This document discusses various rule mining algorithms. It begins with an introduction to data mining and central themes like classification, clustering, association analysis, outlier analysis, and evolution analysis. It then discusses association rule mining (ARM), including definitions of support, confidence, and how ARM finds frequent itemsets and strong association rules. It also covers quantitative rules mining, sequential mining, partially ordered sets (posets), lattices, common algorithmic families like Apriori and FP-growth, and more.
The document provides information about linear and non-linear data structures. It discusses stacks as an example of a linear data structure and describes their last-in, first-out nature. Operations on stacks like push and pop are explained along with algorithms to perform insertion, deletion, and display of items in a stack. Applications of stacks like reversing strings and checking validity of expressions are outlined. The conversion of infix notation to postfix notation is demonstrated through an example.
El documento define Business Intelligence como la habilidad para transformar datos en información y conocimiento para optimizar la toma de decisiones empresariales. Explica que BI apoya la toma de decisiones de usuarios a través de herramientas de análisis de datos accesibles. También describe los principales componentes de BI como almacenes de datos, ETL, minería de datos, y sistemas de soporte a la decisión.
This document provides a summary of lecture 5 on association rule mining. It discusses topics like association rule mining, mining single and multilevel association rules, measurements like support and confidence. It provides examples of mining association rules from transactional databases and relational tables. It describes the Apriori algorithm for mining frequent itemsets and generating association rules. It also discusses techniques like FP-tree for overcoming performance issues of Apriori.
Business intelligence (BI) provides processes, technologies, and tools to help organizations analyze data and make better business decisions. BI technologies gather, store, analyze and provide access to enterprise data. This helps users understand what happened in the past, what is happening currently, and make plans to achieve desired future outcomes. BI provides a single point of access to information, timely answers to business questions, and allows all departments to use data for decision making. Key BI tools include dashboards, key performance indicators, graphical reporting, forecasting, and data visualization. These tools help analyze trends, customer behavior, market conditions, and support risk analysis and decision making.
How to Motivate and Empower Globally-Competitive Teams of Content ProfessionalsSaiff Solutions, Inc.
Barry Saiff is a technical communications leader with 32 years of experience leading writing teams at six US companies. He founded Saiff Solutions, Inc. in 2011 to provide content development services to Fortune 500 companies. In his presentation, he discussed keys to successful management including caring for employees, ensuring access to managers, treating people with respect, empowering employees, and managing cross-cultural teams with integrity. He emphasized the importance of vision, training, respect, empowerment, and expecting excellence from employees.
The document discusses binary search trees and their properties. It explains that a binary search tree is a binary tree where every node's left subtree contains values less than the node's value and the right subtree contains greater values. Operations like search, insert, delete can be done in O(h) time where h is the height of the tree. The height is O(log n) for balanced trees but can be O(n) for unbalanced trees. The document also provides examples of using a binary search tree to sort a set of numbers in O(n log n) time by building the BST and doing an inorder traversal.
This document discusses extending the OpenSMT satisfiability modulo theories (SMT) solver to implement a new theory called "simple order" (SO). It outlines the steps to: 1) Set up files and directories for the new SO solver, 2) Connect the SO solver to OpenSMT, 3) Implement the SO solver by representing constraints as a graph and checking for cycles to determine satisfiability. Key aspects covered include using enodes to represent terms and formulas, implementing adjacency lists and depth-first search to check for cycles in the constraint graph, and computing conflicts by tracking parent edges.
The document provides information about linear and non-linear data structures. It discusses stacks as an example of a linear data structure and describes their last-in, first-out nature. Operations on stacks like push and pop are explained along with algorithms to perform insertion, deletion, and display of items in a stack. Applications of stacks like reversing strings and checking validity of expressions are outlined. The conversion of infix notation to postfix notation is demonstrated through an example.
El documento define Business Intelligence como la habilidad para transformar datos en información y conocimiento para optimizar la toma de decisiones empresariales. Explica que BI apoya la toma de decisiones de usuarios a través de herramientas de análisis de datos accesibles. También describe los principales componentes de BI como almacenes de datos, ETL, minería de datos, y sistemas de soporte a la decisión.
This document provides a summary of lecture 5 on association rule mining. It discusses topics like association rule mining, mining single and multilevel association rules, measurements like support and confidence. It provides examples of mining association rules from transactional databases and relational tables. It describes the Apriori algorithm for mining frequent itemsets and generating association rules. It also discusses techniques like FP-tree for overcoming performance issues of Apriori.
Business intelligence (BI) provides processes, technologies, and tools to help organizations analyze data and make better business decisions. BI technologies gather, store, analyze and provide access to enterprise data. This helps users understand what happened in the past, what is happening currently, and make plans to achieve desired future outcomes. BI provides a single point of access to information, timely answers to business questions, and allows all departments to use data for decision making. Key BI tools include dashboards, key performance indicators, graphical reporting, forecasting, and data visualization. These tools help analyze trends, customer behavior, market conditions, and support risk analysis and decision making.
How to Motivate and Empower Globally-Competitive Teams of Content ProfessionalsSaiff Solutions, Inc.
Barry Saiff is a technical communications leader with 32 years of experience leading writing teams at six US companies. He founded Saiff Solutions, Inc. in 2011 to provide content development services to Fortune 500 companies. In his presentation, he discussed keys to successful management including caring for employees, ensuring access to managers, treating people with respect, empowering employees, and managing cross-cultural teams with integrity. He emphasized the importance of vision, training, respect, empowerment, and expecting excellence from employees.
The document discusses binary search trees and their properties. It explains that a binary search tree is a binary tree where every node's left subtree contains values less than the node's value and the right subtree contains greater values. Operations like search, insert, delete can be done in O(h) time where h is the height of the tree. The height is O(log n) for balanced trees but can be O(n) for unbalanced trees. The document also provides examples of using a binary search tree to sort a set of numbers in O(n log n) time by building the BST and doing an inorder traversal.
This document discusses extending the OpenSMT satisfiability modulo theories (SMT) solver to implement a new theory called "simple order" (SO). It outlines the steps to: 1) Set up files and directories for the new SO solver, 2) Connect the SO solver to OpenSMT, 3) Implement the SO solver by representing constraints as a graph and checking for cycles to determine satisfiability. Key aspects covered include using enodes to represent terms and formulas, implementing adjacency lists and depth-first search to check for cycles in the constraint graph, and computing conflicts by tracking parent edges.
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.
1. The document discusses algorithms for handling collisions in hashing, including open hashing which uses separate chaining with linked lists, and closed hashing which resolves collisions through techniques like linear probing.
2. It also discusses binary search trees and their operations, as well as balanced search trees like AVL and red-black trees which have logarithmic time performance.
3. Finally, it covers multiway search trees including 2-3 trees and how they allow for more than one key per node, providing improved time performance over standard binary search trees.
Association rule mining is a machine learning technique used to discover relationships between variables in large datasets. It involves finding frequent itemsets - sets of items that often occur together - and generating rules based on these itemsets. A common algorithm for association rule mining is the Apriori algorithm, which uses a breadth-first search strategy to count item frequencies and generate candidate itemsets in multiple passes over the transaction data. The algorithm outputs frequent itemsets that meet minimum support and confidence thresholds, from which association rules can be derived.
I am John G. I am a Stochastic Processes Assignment Expert at statisticsassignmenthelp.com. I hold a Masters in Statistics, from London, UK. I have been helping students with their homework for the past 5 years. I solve assignments related to Stochastic Processes.
Visit statisticsassignmenthelp.com or email info@statisticsassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Stochastic Processes Assignments.
1. Hash tables are good for random access of elements but not sequential access. When records need to be accessed sequentially, hashing can be problematic because elements are stored in random locations instead of consecutively.
2. To find the successor of a node in a binary search tree, we take the right child. This operation has a runtime complexity of O(1).
3. When comparing operations like insertion, deletion, and searching between different data structures, arrays generally have the best performance for insertion and searching, while linked lists have better performance for deletion and allow for easy insertion/deletion anywhere. Binary search trees fall between these two.
This document provides an overview of association rule mining and the Apriori algorithm. It begins with basic concepts such as transactions, itemsets, support and confidence. It then describes the Apriori algorithm, which has two steps: 1) find all frequent itemsets that satisfy a minimum support threshold, and 2) generate association rules from the frequent itemsets that satisfy a minimum confidence threshold. The document explains how the Apriori algorithm uses a level-wise search approach and the apriori property to efficiently find frequent itemsets in the transaction database. It also discusses generating rules from the frequent itemsets and some extensions to the basic algorithm.
Insertion:
Insert at the beginning: Add a new node at the beginning of the linked list.
Insert at the end: Add a new node at the end of the linked list.
Insert at a specified position: Add a new node at a specific position in the linked list.
Deletion:
Delete from the beginning: Remove the first node from the linked list.
Delete from the end: Remove the last node from the linked list.
Delete a specific node: Remove a node with a specific value or position from the linked list.
Traversal:
Print the linked list: Display all the elements in the linked list.
Search for a specific element: Find a particular element in the linked list.
Other operations:
Get length of the linked list: Calculate the number of nodes in the linked list.
Reverse the linked list: Reverse the order of elements in the linked list.
Slides 8-49: Detailed Explanation with Examples
Each slide covers one specific topic or operation.
This document provides an overview of association rule mining and the Apriori algorithm. It begins with basic concepts such as transactions, itemsets, support and confidence. It then describes the Apriori algorithm, which finds frequent itemsets in two steps: first generating candidate itemsets and then scanning the database to determine truly frequent itemsets. Finally, it generates rules from the frequent itemsets. The document also discusses alternative data formats, mining with multiple minimum supports, and class association rules.
Association rule mining used in data miningvayumani25
This document provides an overview of the Apriori algorithm for mining association rules. It begins with basic concepts like transactions, itemsets, support and confidence. It then describes the two main steps of the Apriori algorithm: 1) finding all frequent itemsets that satisfy a minimum support threshold and 2) generating association rules from the frequent itemsets that satisfy a minimum confidence threshold. Key aspects of the Apriori algorithm like candidate generation, pruning, and level-wise search are explained through examples. Finally, it discusses some extensions like mining different data formats and multiple minimum support thresholds.
The document discusses association rule mining which aims to discover relationships between items in transactional data. It defines key concepts like support, confidence and association rules. It also describes several algorithms for mining association rules like Apriori, Partition and Pincer-Search. Apriori is a level-wise, candidate generation-based approach that leverages the downward closure property. Partition divides the database to mine local frequent itemsets in parallel. Pincer-Search incorporates bidirectional search to prune candidates more efficiently.
i-Eclat: performance enhancement of Eclat via incremental approach in frequen...TELKOMNIKA JOURNAL
One example of the state-of-the-art vertical rule mining technique is called equivalence class transformation (Eclat) algorithm. Neither horizontal nor vertical data format, both are still suffering from the huge memory consumption. In response to the promising results of mining in a higher volume of data from a vertical format, and taking consideration of dynamic transaction of data in a database, the research proposes a performance enhancement of Eclat algorithm that relies on incremental approach called an Incremental-Eclat (i-Eclat) algorithm. Motivated from the fast intersection in Eclat, this algorithm of performance enhancement adopts via my structured query language (MySQL) database management system (DBMS) as its platform. It serves as the association rule mining database engine in testing benchmark frequent itemset mining (FIMI) datasets from online repository. The MySQL DBMS is chosen in order to reduce the preprocessing stages of datasets. The experimental results indicate that the proposed algorithm outperforms the traditional Eclat with 17% both in chess and T10I4D100K, 69% in mushroom, 5% and 8% in pumsb_star and retail datasets. Thus, among five (5) dense and sparse datasets, the average performance of i-Eclat is concluded to be 23% better than Eclat.
The document discusses the union find algorithm and its time complexity. It defines the union find problem and three operations: MAKE-SET, FIND, and UNION. It describes optimizations like union by rank and path compression that achieve near-linear time complexity of O(m log* n) for m operations on n elements. It proves several lemmas about ranks and buckets to establish this time complexity through an analysis of the costs T1, T2, and T3.
The document describes a pipeline for semantic processing of natural language that begins with parsing text, creates a predicate logic meaning representation, converts it to PENMAN notation, and then performs generation to produce an output parse tree and string. It illustrates this process on English sentences, showing how a meaning representation is constructed from parsed input and then used to generate the same parsed output. The pipeline can also perform translation by changing the language used for generation. It discusses how meaning representations are constructed from parsed trees using Treebank Semantics and how the representations are then prepared and structured for generation to reconstruct the parse trees and sentences.
The document outlines the goals and material to be covered in three upcoming classes on signals and systems. The classes will: (1) define different types of signals and explore the concept of a system, (2) examine linear, time-invariant systems and their representation in the time and frequency domains, and (3) review Fourier series/transforms and their practical applications including sampling, aliasing, and signal conversion.
NYAI #9: Concepts and Questions As Programs by Brenden LakeRizwan Habib
Brenden studies computational problems that are easier for people than they are for machines. He received his Ph.D. in Cognitive Science from MIT in 2014, and his M.S. and B.S. in Symbolic Systems from Stanford University in 2009. He is a recipient of the Robert J. Glushko Prize for Outstanding Doctoral Dissertation in Cognitive Science. His recent research on Bayesian Program Learning has been covered by many media outlets (New York Times, Washington Post, etc.) and was selected by Scientific American as one of the most important advances of 2016.
Both cognitive science and AI can gain by studying the human solutions to difficult computational problems. Brenden's talk will focus concept learning and question asking, two problems that people solve far better than machines. People can learn a new concept from fewer examples, and then use their concepts in richer ways -- for imagination, extrapolation, and explanation, not just classification. Moreover, learning is often an active process; people can ask rich and probing questions in order to reduce uncertainty, while algorithms for active learning ask simple and stereotyped queries. He will also discuss work on program induction as a cognitive model and potential solution for extracting richer concepts from less data, with applications to learning handwritten characters and learning recursive visual concepts from examples. Brenden will end with program synthesis as a model of question asking in simple games.
Proof of O(log *n) time complexity of Union find (Presentation by Wei Li, Zeh...Amrinder Arora
The document discusses the union find algorithm and its time complexity. It defines the union find problem and three operations: MAKE-SET, FIND, and UNION. It describes optimizations like union by rank and path compression that achieve near-linear time complexity of O(m log* n) for m operations on n elements. It proves several lemmas about ranks and buckets to establish this time complexity through an analysis of the costs of find operations.
This document presents an enhanced suffix stripping algorithm to improve information retrieval. It discusses stemming, which reduces words to their root form to increase retrieval efficiency. Porter's stemming algorithm is widely used but has drawbacks. The proposed enhanced algorithm adds new rules to address inaccuracies in Porter's algorithm and reduce over-stemming and under-stemming errors. An analysis shows the enhanced algorithm reduces the index size more than Porter's algorithm and has lower over-stemming and under-stemming indexes, improving retrieval effectiveness.
Random Number Generators :
LCG, Fibonacci, LFSR, GFSR, TGFSR, MT, MT19937,WELL
Tutorials on FInite Fields and associated RNG on github at :
https://github.com/rinnocente/Random_Numbers
The document discusses Docker containers and their architecture. It begins by explaining that Docker originated as a tool called Docker created by dotCloud to manage customer applications in the cloud. It became very popular with developers and dotCloud changed its name to Docker, Inc. and focused its business on Docker. The document then discusses how Docker uses Linux kernel features like control groups (cgroups) and namespaces to isolate containers and their resources. It explains that Docker architecture includes a client, daemon, containers running applications, and an optional distributed data store. Finally, it provides an example of basic Docker commands to check the Docker version and run a test container.
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.
1. The document discusses algorithms for handling collisions in hashing, including open hashing which uses separate chaining with linked lists, and closed hashing which resolves collisions through techniques like linear probing.
2. It also discusses binary search trees and their operations, as well as balanced search trees like AVL and red-black trees which have logarithmic time performance.
3. Finally, it covers multiway search trees including 2-3 trees and how they allow for more than one key per node, providing improved time performance over standard binary search trees.
Association rule mining is a machine learning technique used to discover relationships between variables in large datasets. It involves finding frequent itemsets - sets of items that often occur together - and generating rules based on these itemsets. A common algorithm for association rule mining is the Apriori algorithm, which uses a breadth-first search strategy to count item frequencies and generate candidate itemsets in multiple passes over the transaction data. The algorithm outputs frequent itemsets that meet minimum support and confidence thresholds, from which association rules can be derived.
I am John G. I am a Stochastic Processes Assignment Expert at statisticsassignmenthelp.com. I hold a Masters in Statistics, from London, UK. I have been helping students with their homework for the past 5 years. I solve assignments related to Stochastic Processes.
Visit statisticsassignmenthelp.com or email info@statisticsassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Stochastic Processes Assignments.
1. Hash tables are good for random access of elements but not sequential access. When records need to be accessed sequentially, hashing can be problematic because elements are stored in random locations instead of consecutively.
2. To find the successor of a node in a binary search tree, we take the right child. This operation has a runtime complexity of O(1).
3. When comparing operations like insertion, deletion, and searching between different data structures, arrays generally have the best performance for insertion and searching, while linked lists have better performance for deletion and allow for easy insertion/deletion anywhere. Binary search trees fall between these two.
This document provides an overview of association rule mining and the Apriori algorithm. It begins with basic concepts such as transactions, itemsets, support and confidence. It then describes the Apriori algorithm, which has two steps: 1) find all frequent itemsets that satisfy a minimum support threshold, and 2) generate association rules from the frequent itemsets that satisfy a minimum confidence threshold. The document explains how the Apriori algorithm uses a level-wise search approach and the apriori property to efficiently find frequent itemsets in the transaction database. It also discusses generating rules from the frequent itemsets and some extensions to the basic algorithm.
Insertion:
Insert at the beginning: Add a new node at the beginning of the linked list.
Insert at the end: Add a new node at the end of the linked list.
Insert at a specified position: Add a new node at a specific position in the linked list.
Deletion:
Delete from the beginning: Remove the first node from the linked list.
Delete from the end: Remove the last node from the linked list.
Delete a specific node: Remove a node with a specific value or position from the linked list.
Traversal:
Print the linked list: Display all the elements in the linked list.
Search for a specific element: Find a particular element in the linked list.
Other operations:
Get length of the linked list: Calculate the number of nodes in the linked list.
Reverse the linked list: Reverse the order of elements in the linked list.
Slides 8-49: Detailed Explanation with Examples
Each slide covers one specific topic or operation.
This document provides an overview of association rule mining and the Apriori algorithm. It begins with basic concepts such as transactions, itemsets, support and confidence. It then describes the Apriori algorithm, which finds frequent itemsets in two steps: first generating candidate itemsets and then scanning the database to determine truly frequent itemsets. Finally, it generates rules from the frequent itemsets. The document also discusses alternative data formats, mining with multiple minimum supports, and class association rules.
Association rule mining used in data miningvayumani25
This document provides an overview of the Apriori algorithm for mining association rules. It begins with basic concepts like transactions, itemsets, support and confidence. It then describes the two main steps of the Apriori algorithm: 1) finding all frequent itemsets that satisfy a minimum support threshold and 2) generating association rules from the frequent itemsets that satisfy a minimum confidence threshold. Key aspects of the Apriori algorithm like candidate generation, pruning, and level-wise search are explained through examples. Finally, it discusses some extensions like mining different data formats and multiple minimum support thresholds.
The document discusses association rule mining which aims to discover relationships between items in transactional data. It defines key concepts like support, confidence and association rules. It also describes several algorithms for mining association rules like Apriori, Partition and Pincer-Search. Apriori is a level-wise, candidate generation-based approach that leverages the downward closure property. Partition divides the database to mine local frequent itemsets in parallel. Pincer-Search incorporates bidirectional search to prune candidates more efficiently.
i-Eclat: performance enhancement of Eclat via incremental approach in frequen...TELKOMNIKA JOURNAL
One example of the state-of-the-art vertical rule mining technique is called equivalence class transformation (Eclat) algorithm. Neither horizontal nor vertical data format, both are still suffering from the huge memory consumption. In response to the promising results of mining in a higher volume of data from a vertical format, and taking consideration of dynamic transaction of data in a database, the research proposes a performance enhancement of Eclat algorithm that relies on incremental approach called an Incremental-Eclat (i-Eclat) algorithm. Motivated from the fast intersection in Eclat, this algorithm of performance enhancement adopts via my structured query language (MySQL) database management system (DBMS) as its platform. It serves as the association rule mining database engine in testing benchmark frequent itemset mining (FIMI) datasets from online repository. The MySQL DBMS is chosen in order to reduce the preprocessing stages of datasets. The experimental results indicate that the proposed algorithm outperforms the traditional Eclat with 17% both in chess and T10I4D100K, 69% in mushroom, 5% and 8% in pumsb_star and retail datasets. Thus, among five (5) dense and sparse datasets, the average performance of i-Eclat is concluded to be 23% better than Eclat.
The document discusses the union find algorithm and its time complexity. It defines the union find problem and three operations: MAKE-SET, FIND, and UNION. It describes optimizations like union by rank and path compression that achieve near-linear time complexity of O(m log* n) for m operations on n elements. It proves several lemmas about ranks and buckets to establish this time complexity through an analysis of the costs T1, T2, and T3.
The document describes a pipeline for semantic processing of natural language that begins with parsing text, creates a predicate logic meaning representation, converts it to PENMAN notation, and then performs generation to produce an output parse tree and string. It illustrates this process on English sentences, showing how a meaning representation is constructed from parsed input and then used to generate the same parsed output. The pipeline can also perform translation by changing the language used for generation. It discusses how meaning representations are constructed from parsed trees using Treebank Semantics and how the representations are then prepared and structured for generation to reconstruct the parse trees and sentences.
The document outlines the goals and material to be covered in three upcoming classes on signals and systems. The classes will: (1) define different types of signals and explore the concept of a system, (2) examine linear, time-invariant systems and their representation in the time and frequency domains, and (3) review Fourier series/transforms and their practical applications including sampling, aliasing, and signal conversion.
NYAI #9: Concepts and Questions As Programs by Brenden LakeRizwan Habib
Brenden studies computational problems that are easier for people than they are for machines. He received his Ph.D. in Cognitive Science from MIT in 2014, and his M.S. and B.S. in Symbolic Systems from Stanford University in 2009. He is a recipient of the Robert J. Glushko Prize for Outstanding Doctoral Dissertation in Cognitive Science. His recent research on Bayesian Program Learning has been covered by many media outlets (New York Times, Washington Post, etc.) and was selected by Scientific American as one of the most important advances of 2016.
Both cognitive science and AI can gain by studying the human solutions to difficult computational problems. Brenden's talk will focus concept learning and question asking, two problems that people solve far better than machines. People can learn a new concept from fewer examples, and then use their concepts in richer ways -- for imagination, extrapolation, and explanation, not just classification. Moreover, learning is often an active process; people can ask rich and probing questions in order to reduce uncertainty, while algorithms for active learning ask simple and stereotyped queries. He will also discuss work on program induction as a cognitive model and potential solution for extracting richer concepts from less data, with applications to learning handwritten characters and learning recursive visual concepts from examples. Brenden will end with program synthesis as a model of question asking in simple games.
Proof of O(log *n) time complexity of Union find (Presentation by Wei Li, Zeh...Amrinder Arora
The document discusses the union find algorithm and its time complexity. It defines the union find problem and three operations: MAKE-SET, FIND, and UNION. It describes optimizations like union by rank and path compression that achieve near-linear time complexity of O(m log* n) for m operations on n elements. It proves several lemmas about ranks and buckets to establish this time complexity through an analysis of the costs of find operations.
This document presents an enhanced suffix stripping algorithm to improve information retrieval. It discusses stemming, which reduces words to their root form to increase retrieval efficiency. Porter's stemming algorithm is widely used but has drawbacks. The proposed enhanced algorithm adds new rules to address inaccuracies in Porter's algorithm and reduce over-stemming and under-stemming errors. An analysis shows the enhanced algorithm reduces the index size more than Porter's algorithm and has lower over-stemming and under-stemming indexes, improving retrieval effectiveness.
Similar to Data mining : rule mining algorithms (20)
Random Number Generators :
LCG, Fibonacci, LFSR, GFSR, TGFSR, MT, MT19937,WELL
Tutorials on FInite Fields and associated RNG on github at :
https://github.com/rinnocente/Random_Numbers
The document discusses Docker containers and their architecture. It begins by explaining that Docker originated as a tool called Docker created by dotCloud to manage customer applications in the cloud. It became very popular with developers and dotCloud changed its name to Docker, Inc. and focused its business on Docker. The document then discusses how Docker uses Linux kernel features like control groups (cgroups) and namespaces to isolate containers and their resources. It explains that Docker architecture includes a client, daemon, containers running applications, and an optional distributed data store. Finally, it provides an example of basic Docker commands to check the Docker version and run a test container.
The document discusses several topics related to open networking with FPGAs including:
1) High Performance Reconfigurable Computing (HPRC) and the performance of FPGAs for networking and computing.
2) A demonstration by Huawei and Xilinx of a 400 Gbps core router implemented on FPGA cards.
3) Interchip and interboard communication technologies like Interlaken.
4) OpenFlow and how it allows a controller to programmatically alter the forwarding behavior of switches.
5) Network emulation tools like Mininet that can be used to test OpenFlow applications and topologies without requiring physical hardware.
The document discusses using Maxwell's equations and the Finite-Difference Time-Domain (FDTD) method to simulate indoor WiFi propagation and determine optimal access point placement, noting that while Maxwell's equations can model electromagnetic propagation, accurately simulating real-world materials, effects like scattering and dispersion, and WiFi signals may be computationally challenging.
This document discusses email authentication techniques including TLS, SPF, DKIM and DMARC. It provides information on how these protocols work and how to implement them. Key points covered include how SPF validates the envelope sender address by checking the authorized mail servers for a domain in DNS, and how DKIM cryptographically signs specific parts of emails to validate that the content has not been modified in transit. Configuration examples are given for setting up SPF records and generating DKIM keys.
This document provides an overview of FPGA computing using an Intel/Altera Arria 10 FPGA. It begins with the history of the FPGA computing project and defines what an FPGA is. It then discusses the Intel Arria 10 FPGA used in tests. To measure performance on new architectures, it introduces the concept of the "Seven Dwarfs" benchmark algorithms and arithmetic intensity. The Roofline performance model is explained as a way to estimate performance based on peak flop rate and memory bandwidth. Actual performance results are shown for algorithms like vector addition, stencil code, and matrix multiplication run on the FPGA compared to CPU. OpenCL is discussed as a programming model for FPGAs.
The document discusses various topics related to refreshing computer skills, including:
1. How to easily write simple web pages using Markdown or Markdown editors.
2. How to easily add math to web pages using MathJax, which allows LaTeX equations to be rendered in browsers.
3. Notebooks for mixing text, math, and computation results using Jupyter notebooks, which support various programming kernels like Python, R, and Maxima.
This document summarizes key aspects of computer hardware and architecture. It discusses nodes and networks that make up computer systems. It describes different types of computer instruction sets like CISC and RISC. It outlines various microarchitecture features for high performance computing like superscalar, pipelining, out-of-order execution, and branch prediction. It also covers cache memory organization and algorithms.
This document discusses transport protocols and how they have been optimized for large data transfers but are not as well suited for the small file transfers that now dominate web traffic. It describes several key aspects of TCP including flow control using a sliding window, congestion control algorithms like slow start and congestion avoidance, and mechanisms for detecting and responding to packet loss like fast retransmit. It notes how TCP was adapted over time, including additions like fast recovery, and alternatives like TCP Vegas which aims to avoid rather than just respond to congestion. The document provides historical context and details on TCP implementations.
The document discusses public key cryptography, digital certificates, and Transport Layer Security (TLS). It provides an overview of symmetric and asymmetric key cryptography, algorithms like RSA and ElGamal, the use of digital signatures and certificates, and how TLS uses public key encryption to securely transmit data over the internet, such as for email.
This document discusses challenges and opportunities for end nodes with multigigabit networking. It covers increasing bandwidth capabilities through technologies like DWDM and 10GbE. It also examines hardware challenges for processor, memory, and I/O buses. Software challenges discussed include zero-copy networking, ULNI/OS bypass, and network path pipelining. The document also summarizes network protocols like AQM, ECN, MPLS and their roles in high-speed networking.
Mosix : automatic load balancing and migration rinnocente
The document discusses automatic load balancing and transparent process migration in distributed operating systems. It begins with an introduction and overview of MOSIX, the distributed operating system that is the focus. It then provides overviews of several other distributed operating systems such as Sprite, Charlotte, Accent, Amoeba, and V System. The document outlines different load balancing mechanisms, including job initiation, migration algorithms, and measures used to evaluate processor load. It also covers process migration mechanisms.
The document discusses speculation and speculative execution in modern microprocessors. It explains that processors predict upcoming instructions and speculatively execute them to improve performance. If the prediction is correct, the results are committed, but if not the results are discarded. The document also discusses how transistor counts have increased quadratically compared to linear speed increases, enabling more complex superscalar and pipeline designs to exploit instruction level parallelism.
This document provides an overview of IPv6 including:
- The history and motivations for developing IPv6 due to IPv4 address exhaustion.
- An introduction to IPv6 addressing and prefixes.
- Transition technologies like tunnels to help with gradual IPv6 deployment.
- IPv6 control protocols for tasks like neighbor discovery and routing.
- Details on how IPv6 addresses are represented textually and allocated.
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Nomination are Open!! Don't Miss it
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Open source database for logs
● Easy to setup and operate - just a single executable with sane default configs
● Works great with both structured and plaintext logs
● Uses up to 30x less RAM and up to 15x disk space than Elasticsearch
● Provides simple yet powerful query language for logs - LogsQL
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○ TCP
○ TCP+TLS
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● Additional filtering
● Sorting
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● Transparent historical data migration to object storage
○ Try single-node VictoriaLogs with persistent volumes - it compresses 1TB of production logs from
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For more Alluxio Events: https://www.alluxio.io/events/
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Safelyio automates the delivery and documentation of safety talks, ensuring consistency and accessibility. The microlearning approach breaks down complex safety protocols into manageable, bite-sized pieces, making it easier for employees to absorb and retain information.
This method minimizes disruptions to work schedules, eliminates the hassle of paperwork, and ensures that all safety communications are tracked and recorded accurately. Ultimately, using a digital platform like Safelyio enhances engagement, compliance, and overall safety performance on site. https://safelyio.com/
1. 10 May 2002 Roberto Innocente 1
Data mining:
rule mining algorithms
Roberto Innocente
rinnocente@hotmail.com
2. 10 May 2002 Roberto Innocente 2
Introduction /1
Data mining also known as Knowledge
Discovery in Databases or KDD (Piatesky-
Shapiro 1991), is the process of extracting
useful hidden information from very large
databases in an unsupervised manner.
3. 10 May 2002 Roberto Innocente 3
Introduction /2
Central themes of data mining are:
! Classification
! Cluster analysis
! Associations analysis
! Outlier analysis
! Evolution analysis
4. 10 May 2002 Roberto Innocente 4
ARM /1
(association rules mining)
" Formally introduced in 1993 by Agrawal,
Imielinski and Swami (AIS) in connection with
market basket analysis
" Formalizes statements of the form:
What is the percentage of customers that
together with cheese buy beer ?
5. 10 May 2002 Roberto Innocente 5
ARM /2
" We have a set of items I={i1,i2,..}, and a set of transaction T={t1,t2..}. Each
transaction (like a supermarket bill) is a set of items (or better as it is called an
itemset)
" If U and V are disjoint itemsets, we call support of U=>V the fraction of transactions
that contain U ∪ V and we indicate this with s(U=>V)
" We say that an itemset is frequent if its support is greater than a chosen threshold
called minsupp.
" If A and B are disjoint itemsets, we call confidence of A=>B and indicate with
c(A=>B), the fraction of transactions containing A that contain also B. This is also
called the Bayesian or conditional probability p(B|A).
" We say that a rule is strong if its confidence is greater than a threshold called
minconf.
6. 10 May 2002 Roberto Innocente 6
ARM /3
ARM can then be formulated as:
Given a set I of items and a set T of transactions over I,
produce in an automated manner all association rules
that are more than x% frequent and more than y%
strong.
7. 10 May 2002 Roberto Innocente 7
ARM /4
On the right we have 6
transactions T={1,2,3,4,5,6}
on a set of 5 items
I={A,B,C,D,E}
The itemset BC is present in the
transactions {1,2,3,4,5} so its
support s(B=>C) = 5/6
The confidence of B=>C, given
that BC is present in 5
transactions and B is present
in all 6 transactions, is
c(B=>C) = s(B=>C)/s(B)=5/6
8. 10 May 2002 Roberto Innocente 8
ARM /5
Another possible representation is
the matrix representation, that
can combine the properties of the
so called horizontal and vertical
format.
9. 10 May 2002 Roberto Innocente 9
ARM /6
All algorithms divide the search in two phases :
- Find frequent itemsets
- Find the strong association rules for each
frequent itemset
10. 10 May 2002 Roberto Innocente 10
ARM /7
The second phase can in principle be quite simple.
To find the strong association rules associated with an itemset U,
simply :
for each proper subset A of U :
If s(U)/s(A) is more than minconf then
the rule A=>(U-A) is strong
For this reason, in what follows, only the search for frequent
itemsets will be investigated.
11. 10 May 2002 Roberto Innocente 11
Quantitative rules mining
It is possible to consider the case where an attribute is not boolean (true or false),
but assumes a value. For example age in census data is such an attribute.
It is possible to reduce this case to the case of boolean attributes binning the
range of the attribute value. For example age can be translated to the
following boolean attributes:
# Young (age 0-30)
# Adult (31-65)
# Old (66-)
The expression level of a gene (0-255) can be represented by :
# Low (0-50)
# Medium(51-205)
# High(206-)
12. 10 May 2002 Roberto Innocente 12
Sequential mining /1
In this case the database rows are eventsets with a timestamp:
!110 A,B,E
!150 E,F
!160 A
We are interested in frequent episodes (sequences of eventsets),
like :
!(A,(B,E),F)
(where (B,E) is an eventset) occurring in a time window:
event A precedes the eventset (B,E) that precedes F.
13. 10 May 2002 Roberto Innocente 13
Sequential mining /2
100 110 120 130 140
A
B
E
E
F A
150 160
14. 10 May 2002 Roberto Innocente 14
Sequential mining /3
" It’s been applied for example to the alarms of
the finnish telephone network
" It can be applied to temporal series of gene
expression
15. 10 May 2002 Roberto Innocente 15
Posets /1
Given a set U, a binary relation ≤
reflexive, antisymmetric and
transititve, is called a partial order
(or an order tout-court), and (U,≤)
is called a partially ordered set (
or a poset)
A poset is frequently represented with a
Hasse diagram, a diagram in
which if a ≤ b, then there is an
ascending path from a to b. The
binary relation on N, is divisor of
(usually represented with |) is a
partial order on N.
12
4 6
32
1
Hasse diagram of the
divisors of 12
16. 10 May 2002 Roberto Innocente 16
Posets /2
In a poset, an element that is not less
than any other is said to be
maximal. Clearly, there can be
many maximal elements.
If a maximal element is comparable
with all other elements, then it is
the only maximum.
Maximal
elements
Maximum
Minimal
elements
17. 10 May 2002 Roberto Innocente 17
Posets /3
If (U, ≤) and (V, ≤) are two posets, a pair of
functions f:U->V and g:V->U such that
(u,u’ ∈U; v,v’∈V) :
" if u ≤ u’ then f(u’) ≤ f(u)
" if v ≤ v’ then g(v’) ≤ g(v)
" u ≤ g(f(u))
" v ≤ f(g(v))
are said to be a Galois connection between
the two posets.
From the above properties we can deduce:
f(g(f(u))) = f(u) and g(f(g(v)))=g(v)
U V
anti-
homo
morphism
f
In this example U and V
are linear orders
g
18. 10 May 2002 Roberto Innocente 18
Lattices /1
A poset in which for each pair of
elements u, v it exists an
element z that is the least
upper bound (or join or lub)
and an element w that is the
greatest lower bound (or
meet or glb) is said to be a
lattice.
This allows us to define 2 binary
operators :
z = join(u,v) = u ∪ v
w = meet(u,v) = u ∩ v
f
c
This poset
is not a lattice
because there is
no lub for (b,c)
ed
b
a
19. 10 May 2002 Roberto Innocente 19
Lattices /2
We say that a lattice is complete
if it has glb and lub for each
subset. Every finite lattice is
complete.
A poset is called a join
semilattice (meet
semilattice) if only the join
(meet) exists.
The powerset of a set ordered by
inclusion is a complete
lattice.
Frequent sets are only a meet-
semilattice.
All lattices of order 5
(up to ismorphism)
21. 10 May 2002 Roberto Innocente 21
Algorithmic families /1
There are two ways in which you can run over the lattice of subsets in bottom-up order.
These ways correspond to two families of algorithms :
" breadth first
" depth first
22. 10 May 2002 Roberto Innocente 22
Algorithmic families /2
Infrequent itemsets, have the property that all their supersets are also
infrequent. Infrequent itmesets form a join semilattice. Minimal
infrequent itemsets are sufficient to completely specify the semilattice.
So it makes sense to run over the lattice also in top-down order. Or better,
as in hybrid algorithms, mixing bottom-up with top-down.
Furthermore the search can be performed for :
! all frequent itemsets
! only maximal frequent itemsets
! closed frequent itemsets (will be defined later)
23. 10 May 2002 Roberto Innocente 23
Apriori /1
Presented by Agrawal and Srikant in 1994.
Fast algorithms for mining Association Rules
(IBM Almaden Research Center)
essentially based on the hereditary property that :
All subsets of a frequent itemset are also frequent
It performs a breadth first search.
If l is the maximum length of frequent itemsets then it performs l
scans of the database.
24. 10 May 2002 Roberto Innocente 24
Apriori /2
F(1) = { frequent 1-itemsets}
for (k=2; F(k-1) not empty; k++) {
C(k) = generate_candidates(F(k-1));
forall transactions t in T {
Ct = subset(C(k),t); // Ct are the C(k)
// candidates present in t
forall candidates c in Ct { c.count++: }
}
F(k) = {c in C(k) and c.count >= minsup}
}
Answer = {all F(k) }
25. 10 May 2002 Roberto Innocente 25
Apriori /3
generate_candidates(F(k-1) {
join :
for each pair l1,l2 in F(k-1){
if l1 and l2 are (k-1)-itemsets pairs in F(k-1) that differ just in the last item then
l1 ∪ l2 is a k-itemset candidate
}
pruning:
foreach k-itemset candidate {
if one of its (k-1)-subsets is not frequent then
prune it
}
}
28. 10 May 2002 Roberto Innocente 28
Apriori /6
" To find a frequent k-itemset it requires k passes over
the database
" Frequent itemsets of over 50-60 items are not feasible.
Apriori needs to run over all 2^60-1 frequent subsets
" Just a small example : find all itemsets with
minsup=0.5 in the 2 transactions:
(a1,a2,........,a100)
(a1,a2,........,a100,a101,...,a200)
29. 10 May 2002 Roberto Innocente 29
Partition /1
Presented by Savasere, Omiecinski, Navathe in VLDB conference 1995, it requires 2
passes over the database
" It partitions the database into a number of non-overlapping partitions
" Each partition is read and vertical tidlist (lists of transaction ids) are formed for each
item
" Then all locally (local to the partition) frequent itemsets are generated via tidlist
intersection
" After having scanned all partitions, all local frequent itemsets are merged to form the
global candidates
" Itemsets frequent over all partitions are clearly frequent and so eliminated from the
following pass
" A new scan of the database is performed, it is transformed in the tidlist format and
counts of the global candidates are performed using tidlist intersection
30. 10 May 2002 Roberto Innocente 30
Partition /2
This algorithm uses the vertical format (tidlists).
It performs only 2 scans of the database.
Partitions are calculated in such a way to be able to keep all their tidlists in
memory.
31. 10 May 2002 Roberto Innocente 31
FP-growth /1
Presented by Han, Pei, Yin in 2000.
This method does'nt require candidate generation, but stores in an
efficient novel structure, an FP-tree (a Frequent Pattern tree, a
version of a prefix tree ), the transaction database.
It scans the database once to find frequent items. Frequent items F
are then sorted in descending support count and kept in a list L.
Another scan of the databases is then performed, and for each
transaction: infrequent items are suppressed and the remaining
items are sorted in L-order and inserted in the FP-tree.
32. 10 May 2002 Roberto Innocente 32
FP-growth /2
A null root node is created. Then for each normalized (w/o
infrequent items and sorted in L-order) transaction t :
insert_tree(t,tree) {
if tree has a child node equal to head(t) then
increment the child count by 1
else
create a new child node and set its count to 1
if rest(t) is non empty then
insert_tree(rest(t),tree.child(head(t))
}
33. 10 May 2002 Roberto Innocente 33
FP-growth /3
During the construction of the FP-tree, for each frequent item, a list
linking all its presences in the FP-tree is kept updated.
Now all the information needed to mine frequent patterns is
available in the FP-tree.
Having sorted the items inside transactions in L order, increases the
probability to share prefixes.
It often happens that the FP-tree is much more compact than the
original database.
35. 10 May 2002 Roberto Innocente 35
FP-growth /5
Now, for each frequent item alpha (in reversed L-order):
FP-growth(alpha,tree) {
If tree has a single path P:
for each combination U of nodes in P:
form alpha ∪ U with support equal to the minsupport
of items in U
else:
for each child c of tree:
form beta = c ∪ alpha with support supp(c)
construct the tree of prefixes FP-tree(beta)
if FP-tree(beta) is not empty:
FP-growth(beta,FP-tree(beta)
}
36. 10 May 2002 Roberto Innocente 36
Graphs /1
G=(V,E)
V={v1,v2,v3,v4}
E={(v1,v2),(v2,v3),(v3,v4),
(v4,v1),(v1,v3)}
" A graph has a set of vertices
V, and a set of edges E
" A subgraph G' of a graph G
has part of the vertices of G
and part of the edges G has
between those vertices
v2
v1
v3
v4
G’=(V’,E’) (blue subgraph)
V’={v1,v2,v3)
E’={(v1,v2),(v2,v3),(v3,v1)}
37. 10 May 2002 Roberto Innocente 37
Graphs /2
" A bi-partite graph is a
graph in which the
vertices can be partitioned
into two sets U and V
(with void intersection)
and all the edges of the
graph have a vertex in U
and one in V (there are no
edges between vertices in
U or in V)
U
V
u1
v1
u2
v2u3
v3u4
A bi-partite graph
(U,V,E)
38. 10 May 2002 Roberto Innocente 38
Graphs /3
" A graph is said to be
complete if for each pair
of vertices there is an edge
connecting them
" Complete graphs are
usually indicated by K
" A bi-partite graph is said
to be complete if ...
39. 10 May 2002 Roberto Innocente 39
Graphs /4
" A complete subgraph is said to
be a clique
" A clique that is not contained
in another is said to be a
maximal clique
41. 10 May 2002 Roberto Innocente 41
Max clique /1
Presented by M.Zaki, Parthasarathy, Ogihara, Li in 1997.
It computes frequent 1-itemsets and 2-itemsets as Apriori.
But then it tries to find only all maximal frequent itemsets.
A maximal frequent itemset is a frequent itemset not contained
in another frequent itemset.
All frequent itemsets are subsets of a maximal frequent itemset.
This algorithm is a depth-first algorithm.
It uses the vertical format (tidlists)
42. 10 May 2002 Roberto Innocente 42
Max clique /2
43. 10 May 2002 Roberto Innocente 43
Max clique /3
44. 10 May 2002 Roberto Innocente 44
Max clique /4
Maximal clique generation algorithms are well known and the
following can be used :
" Mulligan and Corneil,1972 (modified Bierstone’s) JACM
" Bron & Kerbosch 1973,CACM
" Chiba & Nishizeki, 1985,SIAM JC
" Tsukiyama et al. 1977,SIAM JC
After having found the maximal cliques, their support is to be
checked to verify that they are really frequent.
45. 10 May 2002 Roberto Innocente 45
Closure operators/systems
If (A, ≤ ) is a complete lattice and
we have a function :
cl: A -> A
such that (u,v ∈ A) :
" if u ≤ v then cl(u) ≤ cl(v)
" u ≤ cl(u )
" cl(cl(u)) = cl(u)
we say that cl is a closure operator
and cl(u) is said to be the closure
of u.
If u = cl(u) , we say that u is close.
(Topological closure is a special
case.)
For any Galois connection G=(f,g)
between the complete lattices
(P,≤) and (Q,≤), the mapping
cl=f•g is a closure on P and
cl’=g•f is a closure operator on
Q.
The restriction of f to cl-closed
elements is a bijection between
cl-closed elements of P and cl’-
closed elements of Q.
46. 10 May 2002 Roberto Innocente 46
Formal Concept Analysis /1
" Introduced by Rudolf Wille around 1982,
Darmstadt (Germany)
" It is an application of lattice theory
" Re-flourished in the last 6/7 years
" The name refers to the fact that the method
applies mainly to the analysis of data, using a
mathematical abstraction of concept (this is the
reason behind the formal prefix)
47. 10 May 2002 Roberto Innocente 47
Formal Concept Analysis /2
Given a set of Objects O, a
set of Attributes A, and
a binary relation I ⊆ O x
A, we say that :
! (O,A,I) is a formal
context
48. 10 May 2002 Roberto Innocente 48
Formal Concept Analysis /3
Through the binary relation I ⊆
O x A we can define two
functions f and g such that
for each subset U of O :
f(U) = {attributes that apply to
all objects in U}
and conversely for each subset V
of A :
g(V) = {objects for which all
attributes in V apply}
The pair (f,g) is also called the
polarity on O and A
determined by I.
49. 10 May 2002 Roberto Innocente 49
Formal Concept Analysis /4
we have that h is a closure operator
on O and h’ is a closure
operator on A.
The Galois connection establishes a
duality between the two closure
systems on O and A.
It is a bijective map between closed
subsets of O and closed subsets
of A.
It can be easily demonstrated
that the polarity (f, g) of a
relation is a Galois
connection between the
powerset of O and the
powerset of A, ordered by
inclusion.
Furthermore, called :
" h = g•f
" h' = f•g
50. 10 May 2002 Roberto Innocente 50
Formal Concept Analysis /5
A concept is a pair (U,V) that comprise a closed
set of objects U, together with a closed set of
attributes connected by the Galois connection.
U is called the extent (or extension) of the
concept and V is called the intent (or
intension)of the concept.
52. 10 May 2002 Roberto Innocente 52
Formal Concept Analysis /7
Concepts form a lattice : the lattice of concepts.
If (U,V) is a concept, then you can't extend the extension U of
the concept in such a way that all the attributes of V apply,
and conversely, you can't extend the intension V such that
it applies to all objects in U.
In the previous slide the sets of objects having an empty set of
attributes, and the sets of attributes having an empty set of
objects are not displayed. Their situation in the Hasse
diagram is very simple: they are connected only to the
empty set and to the complete set. Their closure is the
complete set of objects/attributes.
53. 10 May 2002 Roberto Innocente 53
A-Close /1
Proposed by Pasquier,Bastide, Taouil, Lakhal in 1999.
It is based on Formal Concept Analysis. Let us think to the
set of items as the the set of objects and the set of
transactions as the set of attributes. Then, an itemset is
closed if there is no superset of it that appears in the same
set of transactions.
Conversely, a set of transaction is closed if it's not contained
in a superset of transactions containing the same items.
54. 10 May 2002 Roberto Innocente 54
A-Close /2
What is important is that the support of an itemset is the same
as that of its closure:
s(A) = s(cl(A))
Therefore, you need to remember only the closed itemsets and
their support, to be able to count the support of any itemset.
Further, if you are interested only in frequent itemsets, then
you need only to remember the support of frequent closed
itemsets.
In fact maximal frequent itemsets are closed.
57. 10 May 2002 Roberto Innocente 57
A-Close /5
From the lattice of closed itemsets it is easy to
count the support of every subset.
For example
s(A)=s(cl(A))=s(AB)=4
and
s(BDE)=s(cl(BDE))=s(BCDE)=3
59. 10 May 2002 Roberto Innocente 59
CHARM
An efficient algorithm for mining closed frequent sets, was
proposed by Zaki and Hsiao in 2001.
" It enumerates closed itemsets using a dual itemset/tidset search tree, and
a hybrid search algorithm
" It uses diffsets to reduce memory requirements
60. 10 May 2002 Roberto Innocente 60
Parallel algorithms
" Count distribution : counts are performed locally and re-distributed
between processors
" Candidate distribution: candidates are generated locally and re-
distributed
" Data distribution: transaction are re-distributed
" Parallel frequent closed prefix-tree : what we are
implementing
62. 10 May 2002 Roberto Innocente 62
Bibliography
" Agrawal R.,Imielinski T.,Swami A. : Association rules between Sets of Items in large
Databases, SIGMOD 1993
" Agrawal R., Srikant R. : Fast Algorithms for mining association rules, VLDB 1994
" Savasere A., Omiecinski E., Navathe S.: An efficient algorithm for mining association
rules in large databases
" Zaki M., Parthasarathy S., Ogihara M. : New algorithms for fast discovery of
association rules, KDDM 1998
" Han J., Pei J., Yin Y. : Mining frequent patterns without candidate generation,
SIGMOD 2000
" Ganter B., Wille R.: Formal Concept Analysis:Mathematical Foundations,Springer
1999
" Pasquier N., Bastide Y., Taouil R., Lakhal L.: Discovering frequent closed itemsets for
association rules, ICDT 1999
" Zaki M., Hsiao C.: CHARM : An Efficient Algorithm for closed Itemset Mining, 2001