Online Matrix Factorization via Broyden Updates
\"Omer Deniz Aky{\i}ld{\i}z

TL;DR
This paper introduces an online matrix factorization algorithm that updates the factorization incrementally with each new data point, handling missing data and large datasets efficiently.
Contribution
It presents a novel online algorithm for matrix factorization using Broyden updates, extending to mini-batch processing and missing data handling.
Findings
Efficiently updates matrix factors with each new observation.
Performs well on real datasets compared to existing methods.
Handles missing data and large-scale datasets effectively.
Abstract
In this paper, we propose an online algorithm to compute matrix factorizations. Proposed algorithm updates the dictionary matrix and associated coefficients using a single observation at each time. The algorithm performs low-rank updates to dictionary matrix. We derive the algorithm by defining a simple objective function to minimize whenever an observation is arrived. We extend the algorithm further for handling missing data. We also provide a mini-batch extension which enables to compute the matrix factorization on big datasets. We demonstrate the efficiency of our algorithm on a real dataset and give comparisons with well-known algorithms such as stochastic gradient matrix factorization and nonnegative matrix factorization (NMF).
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Taxonomy
TopicsSparse and Compressive Sensing Techniques · Tensor decomposition and applications · Blind Source Separation Techniques
