18,508 research outputs found
Constructing a Non-Negative Low Rank and Sparse Graph with Data-Adaptive Features
This paper aims at constructing a good graph for discovering intrinsic data
structures in a semi-supervised learning setting. Firstly, we propose to build
a non-negative low-rank and sparse (referred to as NNLRS) graph for the given
data representation. Specifically, the weights of edges in the graph are
obtained by seeking a nonnegative low-rank and sparse matrix that represents
each data sample as a linear combination of others. The so-obtained NNLRS-graph
can capture both the global mixture of subspaces structure (by the low
rankness) and the locally linear structure (by the sparseness) of the data,
hence is both generative and discriminative. Secondly, as good features are
extremely important for constructing a good graph, we propose to learn the data
embedding matrix and construct the graph jointly within one framework, which is
termed as NNLRS with embedded features (referred to as NNLRS-EF). Extensive
experiments on three publicly available datasets demonstrate that the proposed
method outperforms the state-of-the-art graph construction method by a large
margin for both semi-supervised classification and discriminative analysis,
which verifies the effectiveness of our proposed method
KCRC-LCD: Discriminative Kernel Collaborative Representation with Locality Constrained Dictionary for Visual Categorization
We consider the image classification problem via kernel collaborative
representation classification with locality constrained dictionary (KCRC-LCD).
Specifically, we propose a kernel collaborative representation classification
(KCRC) approach in which kernel method is used to improve the discrimination
ability of collaborative representation classification (CRC). We then measure
the similarities between the query and atoms in the global dictionary in order
to construct a locality constrained dictionary (LCD) for KCRC. In addition, we
discuss several similarity measure approaches in LCD and further present a
simple yet effective unified similarity measure whose superiority is validated
in experiments. There are several appealing aspects associated with LCD. First,
LCD can be nicely incorporated under the framework of KCRC. The LCD similarity
measure can be kernelized under KCRC, which theoretically links CRC and LCD
under the kernel method. Second, KCRC-LCD becomes more scalable to both the
training set size and the feature dimension. Example shows that KCRC is able to
perfectly classify data with certain distribution, while conventional CRC fails
completely. Comprehensive experiments on many public datasets also show that
KCRC-LCD is a robust discriminative classifier with both excellent performance
and good scalability, being comparable or outperforming many other
state-of-the-art approaches
Similarity Learning via Kernel Preserving Embedding
Data similarity is a key concept in many data-driven applications. Many
algorithms are sensitive to similarity measures. To tackle this fundamental
problem, automatically learning of similarity information from data via
self-expression has been developed and successfully applied in various models,
such as low-rank representation, sparse subspace learning, semi-supervised
learning. However, it just tries to reconstruct the original data and some
valuable information, e.g., the manifold structure, is largely ignored. In this
paper, we argue that it is beneficial to preserve the overall relations when we
extract similarity information. Specifically, we propose a novel similarity
learning framework by minimizing the reconstruction error of kernel matrices,
rather than the reconstruction error of original data adopted by existing work.
Taking the clustering task as an example to evaluate our method, we observe
considerable improvements compared to other state-of-the-art methods. More
importantly, our proposed framework is very general and provides a novel and
fundamental building block for many other similarity-based tasks. Besides, our
proposed kernel preserving opens up a large number of possibilities to embed
high-dimensional data into low-dimensional space.Comment: Published in AAAI 201
Manifold Elastic Net: A Unified Framework for Sparse Dimension Reduction
It is difficult to find the optimal sparse solution of a manifold learning
based dimensionality reduction algorithm. The lasso or the elastic net
penalized manifold learning based dimensionality reduction is not directly a
lasso penalized least square problem and thus the least angle regression (LARS)
(Efron et al. \cite{LARS}), one of the most popular algorithms in sparse
learning, cannot be applied. Therefore, most current approaches take indirect
ways or have strict settings, which can be inconvenient for applications. In
this paper, we proposed the manifold elastic net or MEN for short. MEN
incorporates the merits of both the manifold learning based dimensionality
reduction and the sparse learning based dimensionality reduction. By using a
series of equivalent transformations, we show MEN is equivalent to the lasso
penalized least square problem and thus LARS is adopted to obtain the optimal
sparse solution of MEN. In particular, MEN has the following advantages for
subsequent classification: 1) the local geometry of samples is well preserved
for low dimensional data representation, 2) both the margin maximization and
the classification error minimization are considered for sparse projection
calculation, 3) the projection matrix of MEN improves the parsimony in
computation, 4) the elastic net penalty reduces the over-fitting problem, and
5) the projection matrix of MEN can be interpreted psychologically and
physiologically. Experimental evidence on face recognition over various popular
datasets suggests that MEN is superior to top level dimensionality reduction
algorithms.Comment: 33 pages, 12 figure
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