2,028 research outputs found
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
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
Manifold Based Deep Learning: Advances and Machine Learning Applications
Manifolds are topological spaces that are locally Euclidean and find applications in dimensionality reduction, subspace learning, visual domain adaptation, clustering, and more. In this dissertation, we propose a framework for linear dimensionality reduction called the proxy matrix optimization (PMO) that uses the Grassmann manifold for optimizing over orthogonal matrix manifolds. PMO is an iterative and flexible method that finds the lower-dimensional projections for various linear dimensionality reduction methods by changing the objective function. PMO is suitable for Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), Canonical Correlation Analysis (CCA), Maximum Autocorrelation Factors (MAF), and Locality Preserving Projections (LPP). We extend PMO to incorporate robust Lp-norm versions of PCA and LDA, which uses fractional p-norms making them more robust to noisy data and outliers. The PMO method is designed to be realized as a layer in a neural network for maximum benefit. In order to do so, the incremental versions of PCA, LDA, and LPP are included in the PMO framework for problems where the data is not all available at once. Next, we explore the topic of domain shift in visual domain adaptation by combining concepts from spherical manifolds and deep learning. We investigate domain shift, which quantifies how well a model trained on a source domain adapts to a similar target domain with a metric called Spherical Optimal Transport (SpOT). We adopt the spherical manifold along with an orthogonal projection loss to obtain the features from the source and target domains. We then use the optimal transport with the cosine distance between the features as a way to measure the gap between the domains. We show, in our experiments with domain adaptation datasets, that SpOT does better than existing measures for quantifying domain shift and demonstrates a better correlation with the gain of transfer across domains
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