A new embedding quality assessment method for manifold learning

TL;DR

This paper introduces NIEQA, a new quantitative method for assessing the quality of manifold learning embeddings, capable of evaluating both local and global preservation regardless of normalization, thus aiding model selection.

Contribution

The paper proposes NIEQA, a novel assessment method that extends evaluation capabilities to normalized embeddings and offers comprehensive local and global quality measures.

Findings

NIEQA effectively evaluates embedding quality on benchmark datasets.

It can assess both isometric and normalized embeddings.

Experimental results confirm its usefulness in model selection.

Abstract

Manifold learning is a hot research topic in the field of computer science. A crucial issue with current manifold learning methods is that they lack a natural quantitative measure to assess the quality of learned embeddings, which greatly limits their applications to real-world problems. In this paper, a new embedding quality assessment method for manifold learning, named as Normalization Independent Embedding Quality Assessment (NIEQA), is proposed. Compared with current assessment methods which are limited to isometric embeddings, the NIEQA method has a much larger application range due to two features. First, it is based on a new measure which can effectively evaluate how well local neighborhood geometry is preserved under normalization, hence it can be applied to both isometric and normalized embeddings. Second, it can provide both local and global evaluations to output an overall assessment. Therefore, NIEQA can serve as a natural tool in model selection and evaluation tasks for manifold learning. Experimental results on benchmark data sets validate the effectiveness of the proposed method.