Structured graph optimization for joint spectral embedding and clustering

Spectral Clustering (SC) is an important method in areas such as data mining, image processing, computer science and so on. It attracts more and more attention owing to its effectiveness in unsupervised learning. However, SC has poor performance in the high-dimensional data. Traditional SC methods conduct the spectral embedding of the affinity matrix among data at the first beginning, and then obtain clustering results by the K-means clustering. The also have drawbacks int two processing steps: the clustering results are sensitive to the affinity matrix which may be inaccurate and the post-processing K-means may also be limited by its initialization problem. In the paper, a new approach which joints spectral embedding and clustering with structured graph optimization (called JSEGO) is proposed. In the new model, the low-dimensional representation of data can first be obtained by the spectral embedding method, which can handle with the high-dimensional data better. Then, the optimization similarity matrix would be obtained with such the embedded data. Furthermore, the learning structure graph gives feedback to the similarity matrix to generate better spectral embedded data. As a result, better similarity matrix and clustering result can be obtained by the iterations simultaneously, which are often conducted in two separate steps in the spectral clustering. As a result, the drawbacks introduced by the two process-ing introduces can be solved. At last, we use an alternative optimization method in the new model and conduct the theoretical analysis by comparing this proposed method with K-means clustering. Experiments based on synthetic data and actual benchmark data prove the advantage of this new approach.(c) 2022 Published by Elsevier B.V.