# Invariant Feature Coding using Tensor Product Representation

## TL;DR

This paper introduces a new invariant feature coding method leveraging tensor product representations to encode transformations, improving discriminative power for tasks like PCA and k-means clustering.

## Contribution

It proposes a novel group-invariant feature coding approach using tensor product representations, explicitly considering group actions for improved feature discrimination.

## Key findings

- Effective on multiple image datasets
- Enhances PCA and k-means with invariant features
- Theoretically proven to retain discriminative information

## Abstract

In this study, a novel feature coding method that exploits invariance for transformations represented by a finite group of orthogonal matrices is proposed. We prove that the group-invariant feature vector contains sufficient discriminative information when learning a linear classifier using convex loss minimization. Based on this result, a novel feature model that explicitly consider group action is proposed for principal component analysis and k-means clustering, which are commonly used in most feature coding methods, and global feature functions. Although the global feature functions are in general complex nonlinear functions, the group action on this space can be easily calculated by constructing these functions as tensor-product representations of basic representations, resulting in an explicit form of invariant feature functions. The effectiveness of our method is demonstrated on several image datasets.