Boosted Sparse Non-linear Distance Metric Learning

TL;DR

This paper introduces a boosting-based nonlinear sparse metric learning algorithm that effectively handles high-dimensional data by ensuring positive semi-definiteness, low rank, and sparsity, improving scalability and capturing complex data structures.

Contribution

It presents a novel boosting framework for nonlinear sparse metric learning that guarantees positive semi-definiteness, low rank, and sparsity, addressing scalability issues in high-dimensional settings.

Findings

Outperforms state-of-the-art metric learning methods in experiments.

Ensures positive semi-definiteness, low rank, and sparsity of the learned metric.

Effectively captures nonlinear structures in high-dimensional data.

Abstract

This paper proposes a boosting-based solution addressing metric learning problems for high-dimensional data. Distance measures have been used as natural measures of (dis)similarity and served as the foundation of various learning methods. The efficiency of distance-based learning methods heavily depends on the chosen distance metric. With increasing dimensionality and complexity of data, however, traditional metric learning methods suffer from poor scalability and the limitation due to linearity as the true signals are usually embedded within a low-dimensional nonlinear subspace. In this paper, we propose a nonlinear sparse metric learning algorithm via boosting. We restructure a global optimization problem into a forward stage-wise learning of weak learners based on a rank-one decomposition of the weight matrix in the Mahalanobis distance metric. A gradient boosting algorithm is devised to obtain a sparse rank-one update of the weight matrix at each step. Nonlinear features are learned by a hierarchical expansion of interactions incorporated within the boosting algorithm. Meanwhile, an early stopping rule is imposed to control the overall complexity of the learned metric. As a result, our approach guarantees three desirable properties of the final metric: positive semi-definiteness, low rank and element-wise sparsity. Numerical experiments show that our learning model compares favorably with the state-of-the-art methods in the current literature of metric learning.