Classification is a machine learning method used in many practical applications: text mining, handwritten character recognition, face recognition, pattern classification, scene labeling, computer vision, natural langage processing. A classifier prediction results and training set information are often used to get a contingency table which is used to quantify the method quality through an evaluation measure. Such measure, typically a numerical value, allows to choose a suitable method among several. Many evaluation measures available in the literature are less accurate for a dataset with imbalanced classes. In this paper, the eigenvalues entropy is used as an evaluation measure for a binary or a multi-class problem. For a binary problem, relations are given between the eigenvalues and some commonly used measures, the sensitivity, the specificity, the area under the operating receiver characteristic curve and the Gini index. A by-product result of this paper is an estimate of the confusion matrix to deal with the curse of the imbalanced classes. Various data examples are used to show the better performance of the proposed evaluation measure over the gold standard measures available in the literature.

Extreme multi-label classification (XMC) aims to identify relevant subsets from numerous labels. Among the various approaches for XMC, tree-based linear models are effective due to their superior efficiency and simplicity. However, the space complexity of tree-based methods is not well-studied. Many past works assume that storing the model is not affordable and apply techniques such as pruning to save space, which may lead to performance loss. In this work, we conduct both theoretical and empirical analyses on the space to store a tree model under the assumption of sparse data, a condition frequently met in text data. We found that, some features may be unused when training binary classifiers in a tree method, resulting in zero values in the weight vectors. Hence, storing only non-zero elements can greatly save space. Our experimental results indicate that tree models can achieve up to a 95% reduction in storage space compared to the standard one-vs-rest method for multi-label text classification. Our research provides a simple procedure to estimate the size of a tree model before training any classifier in the tree nodes. Then, if the model size is already acceptable, this approach can help avoid modifying the model through weight pruning or other techniques.

Pairwise difference learning (PDL) has recently been introduced as a new meta-learning technique for regression. Instead of learning a mapping from instances to outcomes in the standard way, the key idea is to learn a function that takes two instances as input and predicts the difference between the respective outcomes. Given a function of this kind, predictions for a query instance are derived from every training example and then averaged. This paper extends PDL toward the task of classification and proposes a meta-learning technique for inducing a PDL classifier by solving a suitably defined (binary) classification problem on a paired version of the original training data. We analyze the performance of the PDL classifier in a large-scale empirical study and find that it outperforms state-of-the-art methods in terms of prediction performance. Last but not least, we provide an easy-to-use and publicly available implementation of PDL in a Python package.

Prediction using the ground truth sounds like an oxymoron in machine learning. However, such an unrealistic setting was used in hundreds, if not thousands of papers in the area of finding graph representations. To evaluate the multi-label problem of node classification by using the obtained representations, many works assume in the prediction stage that the number of labels of each test instance is known. In practice such ground truth information is rarely available, but we point out that such an inappropriate setting is now ubiquitous in this research area. We detailedly investigate why the situation occurs. Our analysis indicates that with unrealistic information, the performance is likely over-estimated. To see why suitable predictions were not used, we identify difficulties in applying some multi-label techniques. For the use in future studies, we propose simple and effective settings without using practically unknown information. Finally, we take this chance to conduct a fair and serious comparison of major graph-representation learning methods on multi-label node classification.

Many classification applications require accurate probability estimates in addition to good class separation but often classifiers are designed focusing only on the latter. Calibration is the process of improving probability estimates by post-processing but commonly used calibration algorithms work poorly on small data sets and assume the classification task to be binary. Both of these restrictions limit their real-world applicability. Previously introduced Data Generation and Grouping algorithm alleviates the problem posed by small data sets and in this article, we will demonstrate that its application to multi-class problems is also possible which solves the other limitation. Our experiments show that calibration error can be decreased using the proposed approach and the additional computational cost is acceptable.

The classification of multi-class microarray datasets is a hard task because of the small samples size in each class and the heavy overlaps among classes. To effectively solve these problems, we propose novel Error Correcting Output Code (ECOC) algorithm by Enhance Class Separability related Data Complexity measures during encoding process, named as ECOCECS. In this algorithm, two nearest neighbor related DC measures are deployed to extract the intrinsic overlapping information from microarray data. Our ECOC algorithm aims to search an optimal class split scheme by minimizing these measures. The class splitting process ends when each class is separated from others, and then the class assignment scheme is mapped as a coding matrix. Experiments are carried out on five microarray datasets, and results demonstrate the effectiveness and robustness of our method in comparison with six state-of-art ECOC methods. In short, our work confirm the probability of applying DC to ECOC framework.

In ECOC framework, the ternary coding strategy is widely deployed in coding process. It relabels classes with {"-1,0,1" }, where -1/1 means to assign the corresponding classes to the negative/positive group, and label 0 leads to ignore the corresponding classes in the training process. However, the application of hard labels may lose some information about the tendency of class distributions. Instead, we propose a Centroid distance-based Soft coding scheme to indicate such tendency, named as CSECOC. In our algorithm, Sequential Forward Floating Selection (SFFS) is applied to search an optimal class assignment by minimizing the ratio of intra-group and inter-group distance. In this way, a hard coding matrix is generated initially. Then we propose a measure, named as coverage, to describe the probability of a sample in a class falling to a correct group. The coverage of a class a group replace the corresponding hard element, so as to form a soft coding matrix. Compared with the hard ones, such soft elements can reflect the tendency of a class belonging to positive or negative group. Instead of classifiers, regressors are used as base learners in this algorithm. To the best of our knowledge, it is the first time that soft coding scheme has been proposed. The results on five UCI datasets show that compared with some state-of-art ECOC algorithms, our algorithm can produce comparable or better classification accuracy with small scale ensembles.

This paper is mainly concerned with the question of how to decompose multiclass classification problems into binary subproblems. We extend known Jensen-Shannon bounds on the Bayes risk of binary problems to hierarchical multiclass problems and use these bounds to develop a heuristic procedure for constructing hierarchical multiclass decomposition for multinomials. We test our method and compare it to the well known "all-pairs" decomposition. Our tests are performed using a new authorship determination benchmark test of machine learning authors. The new method consistently outperforms the all-pairs decomposition when the number of classes is small and breaks even on larger multiclass problems. Using both methods, the classification accuracy we achieve, using an SVM over a feature set consisting of both high frequency single tokens and high frequency token-pairs, appears to be exceptionally high compared to known results in authorship determination.

The focus of the paper is the problem of learning kernel operators from empirical data. We cast the kernel design problem as the construction of an accurate kernel from simple (and less accurate) base kernels. We use the boosting paradigm to perform the kernel construction process. To do so, we modify the booster so as to accommodate kernel operators. We also devise an efficient weak-learner for simple kernels that is based on generalized eigen vector decomposition. We demonstrate the effectiveness of our approach on synthetic data and on the USPS dataset. On the USPS dataset, the performance of the Perceptron algorithm with learned kernels is systematically better than a fixed RBF kernel.

The focus of the paper is the problem of learning kernel operators from empirical data. We cast the kernel design problem as the construction of an accurate kernel from simple (and less accurate) base kernels. We use the boosting paradigm to perform the kernel construction process. To do so, we modify the booster so as to accommodate kernel operators. We also devise an efficient weak-learner for simple kernels that is based on generalized eigen vector decomposition. We demonstrate the effectiveness of our approach on synthetic data and on the USPS dataset. On the USPS dataset, the performance of the Perceptron algorithm with learned kernels is systematically better than a fixed RBF kernel.