  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.
