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Our solution builds on a kernel-based method called the support vector machine (SVM) for determining the locations of the nodes. The basic SVM algorithm contains two steps: (1) one-region classification using the SVM; and (2) multi-region localization which is a repeated application of one-region classification for a number of different regions. In this paper, we first analyze the error effects of the choice of regions in the multi-region localization, which influences the accuracy of the localization results significantly. The realization of a choice of regions is posed as a beacon node coverage problem, i.e., the spatial distribution of the beacon nodes is determined from the coverage point of view. Second, we develop a method to arrange the regions, which we call expanded coverage region distribution, in order to avoid the problem of border effects in existing solutions. We show that expanded cover region distribution can reduce the localization errors. Our results show that, by optimally choosing and arranging the regions based on our analysis, we can significantly enhance the performance of SVM based localization. Furthermore, the optimal choice of regions to avoid the border effects can be similarly applied in other kernel-based learning methods for localization.

A foundational problem in kernel-based semi-supervised learning is the design of suitable kernels which can properly reflect the underlying data manifold. One of the most well-known semi-supervised kernel learning approaches is the spectral kernel learning methodology which usually tunes the spectra of the graph Laplacian empirically or through optimizing some generalized performance measures. In this study, we proposed a novel approach to do spectral kernel learning based on maximum margin criterion, which is theoretically justified as a more essential semi-supervised kernel learning measure than others, such as kernel target alignment. We have conducted lots of experiments on public data sets, showing promising performance of our scheme.

Kernel-based one-class classification is a special type of classification problem, and is widely used as the outlier detection and novelty detection technique. One of the most commonly used method is the support vector dada description (SVDD). However, the performance is mostly affected by which kernel is used. A promising way is to learn the kernel from the data automatically. In this paper, we focus on the problem of choosing the optimal kernel from a kernel convex hull for the given one-class classification task, and propose a new approach. Kernel methods work by nonlinearly mapping the data into an embedding feature space, and then searching the relations among this space, however this mapping is implicitly performed by the kernel function. How to choose a suitable kernel is a difficult problem. In our method, we first transform the data points linearly so that we obtain a new set whose variances equal unity. Then we choose the minimum embedding ball as the criterion to learn the optimal kernel matrix over the kernel convex hull. It leads to the convex quadratically constrained quadratic programming (QCQP). Experiments results on a collection of benchmark data sets demonstrated the effectiveness of the proposed method.