Narrow Results

Low rank representation (LRR) is widely used to construct a good affinity matrix to cluster data drawn from the union of multiple linear subspaces. However, it is not easy to solve the LRR problem in a closed form, and augmented Lagrange multiplier method (ALM) is usually applied. ALM takes a relative long time dealing with the real-world data. To solve the LRR problem efficiently, we propose an efficient low rank representation (eLRR) algorithm. Given a contaminated data set, we propose a novel way to solve the LRR of the data. We establish a useful theorem which directly gives an approximate solution to our LRR optimization problem. Thus, we can construct a good affinity matrix for subspace clustering. Experimental results with several public databases verify the efficiency and effectiveness of our method.

Subspace clustering analysis algorithms are often employed when dealing with high-dimensional data. As a representative approach, Low-Rank Representation (LRR) of data has achieved great success for subspace segmentation tasks in applications such as image processing. The traditional LRR-related methods consist of two separate tasks: first, the affinity graph construction by using lowrank minimization techniques, and then the spectral clustering, which is done on the affinity graph to get the final segmentation. Since these two steps are independent of each other, this method does not guarantee that the results obtained by the algorithm are globally optimal. In this paper, a method called Robust Structured Low-Rank Representation (RSLRR) is proposed, by integrating the two above mentioned tasks and solve a joint optimization problem. This paper also puts forward a method to solve the joint optimization problem, which can efficiently get both the segmentation and the structured low-rank representation. Experiments on several standard datasets show that, compared with other algorithms, the algorithm proposed in this paper can achieve better clustering results.

Subspace clustering is a challenging high-dimensional data mining task. There have been several approaches proposed in the literature to identify clusters in subspaces, however their performance and quality is highly affected by input parameters. A little research is done so far on identifying proper parameter values automatically. Other observed drawbacks are requirement of multiple database scans resulting into increased demand for computing resources and generation of many redundant clusters. Here, we propose a parameter light subspace clustering method for numerical data hereafter referred to as CLUSLINK. The algorithm is based on single linkage clustering method and works in bottom up, greedy fashion. The only input user has to provide is how coarse or fine the resulting clusters should be, and if not given, the algorithm operates with default values. The empirical results obtained over synthetic and real benchmark datasets show significant improvement in terms of accuracy and execution time.

Subspace clustering aims to seek a multi-subspace representation that is best suitable for data points taken from a high-dimensional space. Sparse representation and low-rank approximation-based methods have become one of the main melodies for subspace clustering. In the existing methods, nuclear norm is used to approximate rank minimization. However, the common deficiency still exists for nuclear norm, which always over-penalizes large singular values and results in a biased solution. In this paper, we propose a nonlinear subspace clustering model that exploits sparsity and low-rank of data in high dimensional feature space by using Schatten-p norm surrogate ($p\in (0,1)$) with learned low-rank kernel. By this manner, the model guarantees that the data mapped in the high-dimensional feature spaces is lower rank and self-expressive. And we show the alternating direction method of multipliers (abbreviated as ADMM) for the corresponding problem in a reproducing kernel Hilbert space. Various experiments on motion segmentation and image clustering display that the proposed model has potentiality in outperforming most of state-of-the-art models in current literature.

In recent years, there has been an increasing interest in multi-view subspace clustering (MSC). However, existing MSC methods fail to take full advantage of the local geometric structure in each manifold throughout the data flow, which is essential for clustering. To remedy this drawback, in this paper, a novel Double Graphs Regularized Multi-view Subspace Clustering (DGRMSC) method is proposed, which aims to harness both global and local structural information of multi-view data in a unified framework. Specifically, DGRMSC first learns a latent representation to exploit the global complementary information of multiple views. Based on the learned latent representation, we learn a self-representation to explore its global cluster structure. Further, Double Graphs Regularization (DGR) is performed on both latent representation and self-representation to take advantage of their local manifold structures simultaneously. Then, we design an iterative algorithm to solve the optimization problem effectively. Comprehensive experiments on several popular multi-view datasets demonstrate the effectiveness of the proposed method.

In this paper, we propose a new subspace clustering algorithm, EPSCMIX (Emerging Partern Subspace Clustering by MIXture models), for solving the problem of clustering microarray expression data. Our method is based on a feature saliency measure which is defined as the probability of feature relevance and is estimated by an Expectation Maximization (EM) algorithm. As this approach employs Emerging Patterns (EP) to get a feature saliency, EPSCMIX can not only model interactions of genes, but also estimate the best number of classes using a meaningful certain set of genes related to each cluster. The robustness of our new approach is demonstrated on a widely-used dataset of colon tissues. Experimental results show the proposed method gives better accuracy in classification than emerging pattern based projected clustering (EPPC) or single EP.