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Related Experiment Video

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Strategic Endothelial Cell Tube Formation Assay: Comparing Extracellular Matrix and Growth Factor Reduced Extracellular Matrix

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Fast optimization of non-negative matrix tri-factorization.

Andrej Čopar¹, Blaž Zupan^1,2, Marinka Zitnik^1,3

¹Faculty of Computer and Information Science, University of Ljubljana, Ljubljana, Slovenia.

|June 12, 2019

Summary

This summary is machine-generated.

New optimization methods for Non-negative matrix tri-factorization (NMTF) significantly outperform traditional multiplicative updates. Projected gradients and coordinate descent offer substantial speed improvements for learning low-dimensional representations.

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Area of Science:

Machine Learning
Data Mining
Numerical Analysis

Background:

Non-negative matrix tri-factorization (NMTF) is key for low-dimensional feature learning in relational data.
Current NMTF optimization using multiplicative updates has limitations and poorly understood failure modes.

Purpose of the Study:

To empirically compare NMTF optimization methods on large datasets.
To identify faster and more robust optimization techniques for NMTF.

Main Methods:

Empirical study on six large datasets.
Comparison of multiplicative update rules against alternating least squares, projected gradients, and coordinate descent.

Main Results:

Projected gradients and coordinate descent methods showed up to 24x faster convergence than multiplicative updates.
Alternating least squares performed well on sparse data but struggled with dense datasets.
Coordinate descent NMTF demonstrated up to 16x faster convergence than established methods.

Conclusions:

Projected gradients and coordinate descent are superior optimization strategies for NMTF.
These methods offer significant speed and potential robustness advantages over traditional multiplicative updates.