Generalized RBF kernel for incomplete data
نویسندگان
چکیده
We construct genRBF kernel, which generalizes the classical Gaussian RBF kernel to the case of incomplete data. We model the uncertainty contained in missing attributes making use of data distribution and associate every point with a conditional probability density function. This allows to embed incomplete data into the function space and to define a kernel between two missing data points based on scalar product in L2. Experiments show that introduced kernel applied to SVM classifier gives better results than other state-of-the-art methods, especially in the case when large number of features is missing. Moreover, it is easy to implement and can be used together with any kernel approaches with no additional modifications.
منابع مشابه
Nystrom Method for Approximating the GMM Kernel
The GMM (generalized min-max) kernel was recently proposed [5] as a measure of data similarity and was demonstrated effective in machine learning tasks. In order to use the GMM kernel for large-scale datasets, the prior work resorted to the (generalized) consistent weighted sampling (GCWS) to convert the GMM kernel to linear kernel. We call this approach as “GMM-GCWS”. In the machine learning l...
متن کاملGeneralized RBF feature maps for Efficient Detection
These kernels combine the benefits of two other important classes of kernels: the homogeneous additive kernels (e.g. the χ2 kernel) and the RBF kernels (e.g. the exponential kernel). However, large scale problems require machine learning techniques of at most linear complexity and these are usually limited to linear kernels. Recently, Maji and Berg [2] and Vedaldi and Zisserman [4] proposed exp...
متن کاملA Fast and Automatic Kernel-based Classification Scheme: GDA+SVM or KNWFE+SVM
For high-dimensional data classification such as hyperspectral image classification, feature extraction is a crucial pre-process for avoiding the Hughes phenomena. Some feature extraction methods such as linear discriminant analysis (LDA), nonparametric weighted feature extraction (NWFE), and their kernel versions, generalized discriminant analysis (GDA) and kernel nonparametric weighted featur...
متن کاملGeneralized Min-Max Kernel and Generalized Consistent Weighted Sampling
We propose the “generalized min-max” (GMM) kernel as a measure of data similarity, where data vectors can have both positive and negative entries. GMM is positive definite as there is an associate hashing method named “generalized consistent weighted sampling” (GCWS) which linearizes this (nonlinear) kernel. A natural competitor of GMM is the radial basis function (RBF) kernel, whose correspond...
متن کاملKernel Design Using Boosting
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 fo...
متن کامل