In the past few years, some nonlinear dimensionality reduction (NLDR) or nonlinear manifold learning methods have aroused a great deal of interest in the machine learning community. These methods are promising in that they can automatically discover the low-dimensional nonlinear manifold in a high-dimensional data space and then embed the data points into a low-dimensional embedding space, usin...

Locally linear embedding (LLE) is a recently proposed method for unsupervised nonlinear dimensionality reduction. It has a number of attractive features: it does not require an iterative algorithm, and just a few parameters need to be set. Two extensions of LLE to supervised feature extraction were independently proposed by the authors of this paper. Here, both methods are unified in a common f...

Locally weighted polynomial regression (LWPR) is a popular instance-based algorithm for learning continuous non-linear mappings. For more than two or three inputs and for more than a few thousand dat-apoints the computational expense of predictions is daunting. We discuss drawbacks with previous approaches to dealing with this problem, and present a new algorithm based on a multiresolution sear...

We give a simple analysis of the PCP with low amortized query complexity of Samorodnitsky and Trevisan [16]. The analysis also applies to the linearity testing over finite fields, giving a better estimate of the acceptance probability in terms of the distance of the tested function to the closest linear function.

The autoencoder is a popular neural network model that learns hidden representations of unlabeled data. Typically, singleor multilayer perceptrons are used in constructing an autoencoder, but we use soft decision trees (i.e., hierarchical mixture of experts) instead. Such trees have internal nodes that implement soft multivariate splits through a gating function and all leaves are weighted by t...

Two-group classification is a key task in decision making and data mining applications. We introduce two new mixed integer programming formulations that make use of multiple separating hyperplanes. They represent a generalization of previous piecewise-linear models that embed rules having the form of hyperplanes, which are used to successively separate the two groups. In fact, the classifiers o...

The inverse spanning tree problem is to make a given spanning tree be a minimum spanning tree on a connected graph via a minimum perturbation on its edge weights. In this paper, a chance-constrained programming model is proposed to handle the inverse spanning tree problem where the edge weights are assumed to be uncertain variables. It is shown that such an uncertain minimum spanning tree can b...

The present paper investigates the word order alternation of English transitive phrasal verbs such as, e.g., to pick up the book versus to pick the book up. It builds on traditional monofactorial analyses, but argues that previously used methods of analysis are grossly inadequate to describe, explain and predict the word order choice by native speakers. A hypothesis integrating virtually all re...