299,950 research outputs found
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
Robust EM algorithm for model-based curve clustering
Model-based clustering approaches concern the paradigm of exploratory data
analysis relying on the finite mixture model to automatically find a latent
structure governing observed data. They are one of the most popular and
successful approaches in cluster analysis. The mixture density estimation is
generally performed by maximizing the observed-data log-likelihood by using the
expectation-maximization (EM) algorithm. However, it is well-known that the EM
algorithm initialization is crucial. In addition, the standard EM algorithm
requires the number of clusters to be known a priori. Some solutions have been
provided in [31, 12] for model-based clustering with Gaussian mixture models
for multivariate data. In this paper we focus on model-based curve clustering
approaches, when the data are curves rather than vectorial data, based on
regression mixtures. We propose a new robust EM algorithm for clustering
curves. We extend the model-based clustering approach presented in [31] for
Gaussian mixture models, to the case of curve clustering by regression
mixtures, including polynomial regression mixtures as well as spline or
B-spline regressions mixtures. Our approach both handles the problem of
initialization and the one of choosing the optimal number of clusters as the EM
learning proceeds, rather than in a two-fold scheme. This is achieved by
optimizing a penalized log-likelihood criterion. A simulation study confirms
the potential benefit of the proposed algorithm in terms of robustness
regarding initialization and funding the actual number of clusters.Comment: In Proceedings of the 2013 International Joint Conference on Neural
Networks (IJCNN), 2013, Dallas, TX, US
The OSCAR for Generalized Linear Models
The Octagonal Selection and Clustering Algorithm in Regression (OSCAR) proposed by Bondell and Reich (2008) has the attractive feature that highly correlated predictors can obtain exactly the same coecient yielding clustering of predictors. Estimation methods are available for linear regression models. It is shown how the OSCAR penalty can be used within the framework of generalized linear models. An algorithm that solves the corresponding maximization problem is given. The estimation method is investigated in a simulation study and the usefulness is demonstrated by an example from water engineering
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