Convex and Network Flow Optimization for Structured Sparsity

We consider a class of learning problems regularized by a structured sparsity-inducing norm defined as the sum of l_2- or l_infinity-norms over groups of variables. Whereas much effort has been put in developing fast optimization techniques when the groups are disjoint or embedded in a hierarchy, we address here the case of general overlapping groups. To this end, we present two different strategies: On the one hand, we show that the proximal operator associated with a sum of l_infinity-norms can be computed exactly in polynomial time by solving a quadratic min-cost flow problem, allowing the use of accelerated proximal gradient methods. On the other hand, we use proximal splitting techniques, and address an equivalent formulation with non-overlapping groups, but in higher dimension and with additional constraints. We propose efficient and scalable algorithms exploiting these two strategies, which are significantly faster than alternative approaches. We illustrate these methods with several problems such as CUR matrix factorization, multi-task learning of tree-structured dictionaries, background subtraction in video sequences, image denoising with wavelets, and topographic dictionary learning of natural image patches.Comment: to appear in the Journal of Machine Learning Research (JMLR

Layout-level Circuit Sizing and Design-for-manufacturability Methods for Embedded RF Passive Circuits

The emergence of multi-band communications standards, and the fast pace of the consumer electronics markets for wireless/cellular applications emphasize the need for fast design closure. In addition, there is a need for electronic product designers to collaborate with manufacturers, gain essential knowledge regarding the manufacturing facilities and the processes, and apply this knowledge during the design process. In this dissertation, efficient layout-level circuit sizing techniques, and methodologies for design-for-manufacturability have been investigated. For cost-effective fabrication of RF modules on emerging technologies, there is a clear need for design cycle time reduction of passive and active RF modules. This is important since new technologies lack extensive design libraries and layout-level electromagnetic (EM) optimization of RF circuits become the major bottleneck for reduced design time. In addition, the design of multi-band RF circuits requires precise control of design specifications that are partially satisfied due to manufacturing variations, resulting in yield loss. In this work, a broadband modeling and a layout-level sizing technique for embedded inductors/capacitors in multilayer substrate has been presented. The methodology employs artificial neural networks to develop a neuro-model for the embedded passives. Secondly, a layout-level sizing technique for RF passive circuits with quasi-lumped embedded inductors and capacitors has been demonstrated. The sizing technique is based on the circuit augmentation technique and a linear optimization framework. In addition, this dissertation presents a layout-level, multi-domain DFM methodology and yield optimization technique for RF circuits for SOP-based wireless applications. The proposed statistical analysis framework is based on layout segmentation, lumped element modeling, sensitivity analysis, and extraction of probability density functions using convolution methods. The statistical analysis takes into account the effect of thermo-mechanical stress and process variations that are incurred in batch fabrication. Yield enhancement and optimization methods based on joint probability functions and constraint-based convex programming has also been presented. The results in this work have been demonstrated to show good correlation with measurement data.Ph.D.Committee Chair: Swaminathan, Madhavan; Committee Member: Fathianathan, Mervyn; Committee Member: Lim, Sung Kyu; Committee Member: Peterson, Andrew; Committee Member: Tentzeris, Mano

A Methodology for Solving the Equations Arising in Nonlinear Parameter Identification Problems: Application to Induction Machines

This dissertation presents a method that can be used to identify the parameters of a class of systems whose regressor models are nonlinear in the parameters. The technique is based on classical elimination theory, and it guarantees that the solution for the parameters which minimize a least-squares criterion can be found in a finite number of steps. The proposed methodology begins with an input-output linear overparameterized model whose parameters are rationally related. After making appropriate substitutions that account for the overparameterization, the problem is transformed into a nonlinear least-squares problem that is not overparameterized. The extrema equations are computed, and a nonlinear transformation is carried out to convert them to polynomial equations in the unknown parameters. It is then show how these polynomial equations can be solved using elimination theory using resultants. The optimization problem reduces to a numerical computation of the roots of a polynomial in a single variable. This nonlinear least-squares method is applied to the identification of the parameters of an induction motor. A major difficulty with the induction motor is that the rotor’s state variables are not available measurements so that the system identification model cannot be made linear in the parameters without overparameterizing the model. Previous work in the literature has avoided this issue by making simplifying assumptions such as a “slowly varying speed”. Here, no such simplifying assumptions are made. This method is implemented online to continuously update the parameter values. Experimental results are presented to verify this method. The application of this nonlinear least-squares method can be extended to many research areas such as the parameter identification for Hammerstein models. In principle, as long as the regressor model is such that the system parameters are rationally related, the proposed method is applicable

Feature Analysis for Classification of Physical Actions using surface EMG Data

Based on recent health statistics, there are several thousands of people with limb disability and gait disorders that require a medical assistance. A robot assisted rehabilitation therapy can help them recover and return to a normal life. In this scenario, a successful methodology is to use the EMG signal based information to control the support robotics. For this mechanism to function properly, the EMG signal from the muscles has to be sensed and then the biological motor intention has to be decoded and finally the resulting information has to be communicated to the controller of the robot. An accurate detection of the motor intention requires a pattern recognition based categorical identification. Hence in this paper, we propose an improved classification framework by identification of the relevant features that drive the pattern recognition algorithm. Major contributions include a set of modified spectral moment based features and another relevant inter-channel correlation feature that contribute to an improved classification performance. Next, we conducted a sensitivity analysis of the classification algorithm to different EMG channels. Finally, the classifier performance is compared to that of the other state-of the art algorithm