1,448 research outputs found
Out-of-sample generalizations for supervised manifold learning for classification
Supervised manifold learning methods for data classification map data samples
residing in a high-dimensional ambient space to a lower-dimensional domain in a
structure-preserving way, while enhancing the separation between different
classes in the learned embedding. Most nonlinear supervised manifold learning
methods compute the embedding of the manifolds only at the initially available
training points, while the generalization of the embedding to novel points,
known as the out-of-sample extension problem in manifold learning, becomes
especially important in classification applications. In this work, we propose a
semi-supervised method for building an interpolation function that provides an
out-of-sample extension for general supervised manifold learning algorithms
studied in the context of classification. The proposed algorithm computes a
radial basis function (RBF) interpolator that minimizes an objective function
consisting of the total embedding error of unlabeled test samples, defined as
their distance to the embeddings of the manifolds of their own class, as well
as a regularization term that controls the smoothness of the interpolation
function in a direction-dependent way. The class labels of test data and the
interpolation function parameters are estimated jointly with a progressive
procedure. Experimental results on face and object images demonstrate the
potential of the proposed out-of-sample extension algorithm for the
classification of manifold-modeled data sets
Embedded Multi-label Feature Selection via Orthogonal Regression
In the last decade, embedded multi-label feature selection methods,
incorporating the search for feature subsets into model optimization, have
attracted considerable attention in accurately evaluating the importance of
features in multi-label classification tasks. Nevertheless, the
state-of-the-art embedded multi-label feature selection algorithms based on
least square regression usually cannot preserve sufficient discriminative
information in multi-label data. To tackle the aforementioned challenge, a
novel embedded multi-label feature selection method, termed global redundancy
and relevance optimization in orthogonal regression (GRROOR), is proposed to
facilitate the multi-label feature selection. The method employs orthogonal
regression with feature weighting to retain sufficient statistical and
structural information related to local label correlations of the multi-label
data in the feature learning process. Additionally, both global feature
redundancy and global label relevancy information have been considered in the
orthogonal regression model, which could contribute to the search for
discriminative and non-redundant feature subsets in the multi-label data. The
cost function of GRROOR is an unbalanced orthogonal Procrustes problem on the
Stiefel manifold. A simple yet effective scheme is utilized to obtain an
optimal solution. Extensive experimental results on ten multi-label data sets
demonstrate the effectiveness of GRROOR
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