NCDREC: A Decomposability Inspired Framework for Top-N Recommendation
|
|
- Silvester Mills
- 5 years ago
- Views:
Transcription
1 NCDREC: A Decomposability Inspired Framework for Top-N Recommendation Athanasios N. Nikolakopoulos,2 John D. Garofalakis,2 Computer Engineering and Informatics Department, University of Patras, Greece 2 Computer Technology Institute & Press Diophantus IEEE/WIC/ACM International Conference on Web Intelligence Warsaw, August 24
2 Outline Introduction & Motivation Introduction & Motivation Recommender Systems - Collaborative Filtering Challenges of Modern CF Algorithms 2 NCDREC Model Criterion for ItemSpace Coverage NCDREC Algorithm: Storage and Computational Issues 3 Evaluation Methodology Quality of Recommendations Long-Tail Recommendations Cold-Start Recommendations 4
3 Introduction & Motivation Recommender Systems - Collaborative Filtering Challenges of Modern CF Algorithms Recommender System Algorithms Recommendation USERS ITEMS List RECOMMENDER. SYSTEM Rating Predictions RATINGS... Collaborative Filtering Recommendation Algorithms Wide deployment in Commercial Environments Significant Research Efforts A. N. Nikolakopoulos and J. D. Garofalakis NCDREC
4 Challenges of Modern CF Algorithms Recommender Systems - Collaborative Filtering Challenges of Modern CF Algorithms Sparsity It is an Intrinsic RS Characteristic related to serious problems: Long-Tail Recommendation Cold start Problem Limited ItemSpace Coverage Traditional CF techniques, such as neighborhood models, are very susceptible to sparsity. Among the most promising approaches in alleviating sparsity related problems are: Dimensionality-Reduction Models Build a reduced latent space which is dense. Graph-Based Models. Exploit transitive relations in the data, while preserving some of the locality.
5 Exploiting Decomposability Recommender Systems - Collaborative Filtering Challenges of Modern CF Algorithms We attack the problem from a different perspective: Sparsity Hierarchy Decomposability. Nearly Completely Decomposable Systems Pioneered by Herbert A. Simon. Many Applications in Diverse Disciplines such as economics, cognitive theory and social sciences, to computer systems performance evaluation, data mining and information retrieval Main Idea: Exploit the innate Hierarchy of the Item Set, and view it as a decomposable space. Can this enrich the Collaborative Filtering Paradigm in an Efficient and Scalable Way? Does this approach offer any qualitative advantages in alleviating sparsity related problems?
6 NCDREC Model Overview NCDREC Model Criterion for ItemSpace Coverage NCDREC Algorithm: Storage and Computational Issues Definitions We define a D-decomposition to be an indexed family of sets D {D,..., D K }, that span the ItemSpace V, We define D v v D k D k to be the proximal set of items of v V, We also define the associated block coupling graph G D (V D, E D ); its vertices correspond to the D-blocks, and an edge between two vertices exists whenever the intersection of these blocks is a non-empty set. Finally, we introduce an aggregation matrix A D R m K, whose jk th element is, if v j D k and zero otherwise. NCDREC Components Main Component: Recommendation vectors produced by projecting the NCD perturbed data onto an f -dimensional space. ColdStart Component:Recommendation vectors are the stationary distributions of a Discrete Markov Chain Model. G R + ɛw W ɛzx X diag(a D e) A D [Z] ik (n k u ) [RA D ] ik, when n k i u >, i and zero otherwise. S(ω) ( α)e + α(βh + ( β)d) H diag(ce) C, where [C] ij r i r j for i j D XY, X diag(a D e) A D, Y diag(a D e) A D, E eω
7 Criterion for ItemSpace Coverage NCDREC Model Criterion for ItemSpace Coverage NCDREC Algorithm: Storage and Computational Issues Theorem (ItemSpace Coverage) If the block coupling graph G D is connected, there exists a unique steady state distribution π of the Markov chain corresponding to matrix S that depends on the preference vector ω; however, irrespectively of any particular such vector, the support of this distribution includes every item of the underlying space. Proof Sketch: When G D is connected, the Markov chain induced by the stochastic matrix S consists of a single irreducible and aperiodic closed set of states, that includes all the items. The above is true for every stochastic vector ω, and for every positive real numbers α, β <. Taking into account the fact that the state space is finite, the resulting Markov chain becomes ergodic. So π i >, for all i, and the support of the distribution that defines the recommendation vector includes every item of the underlying space.
8 NCDREC Model Criterion for ItemSpace Coverage NCDREC Algorithm: Storage and Computational Issues NCDREC Algorithm: Storage and Computational Issues Input: Matrices R R n m, H R m m, X R m K, Y R K m, Z R n K. Parameters α, β, f, ɛ Output: The matrix with recommendation vectors for every user, Π R n m Step : Find the newly added users and collect their preference vectors into matrix Ω. Step 2: Compute Π sparse using the ColdStart Procedure. Step 3: Initialize vector p to be a random unit length vector. Step 4: Compute the modified Lanczos procedure up to step M, using NCD PartialLBD with starting vector p. Step 5: Compute the SVD of the bidiagonal matrix B and use it to extract f < M approximate singular triplets: {ũ j, σ j, ṽ j } {Qu (B) j, σ (B) j, Pv (B) j } Step 6: Orthogonalize against the approximate singular vectors to get a new starting vector p. Step 7: Continue the Lanczos procedure for M more steps using the new starting vector. Step 8: Check for convergence tolerance. If met compute matrix: Π full = ŨΣṼ else go to Step 4 Step 9: Update Π full, replacing the rows that correspond to new users with Π sparse. Return Π full
9 Evaluation Methodology Quality of Recommendations Long-Tail Recommendations Cold-Start Recommendations Datasets Yahoo!R2Music MovieLens Competing Methods Commute Time (CT) Pseudo-Inverse of the user-item graph Laplacian (L ) Matrix Forest Algorithm (MFA) First Passage Time (FP) Katz Algorithm (Katz) Metrics Recall Precision R-Score Normalized Discounted Cumulative Gain (NDCG@k) Mean Reciprocal Rank
10 Full Dist. Recommendations Methodology Randomly sample.4% of the ratings of the dataset probe set P Use each item v j, rated with 5 stars by user u i in P test set T Randomly select another unrated items of the same user for each item in T Form ranked lists by ordering all the items Evaluation Methodology Quality of Recommendations Long-Tail Recommendations Cold-Start Recommendations TABLE I RECOMMENDATION QUALITY ON MOVIELENSM AND YAHOO!R2MUSIC DATASETS USING R-SCORE AND MRR METRICS MovieLensM Yahoo!R2Music R(5) R() MRR R(5) R() MRR NCDREC MFA L FP Katz CT Recall@N Precision/Recall NDCG@N MovieLensM Yahoo!R2Music NCDREC Katz FP MFA L CT
11 Long-Tail Recommendations Methodology (Long Tail) We order the items according to their popularity (measured in terms of number of ratings) We further partition the test set T into two subsets, T head and T tail We discard the popular items and we evaluate NCDREC and the other algorithms on the T tail test set. Evaluation Methodology Quality of Recommendations Long-Tail Recommendations Cold-Start Recommendations TABLE II LONG TAIL RECOMMENDATION QUALITY ON MOVIELENSM AND YAHOO!R2MUSIC DATASETS USING R-SCORE AND MRR METRICS MovieLensM Yahoo!R2Music R(5) R() MRR R(5) R() MRR NCDREC MFA L FP Katz CT Recall@N Precision/Recall NDCG@N MovieLensM Yahoo!R2Music NCDREC Katz FP MFA L CT
12 New Users problem Introduction & Motivation Evaluation Methodology Quality of Recommendations Long-Tail Recommendations Cold-Start Recommendations Methodology Randomly select users having rated at least items and delete 96%, 94%, 92% and 9% of each users ratings. Compare the rankings induced on the modified data with the complete set of ratings. Metrics Spearman s ρ Kendall s τ Degree of Agreement (DOA) Normalized Distance-based Performance Measure (NDPM) Spearman s ρ Kendall s τ % 6% 8% % Percentage of included ratings Degree Of Agreement % 6% 8% % Percentage of included ratings NDPM (the smaller the better) % 6% 8% % 4% 6% 8% % Percentage of included ratings Percentage of included ratings NCDREC Katz FP MFA L CT
13 Future Research Directions & Conclusion Future Work Decomposition Granularity Effect Coarse Grained Sparseness Insensitivity Fine Grained Higher Quality of Recommendations Multiple-Criteria Decompositions How it affects the theoretical properties of the ColdStart Component?
14 Thanks! Q&A
15 /3 /2 /2 /4 /4 /4 /4 /2 /5 /5 /2 /2 Example NCD Proximity Matrix NCDREC Basic SubComponents Example NCD Proximity Matrix Back D D 2 D 3 N v G v v {v, v 2, v 4} v 2 2 {v, v 2, v 4, v 5, v 6, v 7, v 8} v 3 {v 3, v 4, v 5, v 8} v 4 2 {v, v 2, v 3, v 4, v 5, v 8} v 5 2 {v 2, v 3, v 4, v 5, v 6, v 7, v 8} v 6 {v 2, v 5, v 6, v 7, v 8} v 7 {v 2, v 5, v 6, v 7, v 8} v 8 2 {v 2, v 3, v 4, v 5, v 6, v 7, v 8} /2 /2 /2 v v2 v3 v4 v5 v6 v7 v8 D D2 D3 /3 /3 /5 /5 /5 v v2 v3 v4 v5 v6 v7 v8 = D =
16 Example NCD Proximity Matrix NCDREC Basic SubComponents NCD PartialLBD Procedure ColdStart Procedure NCD PartialLBD Back procedure NCD PartialLBD(R, X, Z, p, ɛ) φ X p ; q Rp + ɛzφ; b, q 2 ; u q /b, ; for j = to M do φ Z q j ; r R q j + ɛxφ b j,j p j ; r r [p... p j ] ([p... p j ] r); if j < M then b j,j+ r ; p j+ r/b j,j+ ; φ X p j+ ; q j+ Rp j+ + ɛzφ b j,j+ q j ; q j+ q j+ [q... q j ] ([q... q j ] q j+ ); b j+,j+ q j+ ; q j+ q j+ /b j+,j+ ; end if end for end procedure
17 Example NCD Proximity Matrix NCDREC Basic SubComponents NCD PartialLBD Procedure ColdStart Procedure ColdStart Procedure Back procedure ColdStart(H, X, Y, Ω, α, β) Π Ω; k ; r ; while r > tol and k maxit do k k + ; ˆΠ αβπh; Φ ΠX; ˆΠ ˆΠ + α( β)φy + ( α)ω; r ˆΠ Π ; Π ˆΠ; end while return Π sparse Π end procedure
Random Surfing on Multipartite Graphs
Random Surfing on Multipartite Graphs Athanasios N. Nikolakopoulos, Antonia Korba and John D. Garofalakis Department of Computer Engineering and Informatics, University of Patras December 07, 2016 IEEE
More informationTop-N recommendations in the presence of sparsity: An NCD-based approach
Top-N recommendations in the presence of sparsity: An NCD-based approach arxiv:7.43v2 [cs.ir] 7 Jul 2 Athanasios N. Nikolakopoulos a,b, and John D. Garofalakis a,b, a Department of Computer Engineering
More informationEigenRec: Generalizing PureSVD for Effective and Efficient Top-N Recommendations
KAIS manuscript No. (will be inserted by the editor) EigenRec: Generalizing PureSVD for Effective and Efficient Top-N Recommendations Athanasios N. Nikolakopoulos Vassilis Kalantzis Efstratios Gallopoulos
More informationFactored Proximity Models for Top-N Recommendations
Factored Proximity Models for Top- Recommendations Athanasios. ikolakopoulos 1,3, Vassilis Kalantzis 2, Efstratios Gallopoulos 1 and John D. Garofalakis 1 Department of Computer Engineering and Informatics
More informationDecoupled Collaborative Ranking
Decoupled Collaborative Ranking Jun Hu, Ping Li April 24, 2017 Jun Hu, Ping Li WWW2017 April 24, 2017 1 / 36 Recommender Systems Recommendation system is an information filtering technique, which provides
More informationScaling Neighbourhood Methods
Quick Recap Scaling Neighbourhood Methods Collaborative Filtering m = #items n = #users Complexity : m * m * n Comparative Scale of Signals ~50 M users ~25 M items Explicit Ratings ~ O(1M) (1 per billion)
More informationRecurrent Latent Variable Networks for Session-Based Recommendation
Recurrent Latent Variable Networks for Session-Based Recommendation Panayiotis Christodoulou Cyprus University of Technology paa.christodoulou@edu.cut.ac.cy 27/8/2017 Panayiotis Christodoulou (C.U.T.)
More informationRecommendation Systems
Recommendation Systems Pawan Goyal CSE, IITKGP October 21, 2014 Pawan Goyal (IIT Kharagpur) Recommendation Systems October 21, 2014 1 / 52 Recommendation System? Pawan Goyal (IIT Kharagpur) Recommendation
More informationCollaborative Recommendation with Multiclass Preference Context
Collaborative Recommendation with Multiclass Preference Context Weike Pan and Zhong Ming {panweike,mingz}@szu.edu.cn College of Computer Science and Software Engineering Shenzhen University Pan and Ming
More informationLink Analysis Ranking
Link Analysis Ranking How do search engines decide how to rank your query results? Guess why Google ranks the query results the way it does How would you do it? Naïve ranking of query results Given query
More informationAn Extended Frank-Wolfe Method, with Application to Low-Rank Matrix Completion
An Extended Frank-Wolfe Method, with Application to Low-Rank Matrix Completion Robert M. Freund, MIT joint with Paul Grigas (UC Berkeley) and Rahul Mazumder (MIT) CDC, December 2016 1 Outline of Topics
More informationUpdating PageRank. Amy Langville Carl Meyer
Updating PageRank Amy Langville Carl Meyer Department of Mathematics North Carolina State University Raleigh, NC SCCM 11/17/2003 Indexing Google Must index key terms on each page Robots crawl the web software
More informationRecommendation Systems
Recommendation Systems Popularity Recommendation Systems Predicting user responses to options Offering news articles based on users interests Offering suggestions on what the user might like to buy/consume
More informationDATA MINING LECTURE 8. Dimensionality Reduction PCA -- SVD
DATA MINING LECTURE 8 Dimensionality Reduction PCA -- SVD The curse of dimensionality Real data usually have thousands, or millions of dimensions E.g., web documents, where the dimensionality is the vocabulary
More informationUpdating Markov Chains Carl Meyer Amy Langville
Updating Markov Chains Carl Meyer Amy Langville Department of Mathematics North Carolina State University Raleigh, NC A. A. Markov Anniversary Meeting June 13, 2006 Intro Assumptions Very large irreducible
More informationa Short Introduction
Collaborative Filtering in Recommender Systems: a Short Introduction Norm Matloff Dept. of Computer Science University of California, Davis matloff@cs.ucdavis.edu December 3, 2016 Abstract There is a strong
More informationRecommendation Systems
Recommendation Systems Pawan Goyal CSE, IITKGP October 29-30, 2015 Pawan Goyal (IIT Kharagpur) Recommendation Systems October 29-30, 2015 1 / 61 Recommendation System? Pawan Goyal (IIT Kharagpur) Recommendation
More informationMarkov Chains and Spectral Clustering
Markov Chains and Spectral Clustering Ning Liu 1,2 and William J. Stewart 1,3 1 Department of Computer Science North Carolina State University, Raleigh, NC 27695-8206, USA. 2 nliu@ncsu.edu, 3 billy@ncsu.edu
More informationScalable Hierarchical Recommendations Using Spatial Autocorrelation
Scalable Hierarchical Recommendations Using Spatial Autocorrelation Ayushi Dalmia, Joydeep Das, Prosenjit Gupta, Subhashis Majumder, Debarshi Dutta Ayushi Dalmia, JoydeepScalable Das, Prosenjit Hierarchical
More informationRandom Surfing on Multipartite Graphs
Random Surfing on Multipartite Graphs Athanasios N. Nikolakopoulos, Antonia Korba and John D. Garofalakis Department of Computer Engineering and Informatics, University of Patras {nikolako,korba,garofala}@ceid.upatras.gr
More informationsublinear time low-rank approximation of positive semidefinite matrices Cameron Musco (MIT) and David P. Woodru (CMU)
sublinear time low-rank approximation of positive semidefinite matrices Cameron Musco (MIT) and David P. Woodru (CMU) 0 overview Our Contributions: 1 overview Our Contributions: A near optimal low-rank
More informationDiscrete quantum random walks
Quantum Information and Computation: Report Edin Husić edin.husic@ens-lyon.fr Discrete quantum random walks Abstract In this report, we present the ideas behind the notion of quantum random walks. We further
More informationCollaborative topic models: motivations cont
Collaborative topic models: motivations cont Two topics: machine learning social network analysis Two people: " boy Two articles: article A! girl article B Preferences: The boy likes A and B --- no problem.
More informationPV211: Introduction to Information Retrieval https://www.fi.muni.cz/~sojka/pv211
PV211: Introduction to Information Retrieval https://www.fi.muni.cz/~sojka/pv211 IIR 18: Latent Semantic Indexing Handout version Petr Sojka, Hinrich Schütze et al. Faculty of Informatics, Masaryk University,
More informationA Gradient-based Adaptive Learning Framework for Efficient Personal Recommendation
A Gradient-based Adaptive Learning Framework for Efficient Personal Recommendation Yue Ning 1 Yue Shi 2 Liangjie Hong 2 Huzefa Rangwala 3 Naren Ramakrishnan 1 1 Virginia Tech 2 Yahoo Research. Yue Shi
More informationCollaborative Filtering. Radek Pelánek
Collaborative Filtering Radek Pelánek 2017 Notes on Lecture the most technical lecture of the course includes some scary looking math, but typically with intuitive interpretation use of standard machine
More informationIntroduction to Search Engine Technology Introduction to Link Structure Analysis. Ronny Lempel Yahoo Labs, Haifa
Introduction to Search Engine Technology Introduction to Link Structure Analysis Ronny Lempel Yahoo Labs, Haifa Outline Anchor-text indexing Mathematical Background Motivation for link structure analysis
More informationELE 538B: Mathematics of High-Dimensional Data. Spectral methods. Yuxin Chen Princeton University, Fall 2018
ELE 538B: Mathematics of High-Dimensional Data Spectral methods Yuxin Chen Princeton University, Fall 2018 Outline A motivating application: graph clustering Distance and angles between two subspaces Eigen-space
More informationImpact of Data Characteristics on Recommender Systems Performance
Impact of Data Characteristics on Recommender Systems Performance Gediminas Adomavicius YoungOk Kwon Jingjing Zhang Department of Information and Decision Sciences Carlson School of Management, University
More informationProbabilistic Neighborhood Selection in Collaborative Filtering Systems
Probabilistic Neighborhood Selection in Collaborative Filtering Systems Panagiotis Adamopoulos and Alexander Tuzhilin Department of Information, Operations and Management Sciences Leonard N. Stern School
More informationIntroduction to Information Retrieval
Introduction to Information Retrieval http://informationretrieval.org IIR 18: Latent Semantic Indexing Hinrich Schütze Center for Information and Language Processing, University of Munich 2013-07-10 1/43
More informationPseudocode for calculating Eigenfactor TM Score and Article Influence TM Score using data from Thomson-Reuters Journal Citations Reports
Pseudocode for calculating Eigenfactor TM Score and Article Influence TM Score using data from Thomson-Reuters Journal Citations Reports Jevin West and Carl T. Bergstrom November 25, 2008 1 Overview There
More informationEECS 275 Matrix Computation
EECS 275 Matrix Computation Ming-Hsuan Yang Electrical Engineering and Computer Science University of California at Merced Merced, CA 95344 http://faculty.ucmerced.edu/mhyang Lecture 22 1 / 21 Overview
More informationCollaborative Topic Modeling for Recommending Scientific Articles
Collaborative Topic Modeling for Recommending Scientific Articles Chong Wang and David M. Blei Best student paper award at KDD 2011 Computer Science Department, Princeton University Presented by Tian Cao
More informationUsing SVD to Recommend Movies
Michael Percy University of California, Santa Cruz Last update: December 12, 2009 Last update: December 12, 2009 1 / Outline 1 Introduction 2 Singular Value Decomposition 3 Experiments 4 Conclusion Last
More informationAM205: Assignment 2. i=1
AM05: Assignment Question 1 [10 points] (a) [4 points] For p 1, the p-norm for a vector x R n is defined as: ( n ) 1/p x p x i p ( ) i=1 This definition is in fact meaningful for p < 1 as well, although
More informationRecommender Systems. Dipanjan Das Language Technologies Institute Carnegie Mellon University. 20 November, 2007
Recommender Systems Dipanjan Das Language Technologies Institute Carnegie Mellon University 20 November, 2007 Today s Outline What are Recommender Systems? Two approaches Content Based Methods Collaborative
More informationMarkov Chains CK eqns Classes Hitting times Rec./trans. Strong Markov Stat. distr. Reversibility * Markov Chains
Markov Chains A random process X is a family {X t : t T } of random variables indexed by some set T. When T = {0, 1, 2,... } one speaks about a discrete-time process, for T = R or T = [0, ) one has a continuous-time
More informationLarge-Scale Social Network Data Mining with Multi-View Information. Hao Wang
Large-Scale Social Network Data Mining with Multi-View Information Hao Wang Dept. of Computer Science and Engineering Shanghai Jiao Tong University Supervisor: Wu-Jun Li 2013.6.19 Hao Wang Multi-View Social
More informationFunctional Analysis Review
Outline 9.520: Statistical Learning Theory and Applications February 8, 2010 Outline 1 2 3 4 Vector Space Outline A vector space is a set V with binary operations +: V V V and : R V V such that for all
More informationAMS526: Numerical Analysis I (Numerical Linear Algebra)
AMS526: Numerical Analysis I (Numerical Linear Algebra) Lecture 5: Projectors and QR Factorization Xiangmin Jiao SUNY Stony Brook Xiangmin Jiao Numerical Analysis I 1 / 14 Outline 1 Projectors 2 QR Factorization
More informationDATA MINING LECTURE 13. Link Analysis Ranking PageRank -- Random walks HITS
DATA MINING LECTURE 3 Link Analysis Ranking PageRank -- Random walks HITS How to organize the web First try: Manually curated Web Directories How to organize the web Second try: Web Search Information
More informationCS60021: Scalable Data Mining. Dimensionality Reduction
J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, http://www.mmds.org 1 CS60021: Scalable Data Mining Dimensionality Reduction Sourangshu Bhattacharya Assumption: Data lies on or near a
More informationKnowledge Discovery and Data Mining 1 (VO) ( )
Knowledge Discovery and Data Mining 1 (VO) (707.003) Sample Examination Questions Denis Helic KTI, TU Graz Jan 16, 2014 Denis Helic (KTI, TU Graz) KDDM1 Jan 16, 2014 1 / 22 Exercise Suppose we have a utility
More informationA hybrid reordered Arnoldi method to accelerate PageRank computations
A hybrid reordered Arnoldi method to accelerate PageRank computations Danielle Parker Final Presentation Background Modeling the Web The Web The Graph (A) Ranks of Web pages v = v 1... Dominant Eigenvector
More informationEECS 275 Matrix Computation
EECS 275 Matrix Computation Ming-Hsuan Yang Electrical Engineering and Computer Science University of California at Merced Merced, CA 95344 http://faculty.ucmerced.edu/mhyang Lecture 6 1 / 22 Overview
More informationPreprocessing & dimensionality reduction
Introduction to Data Mining Preprocessing & dimensionality reduction CPSC/AMTH 445a/545a Guy Wolf guy.wolf@yale.edu Yale University Fall 2016 CPSC 445 (Guy Wolf) Dimensionality reduction Yale - Fall 2016
More informationJun Zhang Department of Computer Science University of Kentucky
Application i of Wavelets in Privacy-preserving Data Mining Jun Zhang Department of Computer Science University of Kentucky Outline Privacy-preserving in Collaborative Data Analysis Advantages of Wavelets
More informationRecommender systems, matrix factorization, variable selection and social graph data
Recommender systems, matrix factorization, variable selection and social graph data Julien Delporte & Stéphane Canu stephane.canu@litislab.eu StatLearn, april 205, Grenoble Road map Model selection for
More informationLink Analysis. Leonid E. Zhukov
Link Analysis Leonid E. Zhukov School of Data Analysis and Artificial Intelligence Department of Computer Science National Research University Higher School of Economics Structural Analysis and Visualization
More informationLecture 11: Introduction to Markov Chains. Copyright G. Caire (Sample Lectures) 321
Lecture 11: Introduction to Markov Chains Copyright G. Caire (Sample Lectures) 321 Discrete-time random processes A sequence of RVs indexed by a variable n 2 {0, 1, 2,...} forms a discretetime random process
More informationMatrix Factorization Techniques for Recommender Systems
Matrix Factorization Techniques for Recommender Systems By Yehuda Koren Robert Bell Chris Volinsky Presented by Peng Xu Supervised by Prof. Michel Desmarais 1 Contents 1. Introduction 4. A Basic Matrix
More informationVariable Latent Semantic Indexing
Variable Latent Semantic Indexing Prabhakar Raghavan Yahoo! Research Sunnyvale, CA November 2005 Joint work with A. Dasgupta, R. Kumar, A. Tomkins. Yahoo! Research. Outline 1 Introduction 2 Background
More informationSTA141C: Big Data & High Performance Statistical Computing
STA141C: Big Data & High Performance Statistical Computing Lecture 6: Numerical Linear Algebra: Applications in Machine Learning Cho-Jui Hsieh UC Davis April 27, 2017 Principal Component Analysis Principal
More informationErgodic Theorems. Samy Tindel. Purdue University. Probability Theory 2 - MA 539. Taken from Probability: Theory and examples by R.
Ergodic Theorems Samy Tindel Purdue University Probability Theory 2 - MA 539 Taken from Probability: Theory and examples by R. Durrett Samy T. Ergodic theorems Probability Theory 1 / 92 Outline 1 Definitions
More informationNatural Language Processing. Topics in Information Retrieval. Updated 5/10
Natural Language Processing Topics in Information Retrieval Updated 5/10 Outline Introduction to IR Design features of IR systems Evaluation measures The vector space model Latent semantic indexing Background
More informationMET Workshop: Exercises
MET Workshop: Exercises Alex Blumenthal and Anthony Quas May 7, 206 Notation. R d is endowed with the standard inner product (, ) and Euclidean norm. M d d (R) denotes the space of n n real matrices. When
More informationCS 277: Data Mining. Mining Web Link Structure. CS 277: Data Mining Lectures Analyzing Web Link Structure Padhraic Smyth, UC Irvine
CS 277: Data Mining Mining Web Link Structure Class Presentations In-class, Tuesday and Thursday next week 2-person teams: 6 minutes, up to 6 slides, 3 minutes/slides each person 1-person teams 4 minutes,
More informationClustering based tensor decomposition
Clustering based tensor decomposition Huan He huan.he@emory.edu Shihua Wang shihua.wang@emory.edu Emory University November 29, 2017 (Huan)(Shihua) (Emory University) Clustering based tensor decomposition
More informationRanking-Oriented Evaluation Metrics
Ranking-Oriented Evaluation Metrics Weike Pan College of Computer Science and Software Engineering Shenzhen University W.K. Pan (CSSE, SZU) Ranking-Oriented Evaluation Metrics 1 / 21 Outline 1 Introduction
More informationSQL-Rank: A Listwise Approach to Collaborative Ranking
SQL-Rank: A Listwise Approach to Collaborative Ranking Liwei Wu Depts of Statistics and Computer Science UC Davis ICML 18, Stockholm, Sweden July 10-15, 2017 Joint work with Cho-Jui Hsieh and James Sharpnack
More informationBlock Lanczos Tridiagonalization of Complex Symmetric Matrices
Block Lanczos Tridiagonalization of Complex Symmetric Matrices Sanzheng Qiao, Guohong Liu, Wei Xu Department of Computing and Software, McMaster University, Hamilton, Ontario L8S 4L7 ABSTRACT The classic
More informationSection Notes 9. Midterm 2 Review. Applied Math / Engineering Sciences 121. Week of December 3, 2018
Section Notes 9 Midterm 2 Review Applied Math / Engineering Sciences 121 Week of December 3, 2018 The following list of topics is an overview of the material that was covered in the lectures and sections
More informationRobust Principal Component Pursuit via Alternating Minimization Scheme on Matrix Manifolds
Robust Principal Component Pursuit via Alternating Minimization Scheme on Matrix Manifolds Tao Wu Institute for Mathematics and Scientific Computing Karl-Franzens-University of Graz joint work with Prof.
More informationLecture: Local Spectral Methods (1 of 4)
Stat260/CS294: Spectral Graph Methods Lecture 18-03/31/2015 Lecture: Local Spectral Methods (1 of 4) Lecturer: Michael Mahoney Scribe: Michael Mahoney Warning: these notes are still very rough. They provide
More informationPredicting Neighbor Goodness in Collaborative Filtering
Predicting Neighbor Goodness in Collaborative Filtering Alejandro Bellogín and Pablo Castells {alejandro.bellogin, pablo.castells}@uam.es Universidad Autónoma de Madrid Escuela Politécnica Superior Introduction:
More informationLatent Semantic Indexing (LSI) CE-324: Modern Information Retrieval Sharif University of Technology
Latent Semantic Indexing (LSI) CE-324: Modern Information Retrieval Sharif University of Technology M. Soleymani Fall 2014 Most slides have been adapted from: Profs. Manning, Nayak & Raghavan (CS-276,
More informationMaximum Margin Matrix Factorization for Collaborative Ranking
Maximum Margin Matrix Factorization for Collaborative Ranking Joint work with Quoc Le, Alexandros Karatzoglou and Markus Weimer Alexander J. Smola sml.nicta.com.au Statistical Machine Learning Program
More informationhttps://goo.gl/kfxweg KYOTO UNIVERSITY Statistical Machine Learning Theory Sparsity Hisashi Kashima kashima@i.kyoto-u.ac.jp DEPARTMENT OF INTELLIGENCE SCIENCE AND TECHNOLOGY 1 KYOTO UNIVERSITY Topics:
More informationGeneric Text Summarization
June 27, 2012 Outline Introduction 1 Introduction Notation and Terminology 2 3 4 5 6 Text Summarization Introduction Notation and Terminology Two Types of Text Summarization Query-Relevant Summarization:
More informationApplications of Randomized Methods for Decomposing and Simulating from Large Covariance Matrices
Applications of Randomized Methods for Decomposing and Simulating from Large Covariance Matrices Vahid Dehdari and Clayton V. Deutsch Geostatistical modeling involves many variables and many locations.
More informationCS425: Algorithms for Web Scale Data
CS: Algorithms for Web Scale Data Most of the slides are from the Mining of Massive Datasets book. These slides have been modified for CS. The original slides can be accessed at: www.mmds.org Customer
More informationMatrix Factorization In Recommender Systems. Yong Zheng, PhDc Center for Web Intelligence, DePaul University, USA March 4, 2015
Matrix Factorization In Recommender Systems Yong Zheng, PhDc Center for Web Intelligence, DePaul University, USA March 4, 2015 Table of Contents Background: Recommender Systems (RS) Evolution of Matrix
More informationFinding normalized and modularity cuts by spectral clustering. Ljubjana 2010, October
Finding normalized and modularity cuts by spectral clustering Marianna Bolla Institute of Mathematics Budapest University of Technology and Economics marib@math.bme.hu Ljubjana 2010, October Outline Find
More informationCS 143 Linear Algebra Review
CS 143 Linear Algebra Review Stefan Roth September 29, 2003 Introductory Remarks This review does not aim at mathematical rigor very much, but instead at ease of understanding and conciseness. Please see
More information= P{X 0. = i} (1) If the MC has stationary transition probabilities then, = i} = P{X n+1
Properties of Markov Chains and Evaluation of Steady State Transition Matrix P ss V. Krishnan - 3/9/2 Property 1 Let X be a Markov Chain (MC) where X {X n : n, 1, }. The state space is E {i, j, k, }. The
More informationUsing Markov Chains To Model Human Migration in a Network Equilibrium Framework
Using Markov Chains To Model Human Migration in a Network Equilibrium Framework Jie Pan Department of Mathematics and Computer Science Saint Joseph s University Philadelphia, PA 19131 Anna Nagurney School
More informationHow does Google rank webpages?
Linear Algebra Spring 016 How does Google rank webpages? Dept. of Internet and Multimedia Eng. Konkuk University leehw@konkuk.ac.kr 1 Background on search engines Outline HITS algorithm (Jon Kleinberg)
More informationA Modified PMF Model Incorporating Implicit Item Associations
A Modified PMF Model Incorporating Implicit Item Associations Qiang Liu Institute of Artificial Intelligence College of Computer Science Zhejiang University Hangzhou 31007, China Email: 01dtd@gmail.com
More informationUpdatingtheStationary VectorofaMarkovChain. Amy Langville Carl Meyer
UpdatingtheStationary VectorofaMarkovChain Amy Langville Carl Meyer Department of Mathematics North Carolina State University Raleigh, NC NSMC 9/4/2003 Outline Updating and Pagerank Aggregation Partitioning
More informationSVD, PCA & Preprocessing
Chapter 1 SVD, PCA & Preprocessing Part 2: Pre-processing and selecting the rank Pre-processing Skillicorn chapter 3.1 2 Why pre-process? Consider matrix of weather data Monthly temperatures in degrees
More informationDimension Reduction and Iterative Consensus Clustering
Dimension Reduction and Iterative Consensus Clustering Southeastern Clustering and Ranking Workshop August 24, 2009 Dimension Reduction and Iterative 1 Document Clustering Geometry of the SVD Centered
More informationDimensionality Reduction
394 Chapter 11 Dimensionality Reduction There are many sources of data that can be viewed as a large matrix. We saw in Chapter 5 how the Web can be represented as a transition matrix. In Chapter 9, the
More informationLatent Semantic Indexing (LSI) CE-324: Modern Information Retrieval Sharif University of Technology
Latent Semantic Indexing (LSI) CE-324: Modern Information Retrieval Sharif University of Technology M. Soleymani Fall 2016 Most slides have been adapted from: Profs. Manning, Nayak & Raghavan (CS-276,
More informationStochastic optimization Markov Chain Monte Carlo
Stochastic optimization Markov Chain Monte Carlo Ethan Fetaya Weizmann Institute of Science 1 Motivation Markov chains Stationary distribution Mixing time 2 Algorithms Metropolis-Hastings Simulated Annealing
More informationECE 8201: Low-dimensional Signal Models for High-dimensional Data Analysis
ECE 8201: Low-dimensional Signal Models for High-dimensional Data Analysis Lecture 7: Matrix completion Yuejie Chi The Ohio State University Page 1 Reference Guaranteed Minimum-Rank Solutions of Linear
More informationMedical Question Answering for Clinical Decision Support
Medical Question Answering for Clinical Decision Support Travis R. Goodwin and Sanda M. Harabagiu The University of Texas at Dallas Human Language Technology Research Institute http://www.hlt.utdallas.edu
More informationBinary Principal Component Analysis in the Netflix Collaborative Filtering Task
Binary Principal Component Analysis in the Netflix Collaborative Filtering Task László Kozma, Alexander Ilin, Tapani Raiko first.last@tkk.fi Helsinki University of Technology Adaptive Informatics Research
More informationPage rank computation HPC course project a.y
Page rank computation HPC course project a.y. 2015-16 Compute efficient and scalable Pagerank MPI, Multithreading, SSE 1 PageRank PageRank is a link analysis algorithm, named after Brin & Page [1], and
More information1 Complex Networks - A Brief Overview
Power-law Degree Distributions 1 Complex Networks - A Brief Overview Complex networks occur in many social, technological and scientific settings. Examples of complex networks include World Wide Web, Internet,
More informationMatrix Factorization Techniques For Recommender Systems. Collaborative Filtering
Matrix Factorization Techniques For Recommender Systems Collaborative Filtering Markus Freitag, Jan-Felix Schwarz 28 April 2011 Agenda 2 1. Paper Backgrounds 2. Latent Factor Models 3. Overfitting & Regularization
More informationStatistical ranking problems and Hodge decompositions of graphs and skew-symmetric matrices
Statistical ranking problems and Hodge decompositions of graphs and skew-symmetric matrices Lek-Heng Lim and Yuan Yao 2008 Workshop on Algorithms for Modern Massive Data Sets June 28, 2008 (Contains joint
More information6.207/14.15: Networks Lectures 4, 5 & 6: Linear Dynamics, Markov Chains, Centralities
6.207/14.15: Networks Lectures 4, 5 & 6: Linear Dynamics, Markov Chains, Centralities 1 Outline Outline Dynamical systems. Linear and Non-linear. Convergence. Linear algebra and Lyapunov functions. Markov
More informationCS 3750 Advanced Machine Learning. Applications of SVD and PCA (LSA and Link analysis) Cem Akkaya
CS 375 Advanced Machine Learning Applications of SVD and PCA (LSA and Link analysis) Cem Akkaya Outline SVD and LSI Kleinberg s Algorithm PageRank Algorithm Vector Space Model Vector space model represents
More informationData Mining and Matrices
Data Mining and Matrices 10 Graphs II Rainer Gemulla, Pauli Miettinen Jul 4, 2013 Link analysis The web as a directed graph Set of web pages with associated textual content Hyperlinks between webpages
More informationSummary: A Random Walks View of Spectral Segmentation, by Marina Meila (University of Washington) and Jianbo Shi (Carnegie Mellon University)
Summary: A Random Walks View of Spectral Segmentation, by Marina Meila (University of Washington) and Jianbo Shi (Carnegie Mellon University) The authors explain how the NCut algorithm for graph bisection
More information8.1 Concentration inequality for Gaussian random matrix (cont d)
MGMT 69: Topics in High-dimensional Data Analysis Falll 26 Lecture 8: Spectral clustering and Laplacian matrices Lecturer: Jiaming Xu Scribe: Hyun-Ju Oh and Taotao He, October 4, 26 Outline Concentration
More informationAn Introduction to Algebraic Multigrid (AMG) Algorithms Derrick Cerwinsky and Craig C. Douglas 1/84
An Introduction to Algebraic Multigrid (AMG) Algorithms Derrick Cerwinsky and Craig C. Douglas 1/84 Introduction Almost all numerical methods for solving PDEs will at some point be reduced to solving A
More informationOnline Social Networks and Media. Link Analysis and Web Search
Online Social Networks and Media Link Analysis and Web Search How to Organize the Web First try: Human curated Web directories Yahoo, DMOZ, LookSmart How to organize the web Second try: Web Search Information
More informationFrancois Fouss, Alain Pirotte, Jean-Michel Renders & Marco Saerens. January 31, 2006
A novel way of computing dissimilarities between nodes of a graph, with application to collaborative filtering and subspace projection of the graph nodes Francois Fouss, Alain Pirotte, Jean-Michel Renders
More information