Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Min-max Cut Algorithm for Graph Partitioning and Data Clustering
ICDM '01 Proceedings of the 2001 IEEE International Conference on Data Mining
Multiclass Spectral Clustering
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Non-negative Matrix Factorization with Sparseness Constraints
The Journal of Machine Learning Research
Orthogonal nonnegative matrix t-factorizations for clustering
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Learning Spectral Clustering, With Application To Speech Separation
The Journal of Machine Learning Research
A tutorial on spectral clustering
Statistics and Computing
Projected Gradient Methods for Nonnegative Matrix Factorization
Neural Computation
Weighted Graph Cuts without Eigenvectors A Multilevel Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Non-negative Laplacian Embedding
ICDM '09 Proceedings of the 2009 Ninth IEEE International Conference on Data Mining
Convex Non-negative Matrix Factorization in the Wild
ICDM '09 Proceedings of the 2009 Ninth IEEE International Conference on Data Mining
Convex and Semi-Nonnegative Matrix Factorizations
IEEE Transactions on Pattern Analysis and Machine Intelligence
An improved two-way partitioning algorithm with stable performance [VLSI]
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
New spectral methods for ratio cut partitioning and clustering
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Spectral K-way ratio-cut partitioning and clustering
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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Spectral clustering aims to partition a data set into several groups by using the Laplacian of the graph such that data points in the same group are similar while data points in different groups are dissimilar to each other. Spectral clustering is very simple to implement and has many advantages over the traditional clustering algorithms such as k-means. Non-negative matrix factorization (NMF) factorizes a non-negative data matrix into a product of two non-negative (lower rank) matrices so as to achieve dimension reduction and part-based data representation. In this work, we proved that the spectral clustering under some conditions is equivalent to NMF. Unlike the previous work, we formulate the spectral clustering as a factorization of data matrix (or scaled data matrix) rather than the symmetrical factorization of the symmetrical pairwise similarity matrix as the previous study did. Under the NMF framework, where regularization can be easily incorporated into the spectral clustering, we propose several non-negative and sparse spectral clustering algorithms. Empirical studies on real world data show much better clustering accuracy of the proposed algorithms than some state-of-the-art methods such as ratio cut and normalized cut spectral clustering and non-negative Laplacian embedding.