How to Solve Classification and Regression Problems on High-Dimensional Data with a Supervised Extension of Slow Feature Analysis

Supervised learning from high-dimensional data, e.g., multimedia data, is a challenging task. We propose an extension of slow feature analysis (SFA) for supervised dimensionality reduction called graph-based SFA (GSFA). The algorithm extracts a label-predictive low-dimensional set of features that can be post-processed by typical supervised algorithms to generate the final label or class estimation. GSFA is trained with a so-called training graph, in which the vertices are the samples and the edges represent similarities of the corresponding labels. A new weighted SFA optimization problem is introduced, generalizing the notion of slowness from sequences of samples to such training graphs. We show that GSFA computes an optimal solution to this problem in the considered function space, and propose several types of training graphs. For classification, the most straightforward graph yields features equivalent to those of (nonlinear) Fisher discriminant analysis. Emphasis is on regression, where four different graphs were evaluated experimentally with a subproblem of face detection on photographs. The method proposed is promising particularly when linear models are insufficient, as well as when feature selection is difficult

Power Load Management as a Computational Market

Power load management enables energy utilities to reduce peak loads and thereby save money. Due to the large number of different loads, power load management is a complicated optimization problem. We present a new decentralized approach to this problem by modeling direct load management as a computational market. Our simulation results demonstrate that our approach is very efficient with a superlinear rate of convergence to equilibrium and an excellent scalability, requiring few iterations even when the number of agents is in the order of one thousand. Aframework for analysis of this and similar problems is given which shows how nonlinear optimization and numerical mathematics can be exploited to characterize, compare, and tailor problem-solving strategies in market-oriented programming

Spectrum optimization in multi-user multi-carrier systems with iterative convex and nonconvex approximation methods

Several practical multi-user multi-carrier communication systems are characterized by a multi-carrier interference channel system model where the interference is treated as noise. For these systems, spectrum optimization is a promising means to mitigate interference. This however corresponds to a challenging nonconvex optimization problem. Existing iterative convex approximation (ICA) methods consist in solving a series of improving convex approximations and are typically implemented in a per-user iterative approach. However they do not take this typical iterative implementation into account in their design. This paper proposes a novel class of iterative approximation methods that focuses explicitly on the per-user iterative implementation, which allows to relax the problem significantly, dropping joint convexity and even convexity requirements for the approximations. A systematic design framework is proposed to construct instances of this novel class, where several new iterative approximation methods are developed with improved per-user convex and nonconvex approximations that are both tighter and simpler to solve (in closed-form). As a result, these novel methods display a much faster convergence speed and require a significantly lower computational cost. Furthermore, a majority of the proposed methods can tackle the issue of getting stuck in bad locally optimal solutions, and hence improve solution quality compared to existing ICA methods.Comment: 33 pages, 7 figures. This work has been submitted for possible publicatio