A Selective Overview of Recent Advances in Spectral Clustering and Their Applications

Clustering is a key technique in segmenting data into different groups of similar observations. As clustering is an unsupervised learning method, the latent cluster assignments are unknown a priori and must be inferred via the clustering algorithm. By studying individuals via their cluster assignment, we gain a powerful avenue to explore the data. While there exists a vast literature of clustering algorithms, advances in optimization and graph theory have led to the development of the spectral clustering algorithm. More straightforward clustering methods such as k-means or hierarchical clustering are limited in only being able to infer linear boundaries between groups. The spectral clustering was developed to resolve this bottleneck and efficiently determine non-convex separation boundaries between each cluster. Through this, spectral clustering methods are more applicable to practical data problems and outperform naive alternatives. By iterating on the spectral clustering framework, recent research has tailored these methods to a vast array of domains such as bioinformatics, real-time data analysis, and economics. In this chapter, we introduce the basics of spectral clustering, the similarity matrix, and conventional methods to identify the total number of clusters. Finally, we study various extensions of spectral clustering and explore open questions, which may lead to innovative advancements.