Error-Correcting Factorization

TL;DR

This paper introduces Error-Correcting Factorization (ECF), a novel method for designing ECOC codes that allocates error correction to class pairs, improving multi-class classification accuracy especially for confusable classes.

Contribution

The paper presents a new representation called the design matrix, derives the optimal code length, and formulates ECF as a discrete optimization problem with an efficient solution, enhancing ECOC design.

Findings

ECF outperforms state-of-the-art methods when allocating correction to confusable classes.

The design matrix enables targeted error correction for class pairs.

Optimal code length is derived using rank properties of the design matrix.

Abstract

Error Correcting Output Codes (ECOC) is a successful technique in multi-class classification, which is a core problem in Pattern Recognition and Machine Learning. A major advantage of ECOC over other methods is that the multi- class problem is decoupled into a set of binary problems that are solved independently. However, literature defines a general error-correcting capability for ECOCs without analyzing how it distributes among classes, hindering a deeper analysis of pair-wise error-correction. To address these limitations this paper proposes an Error-Correcting Factorization (ECF) method, our contribution is three fold: (I) We propose a novel representation of the error-correction capability, called the design matrix, that enables us to build an ECOC on the basis of allocating correction to pairs of classes. (II) We derive the optimal code length of an ECOC using rank properties of the design matrix. (III) ECF is formulated as a discrete optimization problem, and a relaxed solution is found using an efficient constrained block coordinate descent approach. (IV) Enabled by the flexibility introduced with the design matrix we propose to allocate the error-correction on classes that are prone to confusion. Experimental results in several databases show that when allocating the error-correction to confusable classes ECF outperforms state-of-the-art approaches.