Personalized Dictionary Learning for Heterogeneous Datasets

TL;DR

This paper proposes a novel framework called Personalized Dictionary Learning (PerDL) for extracting shared and unique features from heterogeneous datasets, with a new algorithm PerMA that guarantees efficient recovery of dictionaries.

Contribution

It formulates the PerDL problem, provides conditions for disentangling shared and unique features, and introduces PerMA, a provably convergent algorithm for this task.

Findings

PerMA converges linearly to the true dictionaries under certain conditions.

The framework effectively handles imbalanced datasets and video surveillance tasks.

PerDL improves feature extraction from heterogeneous data sources.

Abstract

We introduce a relevant yet challenging problem named Personalized Dictionary Learning (PerDL), where the goal is to learn sparse linear representations from heterogeneous datasets that share some commonality. In PerDL, we model each dataset's shared and unique features as global and local dictionaries. Challenges for PerDL not only are inherited from classical dictionary learning (DL), but also arise due to the unknown nature of the shared and unique features. In this paper, we rigorously formulate this problem and provide conditions under which the global and local dictionaries can be provably disentangled. Under these conditions, we provide a meta-algorithm called Personalized Matching and Averaging (PerMA) that can recover both global and local dictionaries from heterogeneous datasets. PerMA is highly efficient; it converges to the ground truth at a linear rate under suitable conditions. Moreover, it automatically borrows strength from strong learners to improve the prediction of weak learners. As a general framework for extracting global and local dictionaries, we show the application of PerDL in different learning tasks, such as training with imbalanced datasets and video surveillance.