Similarity Learning for High-Dimensional Sparse Data

TL;DR

This paper introduces an efficient similarity learning method for high-dimensional sparse data that leverages a convex combination of rank-one matrices and an approximate Frank-Wolfe algorithm, improving scalability and reducing overfitting.

Contribution

It proposes a novel scalable similarity learning approach that optimizes a convex combination of sparse rank-one matrices using an approximate Frank-Wolfe method, suitable for high-dimensional data.

Findings

Effective on real-world high-dimensional datasets

Reduces overfitting by controlling active features

Demonstrates potential for classification and data exploration

Abstract

A good measure of similarity between data points is crucial to many tasks in machine learning. Similarity and metric learning methods learn such measures automatically from data, but they do not scale well respect to the dimensionality of the data. In this paper, we propose a method that can learn efficiently similarity measure from high-dimensional sparse data. The core idea is to parameterize the similarity measure as a convex combination of rank-one matrices with specific sparsity structures. The parameters are then optimized with an approximate Frank-Wolfe procedure to maximally satisfy relative similarity constraints on the training data. Our algorithm greedily incorporates one pair of features at a time into the similarity measure, providing an efficient way to control the number of active features and thus reduce overfitting. It enjoys very appealing convergence guarantees and its time and memory complexity depends on the sparsity of the data instead of the dimension of the feature space. Our experiments on real-world high-dimensional datasets demonstrate its potential for classification, dimensionality reduction and data exploration.