A support vector machine (SVM) is a popular algorithm for classification learning. The classical SVM effectively manages classification tasks defined by means of numerical attributes. However, both numerical and nominal attributes are used in practical tasks and the classical SVM does not fully consider the difference between them. Nominal attributes are usually regarded as numerical after coding. This may deteriorate the performance of learning algorithms. In this study, we propose a novel SVM algorithm for learning with heterogeneous data, known as a heterogeneous SVM (HSVM). The proposed algorithm learns an mapping to embed nominal attributes into a real space by minimizing an estimated generalization error, instead of by direct coding. Extensive experiments are conducted, and some interesting results are obtained. The experiments show that HSVM improves classification performance for both nominal and heterogeneous data.

Monotonic classification is a kind of special task in machine learning and pattern recognition. Monotonicity constraints between features and decision should be taken into account in these tasks. However, most existing techniques are not able to discover and represent the ordinal structures in monotonic datasets. Thus, they are inapplicable to monotonic classification. Feature selection has been proven effective in improving classification performance and avoiding overfitting. To the best of our knowledge, no technique has been specially designed to select features in monotonic classification until now. In this paper, we introduce a function, which is called rank mutual information, to evaluate monotonic consistency between features and decision in monotonic tasks. This function combines the advantages of dominance rough sets in reflecting ordinal structures and mutual information in terms of robustness. Then, rank mutual information is integrated with the search strategy of min-redundancy and max-relevance to compute optimal subsets of features. A collection of numerical experiments are given to show the effectiveness of the proposed technique.

Wind power curve modeling is a challenging task due to the existence of inconsistent data, in which the recorded wind power is far away from the theoretical wind power at a given wind speed. In this case, confronted with these samples, the estimated errors of wind power will become large. Thus, the estimated errors will present two properties: heteroscedasticity and error distribution with a long tail. In this paper, according to the above-mentioned error characteristics, the heteroscedastic spline regression model (HSRM) and robust spline regression model (RSRM) are proposed to obtain more accurate power curves even in the presence of the inconsistent samples. The results of power curve modeling on the real-world data show the effectiveness of HSRM and RSRM in different seasons. As HSRM and RSRM are optimized by variational Bayesian, except the deterministic power curves, probabilistic power curves, which can be used to detect the inconsistent samples, can also be obtained. Additionally, with the data processed by replacing the wind power in the detected inconsistent samples with the wind power on the estimated power curve, the forecasting results show that more accurate wind power forecasts can be obtained using the above-mentioned data processing method.

Given a group photograph, it is interesting and useful to judge whether the characters in it share specific kinship relation, such as father-daughter, father-son, mother-daughter, or mother-son. Recently, facial image-based kinship verification has attracted wide attention in computer vision. Some metric learning algorithms have been developed for improving kinship verification. However, most of the existing algorithms ignore fusing multiple feature representations and utilizing kernel techniques. In this paper, we develop a novel weighted graph embedding-based metric learning (WGEML) framework for kinship verification. Inspired by the fact that family members usually show high similarity in facial features like eyes, noses, and mouths, despite their diversity, we jointly learn multiple metrics by constructing an intrinsic graph and two penalty graphs to characterize the intraclass compactness and interclass separability for each feature representation, respectively, so that both the consistency and complementarity among multiple features can be fully exploited. Meanwhile, combination weights are determined through a weighted graph embedding framework. Furthermore, we present a kernelized version of WGEML to tackle nonlinear problems. Experimental results demonstrate both the effectiveness and efficiency of our proposed methods.

Due to complex semantics, a sample may be associated with multiple labels in various classification and recognition tasks. Multilabel learning generates training models to map feature vectors to multiple labels. There are several significant challenges in multilabel learning. Samples in multilabel learning are usually described with high-dimensional features and some features may be sequentially extracted. Thus, we do not know the full feature set at the beginning of learning, referred to as streaming features. In this paper, we introduce fuzzy mutual information to evaluate the quality of features in multilabel learning, and design efficient algorithms to conduct multilabel feature selection when the feature space is completely known or partially known in advance. These algorithms are called multilabel feature selection with label correlation (MUCO) and multilabel streaming feature selection (MSFS), respectively. MSFS consists of two key steps: online relevance analysis and online redundancy analysis. In addition, we design a metric to measure the correlation between the label sets, and both MUCO and MSFS take label correlation to consideration. The proposed algorithms are not only able to select features from streaming features, but also able to select features for ordinal multilabel learning. However streaming feature selection is more efficient. The proposed algorithms are tested with a collection of multilabel learning tasks. The experimental results illustrate the effectiveness of the proposed algorithms.