Fast Spectral Clustering Using Autoencoders and Landmarks

In this paper, we introduce an algorithm for performing spectral clustering efficiently. Spectral clustering is a powerful clustering algorithm that suffers from high computational complexity, due to eigen decomposition. In this work, we first build the adjacency matrix of the corresponding graph of the dataset. To build this matrix, we only consider a limited number of points, called landmarks, and compute the similarity of all data points with the landmarks. Then, we present a definition of the Laplacian matrix of the graph that enable us to perform eigen decomposition efficiently, using a deep autoencoder. The overall complexity of the algorithm for eigen decomposition is O(np), where n is the number of data points and p is the number of landmarks. At last, we evaluate the performance of the algorithm in different experiments.

[1]  Xinlei Chen,et al.  Large Scale Spectral Clustering with Landmark-Based Representation , 2011, AAAI.

[2]  James T. Kwok,et al.  Time and space efficient spectral clustering via column sampling , 2011, CVPR 2011.

[3]  Mohamed S. Kamel,et al.  Greedy column subset selection for large-scale data sets , 2014, Knowledge and Information Systems.

[4]  Padhraic Smyth,et al.  A Spectral Clustering Approach To Finding Communities in Graph , 2005, SDM.

[5]  Enhong Chen,et al.  Learning Deep Representations for Graph Clustering , 2014, AAAI.

[6]  Ming Shao,et al.  Deep Linear Coding for Fast Graph Clustering , 2015, IJCAI.

[7]  Matthias W. Seeger,et al.  Using the Nyström Method to Speed Up Kernel Machines , 2000, NIPS.

[8]  Anna Choromanska,et al.  Fast Spectral Clustering via the Nyström Method , 2013, ALT.

[9]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[10]  Michael I. Jordan,et al.  On Spectral Clustering: Analysis and an algorithm , 2001, NIPS.

[11]  Ieee Xplore,et al.  IEEE Transactions on Pattern Analysis and Machine Intelligence Information for Authors , 2022, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  Jitendra Malik,et al.  Spectral grouping using the Nystrom method , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[13]  Inderjit S. Dhillon,et al.  Co-clustering documents and words using bipartite spectral graph partitioning , 2001, KDD '01.

[14]  James A. Casbon,et al.  Spectral clustering of protein sequences , 2006, Nucleic acids research.

[15]  Ling Huang,et al.  Fast approximate spectral clustering , 2009, KDD.

[16]  Geoffrey E. Hinton,et al.  Reducing the Dimensionality of Data with Neural Networks , 2006, Science.

[17]  Christos Boutsidis,et al.  Approximate Spectral Clustering via Randomized Sketching , 2013, ArXiv.