Margin Error Bounds for Support Vector Machines on Reproducing Kernel Banach Spaces

Support vector machines, which maximize the margin from patterns to the separation hyperplane subject to correct classification, have received remarkable success in machine learning. Margin error bounds based on Hilbert spaces have been introduced in the literature to justify the strategy of maximizing the margin in SVM. Recently, there has been much interest in developing Banach space methods for machine learning. Large margin classification in Banach spaces is a focus of such attempts. In this letter we establish a margin error bound for the SVM on reproducing kernel Banach spaces, thus supplying statistical justification for large-margin classification in Banach spaces.

Energy Based Large Margin Classification of Gaussian Mixture Model

Large margin GMMs have many parallels to large margin nearest neighbors (LMNN), but with classes modeled by ellipsoids instead of each input data and its target neighbors by hyper-ellipsoid. Large margin GMMs naturally scales to large problems in multi-way classification. Based on large margin GMM classification, we develop a new classification method, i.e., energy based large margin classification of Gaussian mixture mode (ELM-GMM). Experiment shows that this new approach outperforms the large margin GMMs.