556 research outputs found
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
A convex formulation for spectral shrunk clustering
Copyright © 2015, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. 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
Convex Subspace Clustering by Adaptive Block Diagonal Representation
Subspace clustering is a class of extensively studied clustering methods and
the spectral-type approaches are its important subclass whose key first step is
to learn a coefficient matrix with block diagonal structure. To realize this
step, sparse subspace clustering (SSC), low rank representation (LRR) and block
diagonal representation (BDR) were successively proposed and have become the
state-of-the-arts (SOTAs). Among them, the former two minimize their convex
objectives by imposing sparsity and low rankness on the coefficient matrix
respectively, but so-desired block diagonality cannot neccesarily be guaranteed
practically while the latter designs a block diagonal matrix induced
regularizer but sacrifices convexity. For solving this dilemma, inspired by
Convex Biclustering, in this paper, we propose a simple yet efficient
spectral-type subspace clustering method named Adaptive Block Diagonal
Representation (ABDR) which strives to pursue so-desired block diagonality as
BDR by coercively fusing the columns/rows of the coefficient matrix via a
specially designed convex regularizer, consequently, ABDR naturally enjoys
their merits and can adaptively form more desired block diagonality than the
SOTAs without needing to prefix the number of blocks as done in BDR. Finally,
experimental results on synthetic and real benchmarks demonstrate the
superiority of ABDR.Comment: 13 pages, 11 figures, 8 table
Local Component Analysis
Kernel density estimation, a.k.a. Parzen windows, is a popular density
estimation method, which can be used for outlier detection or clustering. With
multivariate data, its performance is heavily reliant on the metric used within
the kernel. Most earlier work has focused on learning only the bandwidth of the
kernel (i.e., a scalar multiplicative factor). In this paper, we propose to
learn a full Euclidean metric through an expectation-minimization (EM)
procedure, which can be seen as an unsupervised counterpart to neighbourhood
component analysis (NCA). In order to avoid overfitting with a fully
nonparametric density estimator in high dimensions, we also consider a
semi-parametric Gaussian-Parzen density model, where some of the variables are
modelled through a jointly Gaussian density, while others are modelled through
Parzen windows. For these two models, EM leads to simple closed-form updates
based on matrix inversions and eigenvalue decompositions. We show empirically
that our method leads to density estimators with higher test-likelihoods than
natural competing methods, and that the metrics may be used within most
unsupervised learning techniques that rely on such metrics, such as spectral
clustering or manifold learning methods. Finally, we present a stochastic
approximation scheme which allows for the use of this method in a large-scale
setting
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