2,059 research outputs found
A Survey on Soft Subspace Clustering
Subspace clustering (SC) is a promising clustering technology to identify
clusters based on their associations with subspaces in high dimensional spaces.
SC can be classified into hard subspace clustering (HSC) and soft subspace
clustering (SSC). While HSC algorithms have been extensively studied and well
accepted by the scientific community, SSC algorithms are relatively new but
gaining more attention in recent years due to better adaptability. In the
paper, a comprehensive survey on existing SSC algorithms and the recent
development are presented. The SSC algorithms are classified systematically
into three main categories, namely, conventional SSC (CSSC), independent SSC
(ISSC) and extended SSC (XSSC). The characteristics of these algorithms are
highlighted and the potential future development of SSC is also discussed.Comment: This paper has been published in Information Sciences Journal in 201
A Convex Formulation for Spectral Shrunk Clustering
Spectral clustering is a fundamental technique in the field of data mining
and information processing. Most existing spectral clustering algorithms
integrate dimensionality reduction into the clustering process assisted by
manifold learning in the original space. However, the manifold in
reduced-dimensional subspace is likely to exhibit altered properties in
contrast with the original space. Thus, applying manifold information obtained
from the original space to the clustering process in a low-dimensional subspace
is prone to inferior performance. Aiming to address this issue, we propose a
novel convex algorithm that mines the manifold structure in the low-dimensional
subspace. In addition, our unified learning process makes the manifold learning
particularly tailored for the clustering. Compared with other related methods,
the proposed algorithm results in more structured clustering result. To
validate the efficacy of the proposed algorithm, we perform extensive
experiments on several benchmark datasets in comparison with some
state-of-the-art clustering approaches. The experimental results demonstrate
that the proposed algorithm has quite promising clustering performance.Comment: AAAI201
Recovering the Optimal Solution by Dual Random Projection
Random projection has been widely used in data classification. It maps
high-dimensional data into a low-dimensional subspace in order to reduce the
computational cost in solving the related optimization problem. While previous
studies are focused on analyzing the classification performance of using random
projection, in this work, we consider the recovery problem, i.e., how to
accurately recover the optimal solution to the original optimization problem in
the high-dimensional space based on the solution learned from the subspace
spanned by random projections. We present a simple algorithm, termed Dual
Random Projection, that uses the dual solution of the low-dimensional
optimization problem to recover the optimal solution to the original problem.
Our theoretical analysis shows that with a high probability, the proposed
algorithm is able to accurately recover the optimal solution to the original
problem, provided that the data matrix is of low rank or can be well
approximated by a low rank matrix.Comment: The 26th Annual Conference on Learning Theory (COLT 2013
- …