A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Orthogonal series density estimation and the kernel eigenvalue problem
Neural Computation
Non-parametric Similarity Measures for Unsupervised Texture Segmentation and Image Retrieval
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Efficient svm training using low-rank kernel representations
The Journal of Machine Learning Research
Kernel independent component analysis
The Journal of Machine Learning Research
Spectral Grouping Using the Nyström Method
IEEE Transactions on Pattern Analysis and Machine Intelligence
Convex Optimization
Linearized cluster assignment via spectral ordering
ICML '04 Proceedings of the twenty-first international conference on Machine learning
K-means clustering via principal component analysis
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Kernel Methods for Measuring Independence
The Journal of Machine Learning Research
Learning Spectral Clustering, With Application To Speech Separation
The Journal of Machine Learning Research
A tutorial on spectral clustering
Statistics and Computing
Improved Nyström low-rank approximation and error analysis
Proceedings of the 25th international conference on Machine learning
Multiway Spectral Clustering with Out-of-Sample Extensions through Weighted Kernel PCA
IEEE Transactions on Pattern Analysis and Machine Intelligence
Spectral K-way ratio-cut partitioning and clustering
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Input space versus feature space in kernel-based methods
IEEE Transactions on Neural Networks
A support vector machine formulation to PCA analysis and its kernel version
IEEE Transactions on Neural Networks
p-PIC: Parallel power iteration clustering for big data
Journal of Parallel and Distributed Computing
Probability-based text clustering algorithm by alternately repeating two operations
Journal of Information Science
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Kernel spectral clustering has been formulated within a primal-dual optimization setting allowing natural extensions to out-of-sample data together with model selection in a learning framework. This becomes important for predictive purposes and for good generalization capabilities. The clustering model is formulated in the primal in terms of mappings to high-dimensional feature spaces typical of support vector machines and kernel-based methodologies. The dual problem corresponds to an eigenvalue decomposition of a centered Laplacian matrix derived from pairwise similarities within the data. The out-of-sample extension can also be used to introduce sparsity and to reduce the computational complexity of the resulting eigenvalue problem. In this paper, we propose several methods to obtain sparse and highly sparse kernel spectral clustering models. The proposed approaches are based on structural properties of the solutions when the clusters are well formed. Experimental results with difficult toy examples and images show the applicability of the proposed sparse models with predictive capabilities.