2,906 research outputs found
Simultaneous Spectral-Spatial Feature Selection and Extraction for Hyperspectral Images
In hyperspectral remote sensing data mining, it is important to take into
account of both spectral and spatial information, such as the spectral
signature, texture feature and morphological property, to improve the
performances, e.g., the image classification accuracy. In a feature
representation point of view, a nature approach to handle this situation is to
concatenate the spectral and spatial features into a single but high
dimensional vector and then apply a certain dimension reduction technique
directly on that concatenated vector before feed it into the subsequent
classifier. However, multiple features from various domains definitely have
different physical meanings and statistical properties, and thus such
concatenation hasn't efficiently explore the complementary properties among
different features, which should benefit for boost the feature
discriminability. Furthermore, it is also difficult to interpret the
transformed results of the concatenated vector. Consequently, finding a
physically meaningful consensus low dimensional feature representation of
original multiple features is still a challenging task. In order to address the
these issues, we propose a novel feature learning framework, i.e., the
simultaneous spectral-spatial feature selection and extraction algorithm, for
hyperspectral images spectral-spatial feature representation and
classification. Specifically, the proposed method learns a latent low
dimensional subspace by projecting the spectral-spatial feature into a common
feature space, where the complementary information has been effectively
exploited, and simultaneously, only the most significant original features have
been transformed. Encouraging experimental results on three public available
hyperspectral remote sensing datasets confirm that our proposed method is
effective and efficient
A dual framework for low-rank tensor completion
One of the popular approaches for low-rank tensor completion is to use the
latent trace norm regularization. However, most existing works in this
direction learn a sparse combination of tensors. In this work, we fill this gap
by proposing a variant of the latent trace norm that helps in learning a
non-sparse combination of tensors. We develop a dual framework for solving the
low-rank tensor completion problem. We first show a novel characterization of
the dual solution space with an interesting factorization of the optimal
solution. Overall, the optimal solution is shown to lie on a Cartesian product
of Riemannian manifolds. Furthermore, we exploit the versatile Riemannian
optimization framework for proposing computationally efficient trust region
algorithm. The experiments illustrate the efficacy of the proposed algorithm on
several real-world datasets across applications.Comment: Aceepted to appear in Advances of Nueral Information Processing
Systems (NIPS), 2018. A shorter version appeared in the NIPS workshop on
Synergies in Geometric Data Analysis 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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