English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Dimensionality reduction, cluster analysis, and sparse representation arebasic components in machine learning. However, their relationships have not yetbeen fully investigated. In this paper, we find that the spectral graph theoryunderlies a series of these elementary methods and can unify them into acomplete framework. The methods include PCA, K-means, Laplacian eigenmap (LE),ratio cut (Rcut), and a new sparse representation method developed by us,called spectral sparse representation (SSR). Further, extended relations toconventional over-complete sparse representations (e.g., method of optimaldirections, KSVD), manifold learning (e.g., kernel PCA, multidimensionalscaling, Isomap, locally linear embedding), and subspace clustering (e.g.,sparse subspace clustering, low-rank representation) are incorporated. We showthat, under an ideal condition from the spectral graph theory, PCA, K-means,LE, and Rcut are unified together. And when the condition is relaxed, theunification evolves to SSR, which lies in the intermediate between PCA/LE andK-mean/Rcut. An efficient algorithm, NSCrt, is developed to solve the sparsecodes of SSR. SSR combines merits of both sides: its sparse codes reducedimensionality of data meanwhile revealing cluster structure. For its inherentrelation to cluster analysis, the codes of SSR can be directly used forclustering. Scut, a clustering approach derived from SSR reaches thestate-of-the-art performance in the spectral clustering family. The one-shotsolution obtained by Scut is comparable to the optimal result of K-means thatare run many times. Experiments on various data sets demonstrate the propertiesand strengths of SSR, NSCrt, and Scut.

Spectral Sparse Representation for Clustering: Evolved from PCA, K-means, Laplacian Eigenmap, and Ratio Cut