. It describes various methods for applying association rule mining to datasets with non-binary attributes, such as discretization techniques and statistics-based approaches. It also discusses challenges like varying discretization intervals and generating rules at different levels of a concept hierarchy. Finally, it provides examples of sequential patterns that can be mined, such as sequences of customer transactions or nuclear accident events.
Predictive modeling aims to generate accurate estimates of future outcomes by analyzing current and historical data using statistical and machine learning techniques. It involves gathering data, exploring the data, building predictive models using algorithms like regression, decision trees, and neural networks, and evaluating the models. Some common predictive modeling techniques include time series analysis, regression analysis, and clustering algorithms.
This chapter aims to teach students how to compute and interpret various numerical descriptive measures of data, including measures of central tendency (mean, median, mode), variation (range, variance, standard deviation), and shape (skewness). It covers how to find quartiles and construct box-and-whisker plots. The chapter also discusses population summary measures, rules for describing variation around the mean, and interpreting correlation coefficients.
This document discusses the limitations of traditional database technologies and introduces associative technology as an evolution in database storage and retrieval. Some key limitations of traditional databases include disparate data sources, lack of timely information, high costs, and complex systems. Associative technology models data in an 'n' normal form that maps data relationally like human memory. It stores single instances of data values and uses bidirectional pointers to associate related data. This approach eliminates data redundancy and allows for fast, flexible querying of complex, large datasets.
This document provides instructions for homework assignment 2c in Computer Science 151. Students are asked to analyze temperature data from Albuquerque over time and write a report summarizing their findings. They will calculate yearly averages, standard deviations, and create a graph to visualize the data. The document explains how to properly structure the data for analysis and graphing using lists, dictionaries, and list comprehensions in Python.
A computational method for system of linear fredholm integral equationsAlexander Decker
This document presents a numerical method for solving systems of linear Fredholm integral equations of the second kind based on cubic spline interpolation. The method involves discretizing the integral equations and approximating the integrals using cubic splines. This produces a system of algebraic equations that can be solved for the unknown functions. The method is demonstrated on an example problem, and results show the method is accurate, with errors improving as the number of subintervals increases. The method performs better than an existing Adomain decomposition method in terms of accuracy.
The document provides an overview of mathematical modeling. It defines mathematical modeling as creating a mathematical representation of a phenomenon to better understand it by matching observations with symbolic representations and informing theory and explanation. The success of a model depends on how accurately it predicts and explains the phenomenon. Other terms for mathematical modeling include computer modeling, computer simulation, and computational mathematics. The document discusses how mathematical modeling fits into the scientific method and outlines typical problem-solving steps for mathematical modeling projects.
This document discusses item-based collaborative filtering for recommender systems. It describes how item-based collaborative filtering works by predicting a target user's rating for an item based on the ratings of similar items. It highlights advantages over user-based filtering like lower computational cost and more stable similarity computations. Key aspects covered include using cosine similarity to calculate item similarities, adjusting for individual rating biases, selecting the top K similar items, and predicting ratings based on similar items' ratings.
Entity matching and entity resolution are becoming more important disciplines in data management over time, based on increasing number of data sources that should be addressed in economy that is undergoing digital transformation process, growing data volumes and increasing requirements related to data privacy. Data matching process is also called record linkage, entity matching or entity resolution in some published works. For long time research about the process was focused on matching entities from same dataset (i.e. deduplication) or from two datasets. Different algorithms used for matching different types of attributes were described in the literature, developed and implemented in data matching and data cleansing platforms. Entity resolution is element of larger entity integration process that include data acquisition, data profiling, data cleansing, schema alignment, data matching and data merge (fusion).
We can use motivating example of global pharmaceutical company with offices in more than 60 countries worldwide that migrated customer data from various legacy systems in different countries to new common CRM system in the cloud. Migration was phased by regions and countries, with new sources and data incrementally added and merged with data already migrated in previous phases. Entity integration in such case require deep understanding of data architectures, data content and each step of the process. Even with such deep understanding, design and implementation of the solution require many iterations in development process that consume human resources, time and financial resources. Reducing the number of iterations by automating and optimizing steps in the process can save vast amount of resources. There is a lot of available literature addressing any of the steps in the process, proposing different options for improvement of results or processing optimization, but the whole process still require a lot of human work and subject matter specific knowledge and many iterations to produce results that will have high F-measure (both high precision and recall). Most of the algorithms used in the various steps of the process are Human in the loop (HITL) algorithms that require human interaction. Human is always part of the simulation and consequently influences the outcome.
This paper is a part of the work in progress aimed to define conceptual framework that will try to automate and optimize some steps of entity integration process and try to reduce requirements for human influence in the process. In this paper focus will be on conceptual process definition, recommended data architecture and use of existing open source solutions for entity integration process automation and optimization.
Lecture 8a: Clustering Validity, Minimum Description Length (MDL), Introduction to Information Theory, Co-clustering using MDL. (ppt,pdf)
Deepayan Chakrabarti, Spiros Papadimitriou, Dharmendra Modha, Christos Faloutsos, Fully Automatic Cross-Associations, KDD 2004, Seattle, August 2004. [PDF]
Some details about MDL and Information Theory can be found in the book “Introduction to Data Mining” by Tan, Steinbach, Kumar (chapters 2,4).
Math 221 Massive Success / snaptutorial.comStephenson164
1. (TCO 1) An Input Area (as it applies to Excel 2010) is defined as______.
2. (TCO 1) In Excel 2010, a sheet tab ________.
3. (TCO 1) Which of the following best describes the AutoComplete function?
4. (TCO 1) Which of the following best describes the order of precedence as it applies to math operations in Excel?
Clustering is an unsupervised learning technique used to group unlabeled data points into clusters based on similarity. It is widely used in data mining applications. The k-means algorithm is one of the simplest clustering algorithms that partitions data into k predefined clusters, where each data point belongs to the cluster with the nearest mean. It works by assigning data points to their closest cluster centroid and recalculating the centroids until clusters stabilize. The k-medoids algorithm is similar but uses actual data points as centroids instead of means, making it more robust to outliers.
This document presents the development of a Web Access Literacy Scale to measure users' abilities to critically evaluate information found online. The researchers conducted a study with 534 participants to develop and validate the scale. Factor analysis resulted in a 7-factor scale measuring logical approach, content verification strategies, inquisitiveness, bias tolerance, search skills, author verification, and objectivity. Scores were higher for those with information literacy experience. The scale can help identify weaknesses and inform the development of literacy training and search tools.
lide 7: Stack Operations - Pop
Description: Removing the top element from the stack.
Process: Retrieve the top element, decrement the stack pointer, and remove the element.
Illustration: Visual representation of the pop operation.
Slide 8: Stack Operations - Peek
Description: Viewing the top element of the stack without removing it.
Process: Access the element pointed by the stack pointer.
Illustration: Visual representation of the peek operation.
Slide 9: Stack Operations - isEmpty
Description: Checking if the stack is empty.
Process: Verify if the stack pointer is at the initial position.
Illustration: Visual representation of the isEmpty operation.
Slide 10-19: Examples and Illustrations
Example 1: Implementing a stack in C++.
Example 2: Evaluating postfix expressions using a stack.
Example 3: Undo mechanism in a text editor.
Illustrations of stack operations with step-by-step explanations.
Slide 20: Real-world Applications
Software Engineering: Function call management, recursion, expression evaluation.
Data Structures: Implementing other data structures (e.g., recursion in tree traversal).
Operating Systems: Memory management, system call management.
Slide 21: Conclusion
Summary of key points covered in the lecture.
Importance of understanding stacks in computer science and software engineering.
Encouragement for further exploration and practice.
This outline provides a comprehensive overview of stacks, their operations, applications, and significance in computer science. You can expand on each slide with detailed explanations, code snippets, diagrams, and examples to create an engaging and informative lecture.
also proved men slide from 10 to 19
ChatGPT
Certainly! Here are additional slides expanding on examples and illustrations from slide 10 to slide 19:
Slide 10: Example 1 - Implementing a Stack in C++
Description: Demonstration of how to implement a stack using an array or linked list in C++.
Code Example: Implementation of the Stack class with push, pop, peek, and isEmpty member functions.
Illustration: Visual representation of the stack structure and operations.
Slide 11: Example 2 - Evaluating Postfix Expressions
Description: Illustration of how to evaluate postfix expressions using a stack.
Process: Step-by-step explanation of how to convert and evaluate a postfix expression.
Code Example: C++ code snippet demonstrating postfix expression evaluation using a stack.
Illustration: Visual representation of the stack during postfix expression evaluation.
Slide 12: Example 3 - Undo Mechanism in Text Editor
Description: Explanation of how a stack can be used to implement an undo mechanism in a text editor.
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.
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.
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.
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.
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.
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.
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.
PyData London 2024: Mistakes were made (Dr. Rebecca Bilbro)Rebecca Bilbro
To honor ten years of PyData London, join Dr. Rebecca Bilbro as she takes us back in time to reflect on a little over ten years working as a data scientist. One of the many renegade PhDs who joined the fledgling field of data science of the 2010's, Rebecca will share lessons learned the hard way, often from watching data science projects go sideways and learning to fix broken things. Through the lens of these canon events, she'll identify some of the anti-patterns and red flags she's learned to steer around.
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.
06-18-2024-Princeton Meetup-Introduction to MilvusTimothy Spann
06-18-2024-Princeton Meetup-Introduction to Milvus
tim.spann@zilliz.com
https://www.linkedin.com/in/timothyspann/
https://x.com/paasdev
https://github.com/tspannhw
https://github.com/milvus-io/milvus
Get Milvused!
https://milvus.io/
Read my Newsletter every week!
https://github.com/tspannhw/FLiPStackWeekly/blob/main/142-17June2024.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/
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Invitation to join Discord: https://discord.com/invite/FjCMmaJng6
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Expand LLMs' knowledge by incorporating external data sources into LLMs and your AI applications.
Build applications with generative AI on Google CloudMárton Kodok
We will explore Vertex AI - Model Garden powered experiences, we are going to learn more about the integration of these generative AI APIs. We are going to see in action what the Gemini family of generative models are for developers to build and deploy AI-driven applications. Vertex AI includes a suite of foundation models, these are referred to as the PaLM and Gemini family of generative ai models, and they come in different versions. We are going to cover how to use via API to: - execute prompts in text and chat - cover multimodal use cases with image prompts. - finetune and distill to improve knowledge domains - run function calls with foundation models to optimize them for specific tasks. At the end of the session, developers will understand how to innovate with generative AI and develop apps using the generative ai industry trends.
1. 1
Joint work with
Ravi Kumar (Google) &
Andrew Tomkins (Google)
Sequences of sets
Austin R. Benson · Cornell
KDD · August 23, 2018 · London
Slides. bit.ly/SoS-KDD
Code. bit.ly/SoS-code
Data. bit.ly/SoS-data
2. Lots of data looks like sequences of sets.
2
EMAIL
Sequence of recipient sets in my email ⟶ one sequence of sets
Collection of email senders ⟶ sequences of sets.
3. Lots of data looks like sequences of sets.
3
Q&A
FORUM
TAGS
4. Lots of data looks like sequences of sets.
4
ACADEMIC COAUTHORSHIP
{Ravi Kumar, Andrew Tomkins} has appeared 4 times in my sequence
of coauthor sets !
5. Our work provides a generative model that captures
the important characteristics of sequences of sets.
5
1. email data
sequence for each account
sets are recipients on emails sent by account
2. Stack Exchange tags
sequence for each user
sets are tags on questions asked by the user
3. Coauthorship
sequence for each academic
sets are coauthors on paper
4. Proximity contact
sequence for each person
sets are people interacting with the person
tags-mathoverflow
tags-math-sx
email-Enron-core
email-Eu-core
contact-prim-school
contact-high-school
coauth-Business
coauth-Geology
6. Our work provides a generative model that captures
the important characteristics of sequences of sets.
6
Applications.
1. Predicting new sets.
2. Generative model ⟶ event likelihood ⟶ anomaly detection.
3. Understanding basic user behaviors.
4. Simulation.
8. Most sets are not entirely novel &
many are exact repeats.
8
tags-mathoverflow
tags-math-sx
email-Enron-core
email-Eu-core
contact-prim-school
contact-high-school
coauth-Business
coauth-Geology
9. Subsets and supersets of prior sets are common.
9
tags-mathoverflow
tags-math-sx
email-Enron-core
email-Eu-core
contact-prim-school
contact-high-school
coauth-Business
coauth-Geology
10. There is recencybias in the repeat behavior.
10
Consistent with previous results on sequences of single items.
[Benson-Kumar-Tomkins 16; Anderson+ 14]
11. size-2 subset counts size-3 subset counts
Dataset data null model data null model
email-Enron-core 5.82 4.34 ± 0.043 4.23 2.67 ± 0.038
email-Eu-core 4.46 3.11 ± 0.008 3.23 2.08 ± 0.007
contact-prim-school 2.36 1.87 ± 0.003 1.35 1.09 ± 0.002
contact-high-school 4.49 3.26 ± 0.007 2.09 1.35 ± 0.004
tags-mathoverflow 1.49 1.41 ± 0.002 1.18 1.15 ± 0.002
tags-math-sx 1.49 1.31 ± 0.001 1.21 1.12 ± 0.001
coauth-Business 1.50 1.30 ± 0.001 1.40 1.24 ± 0.001
coauth-Geology 1.29 1.15 ± 0.000 1.15 1.07 ± 0.000
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There is correlation in what gets repeated.
11
• For each sequence in each dataset, we count the number of
times each size-2 and size-3 subset appears.
• We then count the same statistics under a null model where
elements are randomly places into sets.
12. 12
How do we model the next set in a
sequence given the history?
13. Our Correlated Repeat Unions (CRU) model captures
repeat behavior,recencybias,and correlations.
13
Setup.
Observe sequence of sets S1, …, Sk.
Given number r of repeated elements in Sk+1.
Model selects r elements from .
CRU model.
Start with , given r.
1. Sample set Sk-j from j steps back with recency weight wj.
2. Sample T by keeping each item x in Sk-j with correlation probability p.
3. .
4. Repeat steps 1—3 until .
(if T makes N too large, randomly drop elements from T)
[k
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N = ;<latexit 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N = N [ T<latexit 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|N| = r<latexit 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14. Our Correlated Repeat Unions (CRU) model captures
repeat behavior,recency bias,and correlations.
14
Setup (k = 3).
Observe S1, …, S3: {a, b}, {c}, {a, c, d}.
Given that S4 has 3 repeated elements.
Model selects three elements from {a, b, c, d}.
CRU model (p = 0.8; w1 = 0.6,w2 = 0.3 w3 = 0.1).
{a, b} w3 = 0.1{c} w2 = 0.3{a, c, d} w1 = 0.6
0. N = ;.<latexit 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1. N = {a, c}.<latexit 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2. N = {a, c}.<latexit 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sha1_base64="UnWGOPG7NpsLB9xNGGE4KhYy81s=">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</latexit><latexit sha1_base64="UnWGOPG7NpsLB9xNGGE4KhYy81s=">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</latexit>
3. N = {a, c, b}.<latexit 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0. N = ;.<latexit 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1. N = {a, c, d}.<latexit 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0.8·0.8·0.8
0.8·0.8·0.2
0.8 + 0.2
0.2·0.8 + 0.8·0.8
15. We can learn model parameters with maximum
likelihood estimation.
15
1. Fix correlation probability p and learn recency weights w.
⟶ single p, vector w learned for entire dataset.
2. Grid search over p, gradient descent on w.
⟶ structure of CRU model makes it easy to compute gradients.
16. The optimal correlation probabilityis consistent within
domain but differs between domains.
16
Meanper-setlikelihood
x Baseline model (flat, no structure). Similar to [Anderson+ 14]
CRU model.
17. Learned weights tend to decrease monotonically,
which agrees with recency bias in the data.
17
100
101
102
index
10 3
10 2
10 1
Recencyweightw
contact-prim-school
100
101
102
index
10 3
10 2
Recencyweightw
email-Eu-core
100
101
102
index
10 3
10 2
Recencyweightw
coauth-Geology
100
101
102
index
10 2
Recencyweightw
tags-mathoverflow
Correlation
probability p.
18. Asymptotic behavior depends on the
recency weight model parameters.
18
Theorem.
Let Wj =
Pj
i=1 wi.
If W1 < 1, the model tips with probability 1.
If W1 = 1, then every pair occurs infinitely often.<latexit 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We say that the model tips if
after some point, only one set appears forever more.
(Similar flavor of result to single-item sequence models [Anderson+ 14].)
19. Sequences of sets are a rich type of data.
19
1. The data exhibits complex repetition patterns.
2. Correlated Repeated Unions (CRU) is a model for repeat structure.
3. Optimal correlation probabilities are consistent within domain
but different across domains.
4. Optimal weights look the same across domains—fat tails.
5. Can analyze the asymptotic behavior of the model.
{a, b, c}, {a, b}, {c, d, e, f}, {a, c}, {c}, {a, b, c}, {e, g, h}, {h}, …
{a, b}, {a, x}, {a, y}, {a}, {a}, {a}, {z}, {a, b, x, y, z}, …
{j}, {j, k, l}, {a, j}, {a}, {a, k}, {a, j, k, l}, {j, k, l}, {j, k, l}, {j, k}…
20. Sequences of sets.
20
Austin R. Benson
http://cs.cornell.edu/~arb
@austinbenson
arb@cs.cornell.edu
THANKS!
Slides. bit.ly/SoS-KDD
Code. bit.ly/SoS-code
Data. bit.ly/SoS-data
100
101
102
index
10 3
10 2
Recencyweightw
email-Eu-core