Towards an Explainable Comparison and Alignment of Feature Embeddings

TL;DR

This paper introduces the SPEC framework for interpretable comparison and alignment of feature embeddings by analyzing their clustering structures through spectral methods, applicable to large-scale datasets.

Contribution

The paper proposes a novel spectral kernel-based framework for comparing and aligning feature embeddings, emphasizing interpretability and scalability.

Findings

Effective comparison of embeddings based on clustering differences.

Scalable linear complexity implementation for large datasets.

Successful application to ImageNet and MS-COCO datasets.

Abstract

While several feature embedding models have been developed in the literature, comparisons of these embeddings have largely focused on their numerical performance in classification-related downstream applications. However, an interpretable comparison of different embeddings requires identifying and analyzing mismatches between sample groups clustered within the embedding spaces. In this work, we propose the \emph{Spectral Pairwise Embedding Comparison (SPEC)} framework to compare embeddings and identify their differences in clustering a reference dataset. Our approach examines the kernel matrices derived from two embeddings and leverages the eigendecomposition of the difference kernel matrix to detect sample clusters that are captured differently by the two embeddings. We present a scalable implementation of this kernel-based approach, with computational complexity that grows linearly with the sample size. Furthermore, we introduce an optimization problem using this framework to align two embeddings, ensuring that clusters identified in one embedding are also captured in the other model. We provide numerical results demonstrating the SPEC's application to compare and align embeddings on large-scale datasets such as ImageNet and MS-COCO. The project page is available at https://mjalali.github.io/SPEC/.