Nonlinear dimensionality reduction by manifold embedding has become a popular and powerful approach both for visualization and as preprocessing for predictive tasks, but more efficient optimization algorithms are still crucially needed. MajorizationMinimization (MM) is a promising approach that monotonically decreases the cost function, but it remains unknown how to tightly majorize the manifol...

We have studied electron transport through single redox molecules, perylene tetracarboxylic diimides, covalently bound to two gold electrodes via different linker groups, as a function of electrochemical gate voltage and temperature in different solvents. The conductance of these molecules is sensitive to the linker groups because of different electronic coupling strengths between the molecules...

This paper presents a novel online version of laplacian eigenmap termed as generalized incremental laplacian eigenmap (GENILE), one of the most popular manifold-based dimensionality reduction technique performed by solving the generalized eigenvalue problem. We have used swiss roll and s-curve dataset, the most popular datasets used for manifold-based learning techniques, in this paper as artif...

We propose two novel methods for reducing dimension in training polynomial networks. We consider the class of polynomial networks whose output is the weighted sum of a basis of monomials. Our first method for dimension reduction eliminates redundancy in the training process. Using an implicit matrix structure, we derive iterative methods that converge quickly. A second method for dimension redu...

Locality preserving projection (LPP) is an effective dimensionality reduction method based on manifold learning, which is defined over the graph weighted squared 2-norm distances in the projected subspace. Since squared 2-norm distance is prone to outliers, it is desirable to develop a robust LPP method. In this paper, motivated by existing studies that improve the robustness of statistical lea...

We prove that the theory of EXPTIME degrees with respect to polynomial time Turing and many-one reducibility is undecidable. To do so we use a coding method based on ideal lattices of Boolean algebras which was introduced in Nies 12]. The method can be applied in fact to all time classes given by a time constructible function which dominates all polynomials. By a similar method, we construct an...