In the face of high-dimensional and complex data, effective subspace can preserve specific statistical properties and provide an appropriate representation of data, which generally facilitates the underlying tasks such as clustering or classification. Meanwhile, multiple kernel learning is a technique to combine multiple kernels from different feature spaces effectively. Thus, by incorporating multiple kernels into the process of subspace learning, different feature spaces can be projected into a unified subspace. This paper proposes the Multiple Kernel Subspace Learning (MKSL) for embedding the original space into a unified subspace. Multiple kernels of different feature spaces are combined by MKSL in the process of learning, which can extend the suitability for various applications. Moreover, to generate the optimal combination kernel of subspace learning, we propose a two-step iteration strategy to learn the appropriate kernel weights and transformation matrix of projecting simultaneously. Furthermore, our proposed formulation of MKSL can introduce different prior knowledge such as class information and neighborhood relationships. Thus it is competent to the unsupervised learning, semi-supervised learning, and supervised learning. Extensive experiments are conducted on diverse datasets, and the performances are comprehensively evaluated on different tasks. The experimental results indicate that the proposed algorithm is outstanding in unsupervised clustering task and effective in supervised and semi-supervised classification tasks.

Sampling method is one of the most commonly used techniques in dealing with imbalanced data. Most of the existing undersampling methods randomly select samples from negative class with replacement. However, it may lose some important information of the training data. Moreover, increasing the positive data by oversampling in high imbalanced situations may cause the overlapping problem. To overcome these problems, this paper proposes a hybrid sampling method. The method takes the distributions of the training data into consideration by the information entropy, thus distinguishing the important samples in the undersampling procedure. Meanwhile, since the positive data only extend to the size of each subset of the negative class in the oversampling, the overlapping problem is relieved. Further, the method retains all the data in the training procedure and generates various data views from the original training data. Then each view is handled with an individual basic classifier. Finally, all the basic classifiers are combined by the ensemble method. The newly proposed method is named as Entropy-based Hybrid Sampling Ensemble Learning (EHSEL). In addition, the EHSEL is applied to three different kinds of basic classifiers to validate its robustness. Experiments results show the great effectiveness of the EHSEL on real-world imbalanced data sets.

Multiple Kernel Learning (MKL) algorithm effectively combines different kernels to improve the performance of classification. Most MKL algorithms implicitly map samples into feature space by the form of inner-product. In contrast, Multiple Empirical Kernel Learning (MEKL) can explicitly map the input spaces into feature spaces so that the mapped feature vectors are explicitly represented, which is easy to process and analyze the adaptability of kernels for input space. Meanwhile, in order to pay attention to the structure and discriminant information of samples in empirical feature space, inspired by discriminant locality preserving projections, we introduce the discriminant locality preservation regularization into MEKL framework to propose the Multiple Empirical Kernel Learning with Discriminant Locality Preservation (MEKL-DLP). Experiments conducted on real-world datasets validate the effectiveness of the proposed MEKL-DLP compared with the classical kernel-based algorithms and state-of-art MKL algorithms.