Solving the slate tile classification problem using a DAGSVM multiclassification algorithm based on SVM binary classifiers with a one-versus-all approach
Introduction
Cortes and Vapnik [1] developed the support vector machine (SVM) model in 1995 to solve a binary classification problem. Since then, this model has become a benchmark technique for pattern recognition problems [2] because of its flexibility, prediction capacity, parsimony and the global optimum character.
Different strategies for solving the multiclassification problem have been developed based on constructing SVM binary classifiers [3], [4] according to either the one-versus-one approach, which consists of confronting each class with each other class [5], or the one-versus-all approach, which consists of confronting each class with all the other classes together [6]. Another classification strategy is the directed acyclic graph (DAG) [7] with a perceptron in each node, along with the adaptive version [8] and the integration of neural networks to form a DAG-multilayer perceptron structure [9], [10]. Other studies from around the same period made adaptations to the SVM algorithm; these include the approach by Cramer and Singer [11], [12], [13] based on the design of output codes and the approach by Manikandan [14], which explored the problem of isolated digit recognition.
We describe a new SVM binary classifier strategy for solving the multiclassification problem based on combining the one-versus-all and DAG. The proposed methodology was validated using data sets from the UCI Machine Learning Repository [15], frequently used to evaluate new algorithms [16], [17], [18], [19], [20].
The new classification strategy described in this study was also validated for the problem of classifying slate tiles. In the slate production process, the final stage is the manual classification of tiles in commercial categories. Martinez et al. [21] describe the application of machine learning techniques to the problem of classifying slate tiles on the basis of objective information extracted by a 2D–3D laser scanner [22]. This research work demonstrated the possibility of characterizing the slate tiles according to their defects described by the Spanish UNE-EN 12326–1 standard using a hybrid system that acquires images of the tiles and applies a series of mathematical algorithms to detect the defects.
The article is laid out as follows: first we outline the mathematical background, next we describe the validation of the methodology, then we discuss the results and finally we outline the main lessons learned from our research.
Section snippets
The classification problem
The classification problem can be interpreted as the partitioning of a population of individuals in mutually exclusive subpopulations . If the individuals are characterized by a vector of features with values in a set , and the classes are coded, for instance, by a variable , the classification problem consists of determining classification rule :according to some optimal criterion. That is, each example is assigned to the
Model validation
The model proposed in this study, based on binary SVM classifiers and a DAG with one-versus-all approach was validated using different UCI Machine Learning Repository data sets [15]. The error criterion used for evaluation was the error rate (ER),where represents the indicator function for the set which takes the value 1 when the real value and the estimated value do not coincide and where n represents the number of points in the test set.
To evaluate the
Conclusions
We have validated a novel classification strategy for solving a multiclassification problem based on one-versus-all SVM binary classifiers and the construction of a DAG.
The model was validated using different UCI Machine Learning Repository data sets covering different classification problem scenarios. For these four data sets four multiclassification models were implemented based on the construction of binary SVM classifiers using the one-versus-one, one-versus-all and DAG one-versus-one
Acknowledgements
J.M. Matias’ research and J. Taboada’s research are both funded by the Spanish Ministry of Education and Science under Grant MTM2008-03010 and Grant No. BIA2007-66218, respectively, and J. Martinez’ research is funded by the Spanish Ministry of Science and Technology through research project ECO2011-22650. C. Iglesias is acknowledged to Spanish Ministry of Education for the FPU 12-02283 grant.
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