691 research outputs found
Non-Negative Local Sparse Coding for Subspace Clustering
Subspace sparse coding (SSC) algorithms have proven to be beneficial to
clustering problems. They provide an alternative data representation in which
the underlying structure of the clusters can be better captured. However, most
of the research in this area is mainly focused on enhancing the sparse coding
part of the problem. In contrast, we introduce a novel objective term in our
proposed SSC framework which focuses on the separability of data points in the
coding space. We also provide mathematical insights into how this
local-separability term improves the clustering result of the SSC framework.
Our proposed non-linear local SSC algorithm (NLSSC) also benefits from the
efficient choice of its sparsity terms and constraints. The NLSSC algorithm is
also formulated in the kernel-based framework (NLKSSC) which can represent the
nonlinear structure of data. In addition, we address the possibility of having
redundancies in sparse coding results and its negative effect on graph-based
clustering problems. We introduce the link-restore post-processing step to
improve the representation graph of non-negative SSC algorithms such as ours.
Empirical evaluations on well-known clustering benchmarks show that our
proposed NLSSC framework results in better clusterings compared to the
state-of-the-art baselines and demonstrate the effectiveness of the
link-restore post-processing in improving the clustering accuracy via
correcting the broken links of the representation graph.Comment: 15 pages, IDA 2018 conferenc
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
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