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Sergio Escalera, Oriol Pujol, & Petia Radeva. (2009). Separability of Ternary Codes for Sparse Designs of Error-Correcting Output Codes. PRL - Pattern Recognition Letters, 30(3), 285–297.
Abstract: Error Correcting Output Codes (ECOC) represent a successful framework to deal with multi-class categorization problems based on combining binary classifiers. In this paper, we present a new formulation of the ternary ECOC distance and the error-correcting capabilities in the ternary ECOC framework. Based on the new measure, we stress on how to design coding matrices preventing codification ambiguity and propose a new Sparse Random coding matrix with ternary distance maximization. The results on the UCI Repository and in a real speed traffic categorization problem show that when the coding design satisfies the new ternary measures, significant performance improvement is obtained independently of the decoding strategy applied.
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Sergio Escalera, Alicia Fornes, O. Pujol, Petia Radeva, Gemma Sanchez, & Josep Llados. (2009). Blurred Shape Model for Binary and Grey-level Symbol Recognition. PRL - Pattern Recognition Letters, 30(15), 1424–1433.
Abstract: Many symbol recognition problems require the use of robust descriptors in order to obtain rich information of the data. However, the research of a good descriptor is still an open issue due to the high variability of symbols appearance. Rotation, partial occlusions, elastic deformations, intra-class and inter-class variations, or high variability among symbols due to different writing styles, are just a few problems. In this paper, we introduce a symbol shape description to deal with the changes in appearance that these types of symbols suffer. The shape of the symbol is aligned based on principal components to make the recognition invariant to rotation and reflection. Then, we present the Blurred Shape Model descriptor (BSM), where new features encode the probability of appearance of each pixel that outlines the symbols shape. Moreover, we include the new descriptor in a system to deal with multi-class symbol categorization problems. Adaboost is used to train the binary classifiers, learning the BSM features that better split symbol classes. Then, the binary problems are embedded in an Error-Correcting Output Codes framework (ECOC) to deal with the multi-class case. The methodology is evaluated on different synthetic and real data sets. State-of-the-art descriptors and classifiers are compared, showing the robustness and better performance of the present scheme to classify symbols with high variability of appearance.
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Sergio Escalera, Oriol Pujol, & Petia Radeva. (2010). Re-coding ECOCs without retraining. PRL - Pattern Recognition Letters, 31(7), 555–562.
Abstract: A standard way to deal with multi-class categorization problems is by the combination of binary classifiers in a pairwise voting procedure. Recently, this classical approach has been formalized in the Error-Correcting Output Codes (ECOC) framework. In the ECOC framework, the one-versus-one coding demonstrates to achieve higher performance than the rest of coding designs. The binary problems that we train in the one-versus-one strategy are significantly smaller than in the rest of designs, and usually easier to be learnt, taking into account the smaller overlapping between classes. However, a high percentage of the positions coded by zero of the coding matrix, which implies a high sparseness degree, does not codify meta-class membership information. In this paper, we show that using the training data we can redefine without re-training, in a problem-dependent way, the one-versus-one coding matrix so that the new coded information helps the system to increase its generalization capability. Moreover, the new re-coding strategy is generalized to be applied over any binary code. The results over several UCI Machine Learning repository data sets and two real multi-class problems show that performance improvements can be obtained re-coding the classical one-versus-one and Sparse random designs compared to different state-of-the-art ECOC configurations.
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Sergio Escalera, David Masip, Eloi Puertas, Petia Radeva, & Oriol Pujol. (2011). Online Error-Correcting Output Codes. PRL - Pattern Recognition Letters, 32(3), 458–467.
Abstract: IF JCR CCIA 1.303 2009 54/103
This article proposes a general extension of the error correcting output codes framework to the online learning scenario. As a result, the final classifier handles the addition of new classes independently of the base classifier used. In particular, this extension supports the use of both online example incremental and batch classifiers as base learners. The extension of the traditional problem independent codings one-versus-all and one-versus-one is introduced. Furthermore, two new codings are proposed, unbalanced online ECOC and a problem dependent online ECOC. This last online coding technique takes advantage of the problem data for minimizing the number of dichotomizers used in the ECOC framework while preserving a high accuracy. These techniques are validated on an online setting of 11 data sets from UCI database and applied to two real machine vision applications: traffic sign recognition and face recognition. As a result, the online ECOC techniques proposed provide a feasible and robust way for handling new classes using any base classifier.
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Miguel Angel Bautista, Sergio Escalera, Xavier Baro, Petia Radeva, Jordi Vitria, & Oriol Pujol. (2011). Minimal Design of Error-Correcting Output Codes. PRL - Pattern Recognition Letters, 33(6), 693–702.
Abstract: IF JCR CCIA 1.303 2009 54/103
The classification of large number of object categories is a challenging trend in the pattern recognition field. In literature, this is often addressed using an ensemble of classifiers. In this scope, the Error-correcting output codes framework has demonstrated to be a powerful tool for combining classifiers. However, most state-of-the-art ECOC approaches use a linear or exponential number of classifiers, making the discrimination of a large number of classes unfeasible. In this paper, we explore and propose a minimal design of ECOC in terms of the number of classifiers. Evolutionary computation is used for tuning the parameters of the classifiers and looking for the best minimal ECOC code configuration. The results over several public UCI datasets and different multi-class computer vision problems show that the proposed methodology obtains comparable (even better) results than state-of-the-art ECOC methodologies with far less number of dichotomizers.
Keywords: Multi-class classification; Error-correcting output codes; Ensemble of classifiers
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