A recent theoretical analysis shows the equivalence between non-negative matrix factorization (NMF) and spectral clustering based approach to subspace clustering. As NMF and many of its variants are essentially linear, we introduce a nonlinear NMF with explicit orthogonality and derive general kernelbased orthogonal multiplicative update rules to solve the subspace clustering problem. In nonlin...

Article history: Received 17 December 2009 Received in revised form 11 December 2010 Accepted 13 December 2010 Available online 24 December 2010 The use of centroids as prototypes for clustering text documents with the k-means family of methods isnot always thebest choice for representing text clusters due to thehighdimensionality, sparsity, and low quality of text data. Especially for the case...

Spectral clustering is a method of subspace clustering which is suitable for the data of any shape and converges to global optimal solution. By combining concepts of shared nearest neighbors and geodesic distance with spectral clustering, a self-adaptive spectral clustering based on geodesic distance and shared nearest neighbors was proposed. Experiments show that the improved spectral clusteri...

Subspace clustering is a challenging task in the field of data mining. Traditional distance measures fail to differentiate the furthest point from the nearest point in very high dimensional data space. To tackle the problem, we design minimal subspace distance which measures the similarity between two points in the subspace where they are nearest to each other. It can discover subspace clusters...

We explore in this paper efficient algorithmic solutions to robust subspace segmentation. We propose the SSQP, namely Subspace Segmentation via Quadratic Programming, to partition data drawn from multiple subspaces into multiple clusters. The basic idea of SSQP is to express each datum as the linear combination of other data regularized by an overall term targeting zero reconstruction coefficie...

Representation of human actions as a sequence of human body movements or action attributes enables the development of models for human activity recognition and summarization. We present an extension of the low-rank representation (LRR) model, termed the clustering-aware structure-constrained low-rank representation (CS-LRR) model, for unsupervised learning of human action attributes from video ...

We propose a symmetric low-rank representation (SLRR) method for subspace clustering, which assumes that a data set is approximately drawn from the union of multiple subspaces. The proposed technique can reveal the membership of multiple subspaces through the self-expressiveness property of the data. In particular, the SLRR method considers a collaborative representation combined with low-rank ...

Clustering is one of the most important techniques in data mining. This chapter presents a survey of popular approaches for data clustering, including well-known clustering techniques, such as partitioning clustering, hierarchical clustering, density-based clustering and grid-based clustering, and recent advances in clustering, such as subspace clustering, text clustering and data stream cluste...

Sparse subspace clustering (SSC) is one of the current state-of-the-art method for partitioning data points into the union of subspaces, with strong theoretical guarantees. However, it is not practical for large data sets as it requires solving a LASSO problem for each data point, where the number of variables in each LASSO problem is the number of data points. To improve the scalability of SSC...

traditional leveraging statistical methods for analyzing today’s large volumes of spatial data have high computational burdens. to eliminate the deficiency, relatively modern data mining techniques have been recently applied in different spatial analysis tasks with the purpose of autonomous knowledge extraction from high-volume spatial data. fortunately, geospatial data is considered a proper s...