Smoothing Tensor Factorization on Spatio-Temporal Data Pubblico

Abstract

As spatio-temporal data violates many assumptions required in traditional machine learning/ data mining algorithms, tensor factorization (TF) has often been adopted in analyzing such data. Yet, the non-smooth factors that TF outputs sometimes misrepresent the underlying structure of the data and hinder the interpretability without domain knowledge. With the goal of smoothing the factors, we proposed three approaches: i) adopting Tikhnov regularization to CP_OPT; ii) adopt CP_OPT_SMOOTH in ParCube; iii) ParCube with neighbor padding. In order to examine the performance of these algorithms, we performed numerical experiments on the New York Uber Pickups dataset provided by FROSTT. Our results show that i) CP_OPT_SMOOTH improves the smoothness and the runtime with certain cost of accuracy; ii) with CP_OPT_SMOOTH, CP_OPT can now be adopted in ParCube but with some sacrifice in accuracy; iii) neighbor padding improves the smoothness while maintaining high accuracy. 

Table of Contents

1 Introduction 1

1.1 Contributions ............................... 4

2 Background 6

2.1 Notation .................................. 6

2.2 Tensor and Common Operators .................... 7

2.3 Matrix & Tensor Factorization...................... 9

2.3.1 CP_ALS............................... 11

2.3.2 CP_NMU.............................. 12

2.3.3 CP_OPT .............................. 14

2.4 Parallelizable Tensor Factorization (ParCube) . . . . . . . . . . . . 15

2.5 Smoothing................................. 17

3 Approach 19

3.1 CP_OPT_SMOOTH ............................ 20

3.2 ParCube with CP_OPT_SMOOTH ................... 22

3.3 ParCube_Neighbor ............................ 22

4 Experiments 25

4.1 Data Description and Preprocessing.................. 25

4.2 Evaluation Metrics ............................ 26

4.3 Results ................................... 28

4.3.1 Smoothing on CP_OPT...................... 28

4.3.2 ParCube with CP_OPT_SMOOTH ............... 36

4.3.3 ParCube_Neighbor........................ 40

5 Conclusion 43

5.1 CurrentWork ............................... 43

5.2 FutureDirections............................. 45

Appendix A - ParCube Algorithms 46

Appendix B - Complete Result of CP_OPT_SMOOTH 49 

About this Honors Thesis

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School	Emory College
Department	Mathematics
Degree	B.S.
Submission	Honors Thesis
Language	English
Research Field	Computer Science Mathematics
Parola chiave	tensor factorization parallel computing spatio-temporal data smoothing
Committee Chair / Thesis Advisor	Joyce Ho, Emory University
Committee Members	Shomu Banerjee, Emory University Lars Ruthotto, Emory University

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