21,835 research outputs found
Semi-Supervised Sparse Coding
Sparse coding approximates the data sample as a sparse linear combination of
some basic codewords and uses the sparse codes as new presentations. In this
paper, we investigate learning discriminative sparse codes by sparse coding in
a semi-supervised manner, where only a few training samples are labeled. By
using the manifold structure spanned by the data set of both labeled and
unlabeled samples and the constraints provided by the labels of the labeled
samples, we learn the variable class labels for all the samples. Furthermore,
to improve the discriminative ability of the learned sparse codes, we assume
that the class labels could be predicted from the sparse codes directly using a
linear classifier. By solving the codebook, sparse codes, class labels and
classifier parameters simultaneously in a unified objective function, we
develop a semi-supervised sparse coding algorithm. Experiments on two
real-world pattern recognition problems demonstrate the advantage of the
proposed methods over supervised sparse coding methods on partially labeled
data sets
Robust Image Analysis by L1-Norm Semi-supervised Learning
This paper presents a novel L1-norm semi-supervised learning algorithm for
robust image analysis by giving new L1-norm formulation of Laplacian
regularization which is the key step of graph-based semi-supervised learning.
Since our L1-norm Laplacian regularization is defined directly over the
eigenvectors of the normalized Laplacian matrix, we successfully formulate
semi-supervised learning as an L1-norm linear reconstruction problem which can
be effectively solved with sparse coding. By working with only a small subset
of eigenvectors, we further develop a fast sparse coding algorithm for our
L1-norm semi-supervised learning. Due to the sparsity induced by sparse coding,
the proposed algorithm can deal with the noise in the data to some extent and
thus has important applications to robust image analysis, such as noise-robust
image classification and noise reduction for visual and textual bag-of-words
(BOW) models. In particular, this paper is the first attempt to obtain robust
image representation by sparse co-refinement of visual and textual BOW models.
The experimental results have shown the promising performance of the proposed
algorithm.Comment: This is an extension of our long paper in ACM MM 201
Sample Complexity Analysis for Learning Overcomplete Latent Variable Models through Tensor Methods
We provide guarantees for learning latent variable models emphasizing on the
overcomplete regime, where the dimensionality of the latent space can exceed
the observed dimensionality. In particular, we consider multiview mixtures,
spherical Gaussian mixtures, ICA, and sparse coding models. We provide tight
concentration bounds for empirical moments through novel covering arguments. We
analyze parameter recovery through a simple tensor power update algorithm. In
the semi-supervised setting, we exploit the label or prior information to get a
rough estimate of the model parameters, and then refine it using the tensor
method on unlabeled samples. We establish that learning is possible when the
number of components scales as , where is the observed
dimension, and is the order of the observed moment employed in the tensor
method. Our concentration bound analysis also leads to minimax sample
complexity for semi-supervised learning of spherical Gaussian mixtures. In the
unsupervised setting, we use a simple initialization algorithm based on SVD of
the tensor slices, and provide guarantees under the stricter condition that
(where constant can be larger than ), where the
tensor method recovers the components under a polynomial running time (and
exponential in ). Our analysis establishes that a wide range of
overcomplete latent variable models can be learned efficiently with low
computational and sample complexity through tensor decomposition methods.Comment: Title change
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