Nonparametric Feature Extraction from Dendrograms

We propose feature extraction from dendrograms in a nonparametric way. The Minimax distance measures correspond to building a dendrogram with single linkage criterion, with defining specific forms of a level function and a distance function over that. Therefore, we extend this method to arbitrary dendrograms. We develop a generalized framework wherein different distance measures can be inferred from different types of dendrograms, level functions and distance functions. Via an appropriate embedding, we compute a vector-based representation of the inferred distances, in order to enable many numerical machine learning algorithms to employ such distances. Then, to address the model selection problem, we study the aggregation of different dendrogram-based distances respectively in solution space and in representation space in the spirit of deep representations. In the first approach, for example for the clustering problem, we build a graph with positive and negative edge weights according to the consistency of the clustering labels of different objects among different solutions, in the context of ensemble methods. Then, we use an efficient variant of correlation clustering to produce the final clusters. In the second approach, we investigate the sequential combination of different distances and features sequentially in the spirit of multi-layered architectures to obtain the final features. Finally, we demonstrate the effectiveness of our approach via several numerical studies

Deep Divergence-Based Approach to Clustering

A promising direction in deep learning research consists in learning representations and simultaneously discovering cluster structure in unlabeled data by optimizing a discriminative loss function. As opposed to supervised deep learning, this line of research is in its infancy, and how to design and optimize suitable loss functions to train deep neural networks for clustering is still an open question. Our contribution to this emerging field is a new deep clustering network that leverages the discriminative power of information-theoretic divergence measures, which have been shown to be effective in traditional clustering. We propose a novel loss function that incorporates geometric regularization constraints, thus avoiding degenerate structures of the resulting clustering partition. Experiments on synthetic benchmarks and real datasets show that the proposed network achieves competitive performance with respect to other state-of-the-art methods, scales well to large datasets, and does not require pre-training steps

Kernel Truncated Regression Representation for Robust Subspace Clustering

Subspace clustering aims to group data points into multiple clusters of which each corresponds to one subspace. Most existing subspace clustering approaches assume that input data lie on linear subspaces. In practice, however, this assumption usually does not hold. To achieve nonlinear subspace clustering, we propose a novel method, called kernel truncated regression representation. Our method consists of the following four steps: 1) projecting the input data into a hidden space, where each data point can be linearly represented by other data points; 2) calculating the linear representation coefficients of the data representations in the hidden space; 3) truncating the trivial coefficients to achieve robustness and block-diagonality; and 4) executing the graph cutting operation on the coefficient matrix by solving a graph Laplacian problem. Our method has the advantages of a closed-form solution and the capacity of clustering data points that lie on nonlinear subspaces. The first advantage makes our method efficient in handling large-scale datasets, and the second one enables the proposed method to conquer the nonlinear subspace clustering challenge. Extensive experiments on six benchmarks demonstrate the effectiveness and the efficiency of the proposed method in comparison with current state-of-the-art approaches.Comment: 14 page

Unsupervised Feature Selection with Adaptive Structure Learning

The problem of feature selection has raised considerable interests in the past decade. Traditional unsupervised methods select the features which can faithfully preserve the intrinsic structures of data, where the intrinsic structures are estimated using all the input features of data. However, the estimated intrinsic structures are unreliable/inaccurate when the redundant and noisy features are not removed. Therefore, we face a dilemma here: one need the true structures of data to identify the informative features, and one need the informative features to accurately estimate the true structures of data. To address this, we propose a unified learning framework which performs structure learning and feature selection simultaneously. The structures are adaptively learned from the results of feature selection, and the informative features are reselected to preserve the refined structures of data. By leveraging the interactions between these two essential tasks, we are able to capture accurate structures and select more informative features. Experimental results on many benchmark data sets demonstrate that the proposed method outperforms many state of the art unsupervised feature selection methods