1,136 research outputs found
Discriminative Elastic-Net Regularized Linear Regression
In this paper, we aim at learning compact and discriminative linear regression models. Linear regression has been widely used in different problems. However, most of the existing linear regression methods exploit the conventional zeroone matrix as the regression targets, which greatly narrows the flexibility of the regression model. Another major limitation of theses methods is that the learned projection matrix fails to precisely project the image features to the target space due to their weak discriminative capability. To this end, we present an elastic-net regularized linear regression (ENLR) framework, and develop two robust linear regression models which possess the following special characteristics. First, our methods exploit two particular strategies to enlarge the margins of different classes by relaxing the strict binary targets into a more feasible variable matrix. Second, a robust elastic-net regularization of singular values is introduced to enhance the compactness and effectiveness of the learned projection matrix. Third, the resulting optimization problem of ENLR has a closed-form solution in each iteration, which can be solved efficiently. Finally, rather than directly exploiting the projection matrix for recognition, our methods employ the transformed features as the new discriminate representations to make final image classification. Compared with the traditional linear regression model and some of its variants, our method is much more accurate in image classification. Extensive experiments conducted on publicly available datasets well demonstrate that the proposed framework can outperform the state-of-the-art methods. The MATLAB codes of our methods can be available at http://www.yongxu.org/lunwen.html
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
Regularized brain reading with shrinkage and smoothing
Functional neuroimaging measures how the brain responds to complex stimuli.
However, sample sizes are modest, noise is substantial, and stimuli are high
dimensional. Hence, direct estimates are inherently imprecise and call for
regularization. We compare a suite of approaches which regularize via
shrinkage: ridge regression, the elastic net (a generalization of ridge
regression and the lasso), and a hierarchical Bayesian model based on small
area estimation (SAE). We contrast regularization with spatial smoothing and
combinations of smoothing and shrinkage. All methods are tested on functional
magnetic resonance imaging (fMRI) data from multiple subjects participating in
two different experiments related to reading, for both predicting neural
response to stimuli and decoding stimuli from responses. Interestingly, when
the regularization parameters are chosen by cross-validation independently for
every voxel, low/high regularization is chosen in voxels where the
classification accuracy is high/low, indicating that the regularization
intensity is a good tool for identification of relevant voxels for the
cognitive task. Surprisingly, all the regularization methods work about equally
well, suggesting that beating basic smoothing and shrinkage will take not only
clever methods, but also careful modeling.Comment: Published at http://dx.doi.org/10.1214/15-AOAS837 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Bounded Coordinate-Descent for Biological Sequence Classification in High Dimensional Predictor Space
We present a framework for discriminative sequence classification where the
learner works directly in the high dimensional predictor space of all
subsequences in the training set. This is possible by employing a new
coordinate-descent algorithm coupled with bounding the magnitude of the
gradient for selecting discriminative subsequences fast. We characterize the
loss functions for which our generic learning algorithm can be applied and
present concrete implementations for logistic regression (binomial
log-likelihood loss) and support vector machines (squared hinge loss).
Application of our algorithm to protein remote homology detection and remote
fold recognition results in performance comparable to that of state-of-the-art
methods (e.g., kernel support vector machines). Unlike state-of-the-art
classifiers, the resulting classification models are simply lists of weighted
discriminative subsequences and can thus be interpreted and related to the
biological problem
Pathway-Based Genomics Prediction using Generalized Elastic Net.
We present a novel regularization scheme called The Generalized Elastic Net (GELnet) that incorporates gene pathway information into feature selection. The proposed formulation is applicable to a wide variety of problems in which the interpretation of predictive features using known molecular interactions is desired. The method naturally steers solutions toward sets of mechanistically interlinked genes. Using experiments on synthetic data, we demonstrate that pathway-guided results maintain, and often improve, the accuracy of predictors even in cases where the full gene network is unknown. We apply the method to predict the drug response of breast cancer cell lines. GELnet is able to reveal genetic determinants of sensitivity and resistance for several compounds. In particular, for an EGFR/HER2 inhibitor, it finds a possible trans-differentiation resistance mechanism missed by the corresponding pathway agnostic approach
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 Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de Ingeniería y Ciencias Hídricas. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional; ArgentinaFil: Rufiner, Hugo Leonardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de Ingeniería y Ciencias Hídricas. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional; Argentina. Universidad Nacional de Entre Ríos. Facultad de Ingeniería; ArgentinaFil: Spies, Ruben Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico 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 Ingeniería Química; Argentin
Binary Linear Classification and Feature Selection via Generalized Approximate Message Passing
For the problem of binary linear classification and feature selection, we
propose algorithmic approaches to classifier design based on the generalized
approximate message passing (GAMP) algorithm, recently proposed in the context
of compressive sensing. We are particularly motivated by problems where the
number of features greatly exceeds the number of training examples, but where
only a few features suffice for accurate classification. We show that
sum-product GAMP can be used to (approximately) minimize the classification
error rate and max-sum GAMP can be used to minimize a wide variety of
regularized loss functions. Furthermore, we describe an
expectation-maximization (EM)-based scheme to learn the associated model
parameters online, as an alternative to cross-validation, and we show that
GAMP's state-evolution framework can be used to accurately predict the
misclassification rate. Finally, we present a detailed numerical study to
confirm the accuracy, speed, and flexibility afforded by our GAMP-based
approaches to binary linear classification and feature selection
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