4,152 research outputs found
Variable selection for the multicategory SVM via adaptive sup-norm regularization
The Support Vector Machine (SVM) is a popular classification paradigm in
machine learning and has achieved great success in real applications. However,
the standard SVM can not select variables automatically and therefore its
solution typically utilizes all the input variables without discrimination.
This makes it difficult to identify important predictor variables, which is
often one of the primary goals in data analysis. In this paper, we propose two
novel types of regularization in the context of the multicategory SVM (MSVM)
for simultaneous classification and variable selection. The MSVM generally
requires estimation of multiple discriminating functions and applies the argmax
rule for prediction. For each individual variable, we propose to characterize
its importance by the supnorm of its coefficient vector associated with
different functions, and then minimize the MSVM hinge loss function subject to
a penalty on the sum of supnorms. To further improve the supnorm penalty, we
propose the adaptive regularization, which allows different weights imposed on
different variables according to their relative importance. Both types of
regularization automate variable selection in the process of building
classifiers, and lead to sparse multi-classifiers with enhanced
interpretability and improved accuracy, especially for high dimensional low
sample size data. One big advantage of the supnorm penalty is its easy
implementation via standard linear programming. Several simulated examples and
one real gene data analysis demonstrate the outstanding performance of the
adaptive supnorm penalty in various data settings.Comment: Published in at http://dx.doi.org/10.1214/08-EJS122 the Electronic
Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Pareto-Path Multi-Task Multiple Kernel Learning
A traditional and intuitively appealing Multi-Task Multiple Kernel Learning
(MT-MKL) method is to optimize the sum (thus, the average) of objective
functions with (partially) shared kernel function, which allows information
sharing amongst tasks. We point out that the obtained solution corresponds to a
single point on the Pareto Front (PF) of a Multi-Objective Optimization (MOO)
problem, which considers the concurrent optimization of all task objectives
involved in the Multi-Task Learning (MTL) problem. Motivated by this last
observation and arguing that the former approach is heuristic, we propose a
novel Support Vector Machine (SVM) MT-MKL framework, that considers an
implicitly-defined set of conic combinations of task objectives. We show that
solving our framework produces solutions along a path on the aforementioned PF
and that it subsumes the optimization of the average of objective functions as
a special case. Using algorithms we derived, we demonstrate through a series of
experimental results that the framework is capable of achieving better
classification performance, when compared to other similar MTL approaches.Comment: Accepted by IEEE Transactions on Neural Networks and Learning System
On Security and Sparsity of Linear Classifiers for Adversarial Settings
Machine-learning techniques are widely used in security-related applications,
like spam and malware detection. However, in such settings, they have been
shown to be vulnerable to adversarial attacks, including the deliberate
manipulation of data at test time to evade detection. In this work, we focus on
the vulnerability of linear classifiers to evasion attacks. This can be
considered a relevant problem, as linear classifiers have been increasingly
used in embedded systems and mobile devices for their low processing time and
memory requirements. We exploit recent findings in robust optimization to
investigate the link between regularization and security of linear classifiers,
depending on the type of attack. We also analyze the relationship between the
sparsity of feature weights, which is desirable for reducing processing cost,
and the security of linear classifiers. We further propose a novel octagonal
regularizer that allows us to achieve a proper trade-off between them. Finally,
we empirically show how this regularizer can improve classifier security and
sparsity in real-world application examples including spam and malware
detection
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
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