4,822 research outputs found
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
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
Sparse Transfer Learning for Interactive Video Search Reranking
Visual reranking is effective to improve the performance of the text-based
video search. However, existing reranking algorithms can only achieve limited
improvement because of the well-known semantic gap between low level visual
features and high level semantic concepts. In this paper, we adopt interactive
video search reranking to bridge the semantic gap by introducing user's
labeling effort. We propose a novel dimension reduction tool, termed sparse
transfer learning (STL), to effectively and efficiently encode user's labeling
information. STL is particularly designed for interactive video search
reranking. Technically, it a) considers the pair-wise discriminative
information to maximally separate labeled query relevant samples from labeled
query irrelevant ones, b) achieves a sparse representation for the subspace to
encodes user's intention by applying the elastic net penalty, and c) propagates
user's labeling information from labeled samples to unlabeled samples by using
the data distribution knowledge. We conducted extensive experiments on the
TRECVID 2005, 2006 and 2007 benchmark datasets and compared STL with popular
dimension reduction algorithms. We report superior performance by using the
proposed STL based interactive video search reranking.Comment: 17 page
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