11,013 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
Joint & Progressive Learning from High-Dimensional Data for Multi-Label Classification
Despite the fact that nonlinear subspace learning techniques (e.g. manifold
learning) have successfully applied to data representation, there is still room
for improvement in explainability (explicit mapping), generalization
(out-of-samples), and cost-effectiveness (linearization). To this end, a novel
linearized subspace learning technique is developed in a joint and progressive
way, called \textbf{j}oint and \textbf{p}rogressive \textbf{l}earning
str\textbf{a}teg\textbf{y} (J-Play), with its application to multi-label
classification. The J-Play learns high-level and semantically meaningful
feature representation from high-dimensional data by 1) jointly performing
multiple subspace learning and classification to find a latent subspace where
samples are expected to be better classified; 2) progressively learning
multi-coupled projections to linearly approach the optimal mapping bridging the
original space with the most discriminative subspace; 3) locally embedding
manifold structure in each learnable latent subspace. Extensive experiments are
performed to demonstrate the superiority and effectiveness of the proposed
method in comparison with previous state-of-the-art methods.Comment: accepted in ECCV 201
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Face image super-resolution using 2D CCA
In this paper a face super-resolution method using two-dimensional canonical correlation analysis (2D CCA) is presented. A detail compensation step is followed to add high-frequency components to the reconstructed high-resolution face. Unlike most of the previous researches on face super-resolution algorithms that first transform the images into vectors, in our approach the relationship between the high-resolution and the low-resolution face image are maintained in their original 2D representation. In addition, rather than approximating the entire face, different parts of a face image are super-resolved separately to better preserve the local structure. The proposed method is compared with various state-of-the-art super-resolution algorithms using multiple evaluation criteria including face recognition performance. Results on publicly available datasets show that the proposed method super-resolves high quality face images which are very close to the ground-truth and performance gain is not dataset dependent. The method is very efficient in both the training and testing phases compared to the other approaches. © 2013 Elsevier B.V
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