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Texture Descriptors for The Generic Pattern Classification Problem 107

Min-Sum matrix Products (MSP) (Felzenszwalb & McAuley, 2011), which has been
shown to efficiently solve the Maximum-A-Posteriori (MAP) inference problem,
Nonnegative Matrix Factorization (NMF) (Seung & Lee, 2001), which has become a
popular choice for solving general pattern recognition problems, and the Matrix-pattern-
oriented Modified Ho-Kashyap classifier (MatMHKS) (S. Chen, Wang, & Tian, 2007),
which significantly decreases memory requirements. MatMHKS has recently been
expanded to UMatMHKS (H. Wang & Ahuja, 2005), so named because it combines
matrix learning with Universum learning (Weston, Collobert, Sinz, Bottou, & Vapnik,
2006), a combination that was shown in that study to improve the generalization
performance of classifiers.
In the last ten years, many studies focused on generic classification problems have
investigated the discriminative gains offered by matrix feature extraction methods (see,
for instance, (S. C. Chen, Zhu, Zhang, & Yang, 2005; Liu & Chen, 2006; Z. Wang &
Chen, 2008; Z. Wang et al., 2008)). Relevant to the work presented here is the
development of novel methods that take vectors and reshape them into matrices so that
state-of-the-art two-dimensional feature extraction methods can be applied. Some studies
along these lines include the reshaping methods investigated in (Z. Wang & Chen, 2008)
and (Z. Wang et al., 2008) that were found capable of diversifying the design of
classifiers, a diversification that was then exploited by a technique based on AdaBoost. In
(Kim & Choi, 2007) a composite feature matrix representation, derived from discriminant
analysis, was proposed. A composite feature takes a number of primitive features and
corresponds them to an input variable. In (Loris Nanni, 2011) Local Ternary Patterns
(LTP), a variant of LBP, were extracted from vectors rearranged into fifty matrices by
random assignment; an SVM was then trained on each of these matrices, and the results
were combined using the mean rule. This method led the authors in (Loris Nanni, 2011)
to observe that both one-dimensional vector descriptors and two-dimensional texture
descriptors can be combined to improve classifier performance; moreover, it was shown
that linear SVMs consistently perform well with texture descriptors.
In this work, we propose a new classification system, composed of an ensemble of
Support Vector Machines (SVMs). The ensemble is built training each SVM with a
different set of features. Three novel approaches for representing a feature vector as an
image are proposed; texture descriptors are then extracted from the images and used to
train an SVM. To validate this idea, several experiments are carried out on several
datasets.

Proposed Approach

As mentioned in the introduction, it is quite common to represent a pattern as a one
dimensional feature vector, but a vector is not necessarily the most effect shape for