We develop a super-fast kernel density estimation algorithm (FastKDE) and based on this a fast kernel independent component analysis algorithm (KDICA). FastKDE calculates the kernel density estimator exactly and its computation only requires sorting n numbers plus roughly 2n evaluations of the exponential function, where n is the sample size. KDICA converges as quickly as parametric ICA algorit...

This paper considers the economic lot and delivery scheduling problem in a two-echelon supply chains, where a single supplier produces multiple components on a flexible flow line (FFL) and delivers them directly to an assembly facility (AF). The objective is to determine a cyclic schedule that minimizes the sum of transportation, setup and inventory holding costs per unit time without shortage....

Kernel ridge regression (KRR) is a popular scheme for non-linear non-parametric learning. However, existing implementations of KRR require that all the data stored in main memory, which severely limits use contexts where size far exceeds memory size. Such applications are increasingly common mining, bioinformatics, and control. A powerful paradigm computing on sets too large streaming model com...

Previous studies of Non-Parametric Kernel Learning (NPKL) usually formulate the learning task as a Semi-Definite Programming (SDP) problem that is often solved by some general purpose SDP solvers. However, for N data examples, the time complexity of NPKL using a standard interiorpoint SDP solver could be as high as O(N6.5), which prohibits NPKL methods applicable to real applications, even for ...

In multi-class categorization problems with a very large or unbounded number of classes, it is often not computationally feasible to train and/or test a kernel-based classifier. One solution is to use a fast computation to pre-select a subset of the classes for reranking with a kernel method, but even then tractability can be a problem. We investigate using trained multilayer perceptron probabi...

The computation and memory required for kernel machines with N training samples is at least O(N). Such a complexity is significant even for moderate size problems and is prohibitive for large datasets. We present an approximation technique based on the improved fast Gauss transform to reduce the computation to O(N). We also give an error bound for the approximation, and provide experimental res...

A simple method for solving Prandtl's integro-differential equation is proposed based on a new reproducing kernel space. Using a transformation and modifying the traditional reproducing kernel method, the singular term is removed and the analytical representation of the exact solution is obtained in the form of series in the new reproducing kernel space. Compared with known investigations, its ...

Our goal is to improve the training and prediction time of Nyström method, which is a widely-used technique for generating low-rank kernel matrix approximations. When applying the Nyström approximation for large-scale applications, both training and prediction time is dominated by computing kernel values between a data point and all landmark points. With m landmark points, this computation requ...