3,232 research outputs found
Large Margin Image Set Representation and Classification
In this paper, we propose a novel image set representation and classification
method by maximizing the margin of image sets. The margin of an image set is
defined as the difference of the distance to its nearest image set from
different classes and the distance to its nearest image set of the same class.
By modeling the image sets by using both their image samples and their affine
hull models, and maximizing the margins of the images sets, the image set
representation parameter learning problem is formulated as an minimization
problem, which is further optimized by an expectation -maximization (EM)
strategy with accelerated proximal gradient (APG) optimization in an iterative
algorithm. To classify a given test image set, we assign it to the class which
could provide the largest margin. Experiments on two applications of
video-sequence-based face recognition demonstrate that the proposed method
significantly outperforms state-of-the-art image set classification methods in
terms of both effectiveness and efficiency
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
Nonlinear Supervised Dimensionality Reduction via Smooth Regular Embeddings
The recovery of the intrinsic geometric structures of data collections is an
important problem in data analysis. Supervised extensions of several manifold
learning approaches have been proposed in the recent years. Meanwhile, existing
methods primarily focus on the embedding of the training data, and the
generalization of the embedding to initially unseen test data is rather
ignored. In this work, we build on recent theoretical results on the
generalization performance of supervised manifold learning algorithms.
Motivated by these performance bounds, we propose a supervised manifold
learning method that computes a nonlinear embedding while constructing a smooth
and regular interpolation function that extends the embedding to the whole data
space in order to achieve satisfactory generalization. The embedding and the
interpolator are jointly learnt such that the Lipschitz regularity of the
interpolator is imposed while ensuring the separation between different
classes. Experimental results on several image data sets show that the proposed
method outperforms traditional classifiers and the supervised dimensionality
reduction algorithms in comparison in terms of classification accuracy in most
settings
Implicitly Constrained Semi-Supervised Linear Discriminant Analysis
Semi-supervised learning is an important and active topic of research in
pattern recognition. For classification using linear discriminant analysis
specifically, several semi-supervised variants have been proposed. Using any
one of these methods is not guaranteed to outperform the supervised classifier
which does not take the additional unlabeled data into account. In this work we
compare traditional Expectation Maximization type approaches for
semi-supervised linear discriminant analysis with approaches based on intrinsic
constraints and propose a new principled approach for semi-supervised linear
discriminant analysis, using so-called implicit constraints. We explore the
relationships between these methods and consider the question if and in what
sense we can expect improvement in performance over the supervised procedure.
The constraint based approaches are more robust to misspecification of the
model, and may outperform alternatives that make more assumptions on the data,
in terms of the log-likelihood of unseen objects.Comment: 6 pages, 3 figures and 3 tables. International Conference on Pattern
Recognition (ICPR) 2014, Stockholm, Swede
A Novel Hybrid Dimensionality Reduction Method using Support Vector Machines and Independent Component Analysis
Due to the increasing demand for high dimensional data analysis from various applications such as electrocardiogram signal analysis and gene expression analysis for cancer detection, dimensionality reduction becomes a viable process to extracts essential information from data such that the high-dimensional data can be represented in a more condensed form with much lower dimensionality to both improve classification accuracy and reduce computational complexity. Conventional dimensionality reduction methods can be categorized into stand-alone and hybrid approaches. The stand-alone method utilizes a single criterion from either supervised or unsupervised perspective. On the other hand, the hybrid method integrates both criteria. Compared with a variety of stand-alone dimensionality reduction methods, the hybrid approach is promising as it takes advantage of both the supervised criterion for better classification accuracy and the unsupervised criterion for better data representation, simultaneously. However, several issues always exist that challenge the efficiency of the hybrid approach, including (1) the difficulty in finding a subspace that seamlessly integrates both criteria in a single hybrid framework, (2) the robustness of the performance regarding noisy data, and (3) nonlinear data representation capability.
This dissertation presents a new hybrid dimensionality reduction method to seek projection through optimization of both structural risk (supervised criterion) from Support Vector Machine (SVM) and data independence (unsupervised criterion) from Independent Component Analysis (ICA). The projection from SVM directly contributes to classification performance improvement in a supervised perspective whereas maximum independence among features by ICA construct projection indirectly achieving classification accuracy improvement due to better intrinsic data representation in an unsupervised perspective. For linear dimensionality reduction model, I introduce orthogonality to interrelate both projections from SVM and ICA while redundancy removal process eliminates a part of the projection vectors from SVM, leading to more effective dimensionality reduction. The orthogonality-based linear hybrid dimensionality reduction method is extended to uncorrelatedness-based algorithm with nonlinear data representation capability. In the proposed approach, SVM and ICA are integrated into a single framework by the uncorrelated subspace based on kernel implementation.
Experimental results show that the proposed approaches give higher classification performance with better robustness in relatively lower dimensions than conventional methods for high-dimensional datasets
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