Low-rank matrix decomposition has gained great popularity recently in scaling up kernel methods to large amounts of data. However, some limitations could prevent them from working effectively in certain domains. For example, many existing approaches are intrinsically unsupervised, which does not incorporate side information (e.g., class labels) to produce task specific decompositions; also, the...

Determinantal point processes (DPPs) are appealing models for subset selection problems where diversity is desired. They offer surprisingly efficient inference, including sampling in O(N) time and O(N) space, where N is the number of base items. However, in some applications, N may grow so large that sampling from a DPP becomes computationally infeasible. This is especially true in settings whe...

In this talk, we discuss recent results on common techniques for scaling up nonparametric methods such as kernel methods and Gaussian processes. In particular, we focus on data dependent and independent sub-sampling methods, namely Nystrom and random features, and study their generalization properties within a statistical learning theory framework. On the one hand we show that these methods can...

The Nyström method has long been popular for scaling up kernel methods. Its theoretical guarantees and empirical performance rely critically on the quality of the landmarks selected. We study landmark selection for Nyström using Determinantal Point Processes (DPPs), discrete probability models that allow tractable generation of diverse samples. We prove that landmarks selected via DPPs guarante...

The Nyström method has been popular for generating the low-rank approximation of kernel matrices that arise in many machine learning problems. The approximation quality of the Nyström method depends crucially on the number of selected landmark points and the selection procedure. In this paper, we present a novel algorithm to compute the optimal Nyström low-approximation when the number of landm...

We address the problem of efficient sparse fixed-rank (SFR) matrix decomposition, i.e., splitting a corrupted matrix M into an uncorrupted matrix L of rank r and a sparse matrix of outliers S. Fixed-rank constraints are usually imposed by the physical restrictions of the system under study. Here we propose a method to perform accurate and very efficient S-FR decomposition that is more suitable ...

In this article, we consider the radiation characteristics of a THz antenna made circular dielectric rod decorated with conformal graphene strip and illuminated by field line magnetic current. The has arbitrary angular size location its surface impedance is characterized Kubo theory. Our mathematically accurate analysis uses dedicated hypersingular integral equation for current induced on strip...

With the development of human motion capture, realistic human motion capture data has been widely implemented to many fields. However, segmenting motion capture data sequences manually into distinct behavior is time-consuming and laborious. In this paper, we introduce an efficient unsupervised method based on graph partition for automatically segmenting motion capture data. For the N-Frame moti...

Chaotic time series can well reflect the nonlinearity and non-stationarity of real environment changes. The traditional kernel adaptive filter (KAF) with second-order statistical characteristics suffers performance degeneration dramatically for predicting chaotic containing noises outliers. In order to improve robustness filters in presence impulsive noise, a nonlinear similarity measure named ...

Nystrom (1990) described high tech markets as marketing dependent and technologically driven. Unfortunately, there is evidence that this linkage is not often recognized by organizations (Gupta, Ray and Wilemon 1985). High tech markets are characterized as complex. In addition, they exist under rapidly changing technological conditions which lead to shorter life cycles (Davidow 1986) and the nee...