3,012 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
Generalized Sparse Discriminant Analysis for Event-Related Potential Classification
A brain computer interface (BCI) is a system which provides direct communication between the mind of a person and the outside world by using only brain activity (EEG). The event-related potential (ERP)-based BCI problem consists of a binary pattern recognition. Linear discriminant analysis (LDA) is widely used to solve this type of classification problems, but it fails when the number of features is large relative to the number of observations. In this work we propose a penalized version of the sparse discriminant analysis (SDA), called generalized sparse discriminant analysis (GSDA), for binary classification. This method inherits both the discriminative feature selection and classification properties of SDA and it also improves SDA performance through the addition of Kullback-Leibler class discrepancy information. The GSDA method is designed to automatically select the optimal regularization parameters. Numerical experiments with two real ERP-EEG datasets show that, on one hand, GSDA outperforms standard SDA in the sense of classification performance, sparsity and required computing time, and, on the other hand, it also yields better overall performances, compared to well-known ERP classification algorithms, for single-trial ERP classification when insufficient training samples are available. Hence, GSDA constitute a potential useful method for reducing the calibration times in ERP-based BCI systems.Fil: Peterson, Victoria. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - Santa Fe. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de IngenierÃa y Ciencias HÃdricas. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional; ArgentinaFil: Rufiner, Hugo Leonardo. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - Santa Fe. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de IngenierÃa y Ciencias HÃdricas. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional; Argentina. Universidad Nacional de Entre RÃos. Facultad de IngenierÃa; ArgentinaFil: Spies, Ruben Daniel. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina. Universidad Nacional del Litoral. Facultad de IngenierÃa QuÃmica; Argentin
Dimension Reduction by Mutual Information Discriminant Analysis
In the past few decades, researchers have proposed many discriminant analysis
(DA) algorithms for the study of high-dimensional data in a variety of
problems. Most DA algorithms for feature extraction are based on
transformations that simultaneously maximize the between-class scatter and
minimize the withinclass scatter matrices. This paper presents a novel DA
algorithm for feature extraction using mutual information (MI). However, it is
not always easy to obtain an accurate estimation for high-dimensional MI. In
this paper, we propose an efficient method for feature extraction that is based
on one-dimensional MI estimations. We will refer to this algorithm as mutual
information discriminant analysis (MIDA). The performance of this proposed
method was evaluated using UCI databases. The results indicate that MIDA
provides robust performance over different data sets with different
characteristics and that MIDA always performs better than, or at least
comparable to, the best performing algorithms.Comment: 13pages, 3 tables, International Journal of Artificial Intelligence &
Application
Effective Discriminative Feature Selection with Non-trivial Solutions
Feature selection and feature transformation, the two main ways to reduce
dimensionality, are often presented separately. In this paper, a feature
selection method is proposed by combining the popular transformation based
dimensionality reduction method Linear Discriminant Analysis (LDA) and sparsity
regularization. We impose row sparsity on the transformation matrix of LDA
through -norm regularization to achieve feature selection, and
the resultant formulation optimizes for selecting the most discriminative
features and removing the redundant ones simultaneously. The formulation is
extended to the -norm regularized case: which is more likely to
offer better sparsity when . Thus the formulation is a better
approximation to the feature selection problem. An efficient algorithm is
developed to solve the -norm based optimization problem and it is
proved that the algorithm converges when . Systematical experiments
are conducted to understand the work of the proposed method. Promising
experimental results on various types of real-world data sets demonstrate the
effectiveness of our algorithm
GhostVLAD for set-based face recognition
The objective of this paper is to learn a compact representation of image
sets for template-based face recognition. We make the following contributions:
first, we propose a network architecture which aggregates and embeds the face
descriptors produced by deep convolutional neural networks into a compact
fixed-length representation. This compact representation requires minimal
memory storage and enables efficient similarity computation. Second, we propose
a novel GhostVLAD layer that includes {\em ghost clusters}, that do not
contribute to the aggregation. We show that a quality weighting on the input
faces emerges automatically such that informative images contribute more than
those with low quality, and that the ghost clusters enhance the network's
ability to deal with poor quality images. Third, we explore how input feature
dimension, number of clusters and different training techniques affect the
recognition performance. Given this analysis, we train a network that far
exceeds the state-of-the-art on the IJB-B face recognition dataset. This is
currently one of the most challenging public benchmarks, and we surpass the
state-of-the-art on both the identification and verification protocols.Comment: Accepted by ACCV 201
Feature Selection and Dimensionality Reduction in Genomics and Proteomics
International audienceFinding reliable, meaningful patterns in data with high numbers of attributes can be extremely difficult. Feature selection helps us to decide what attributes or combination of attributes are most important for finding these patterns. In this chapter, we study feature selection methods for building classification models from high-throughput genomic (microarray) and proteomic (mass spectrometry) data sets. Thousands of feature candidates must be analyzed, compared and combined in such data sets. We describe the basics of four different approaches used for feature selection and illustrate their effects on an MS cancer proteomic data set. The closing discussion provides assistance in performing an analysis in high-dimensional genomic and proteomic data
Parsimonious Mahalanobis Kernel for the Classification of High Dimensional Data
The classification of high dimensional data with kernel methods is considered
in this article. Exploit- ing the emptiness property of high dimensional
spaces, a kernel based on the Mahalanobis distance is proposed. The computation
of the Mahalanobis distance requires the inversion of a covariance matrix. In
high dimensional spaces, the estimated covariance matrix is ill-conditioned and
its inversion is unstable or impossible. Using a parsimonious statistical
model, namely the High Dimensional Discriminant Analysis model, the specific
signal and noise subspaces are estimated for each considered class making the
inverse of the class specific covariance matrix explicit and stable, leading to
the definition of a parsimonious Mahalanobis kernel. A SVM based framework is
used for selecting the hyperparameters of the parsimonious Mahalanobis kernel
by optimizing the so-called radius-margin bound. Experimental results on three
high dimensional data sets show that the proposed kernel is suitable for
classifying high dimensional data, providing better classification accuracies
than the conventional Gaussian kernel
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