Efficient algorithms for learning kernels from multiple similarity matrices with general convex loss functions

In this paper we consider the problem of learning an n × n kernel matrix from m(1) similarity matrices under general convex loss. Past research have extensively studied the m = 1 case and have derived several algorithms which require sophisticated techniques like ACCP, SOCP, etc. The existing algorithms do not apply if one uses arbitrary losses and often can not handle m > 1 case. We present several provably convergent iterative algorithms, where each iteration requires either an SVM or a Multiple Kernel Learning (MKL) solver for m > 1 case. One of the major contributions of the paper is to extend the well knownMirror Descent(MD) framework to handle Cartesian product of psd matrices. This novel extension leads to an algorithm, called EMKL, which solves the problem in O(m2 log n 2) iterations; in each iteration one solves an MKL involving m kernels and m eigen-decomposition of n × n matrices. By suitably defining a restriction on the objective function, a faster version of EMKL is proposed, called REKL,which avoids the eigen-decomposition. An alternative to both EMKL and REKL is also suggested which requires only an SVMsolver. Experimental results on real world protein data set involving several similarity matrices illustrate the efficacy of the proposed algorithms.

Superconductivity of embedded lead nano particles in metallic and amorphous matrices

Nanodispersed lead in metallic and amorphous matrices was synthesized by rapid solidification processing. The optimum microstructure was tailored to avoid percolation of the particles. With these embedded particles it is possible to study quantitatively the effect of size on the superconducting transition temperature by carrying out quantitative microstructural characterization and magnetic measurements. Our results suggest the role of the matrices in enhancement or depression of superconducting transition temperature of lead. The origin of this difference in behavior with respect to different matrices and sizes is discussed.

Thermally induced phase separation in P alpha MSAN/PMMA blends in presence of functionalized multiwall carbon nanotubes: Rheology, morphology and electrical conductivity

The focus of this work is the evaluation and analysis of the state of dispersion of functionalized multiwall carbon nanotubes (CNTs), within different morphologies formed, in a model LCST blend (poly[(alpha-methylstyrene)-co-(acrylonitrile)]/poly(methyl-methacryla te), P alpha MSAN/PMMA). Blend compositions that are expected to yield droplet-matrix (85/15 P alpha MSAN/PMMA and 15/85 P alpha MSAN/PMMA, wt/wt) and co-continuous morphologies (60/40 P alpha MSAN/PMMA, wt/wt) upon phase separation have been combined with two types of CNTs; carboxylic acid functionalized (CNTCOOH) and polyethylene modified (CNTPE) up to 2 wt%. Thermally induced phase separation in the blends has been studied in-situ by rheology and dielectric (conductivity) spectroscopy in terms of morphological evolution and CNT percolation. The state of dispersion of CNTs has been evaluated by transmission electron microscopy. The experimental results indicate that the final blend morphology and the surface functionalization of CNT are the main factors that govern percolation. In presence of either of the CNTs, 60/40 P alpha MSAN/PMMA blends yield a droplet-matrix morphology rather than co-continuous and do not show any percolation. On the other hand, both 85/15 P alpha MSAN/PMMA and 15/85 P alpha MSAN/PMMA blends containing CNTPEs show percolation in the rheological and electrical properties. Interestingly, the conductivity spectroscopy measurements demonstrate that the 15/85 P alpha MSAN/PMMA blends with CNTPEs that show insulating properties at room temperature for the miscible blends reveal highly conducting properties in the phase separated blends (melt state) as a result of phase separation. By quenching this morphology, the conductivity can be retained in the blends even in the solid state. (C) 2011 Elsevier Ltd. All rights reserved.

Closed form solutions for element equilibrium and flexibility matrices of eight node rectangular plate bending element using integrated force method

Closed form solutions for equilibrium and flexibility matrices of the Mindlin-Reissner theory based eight-node rectangular plate bending element (MRP8) using integrated Force Method (IFM) are presented in this paper. Though these closed form solutions of equilibrium and flexibility matrices are applicable to plate bending problems with square/rectangular boundaries, they reduce the computational time significantly and give more exact solutions. Presented closed form solutions are validated by solving large number of standard square/rectangular plate bending benchmark problems for deflections and moments and the results are compared with those of similar displacement-based eight-node quadrilateral plate bending elements available in the literature. The results are also compared with the exact solutions.

Efficient Methods for Robust Classification Under Uncertainty in Kernel Matrices

In this paper we study the problem of designing SVM classifiers when the kernel matrix, K, is affected by uncertainty. Specifically K is modeled as a positive affine combination of given positive semi definite kernels, with the coefficients ranging in a norm-bounded uncertainty set. We treat the problem using the Robust Optimization methodology. This reduces the uncertain SVM problem into a deterministic conic quadratic problem which can be solved in principle by a polynomial time Interior Point (IP) algorithm. However, for large-scale classification problems, IP methods become intractable and one has to resort to first-order gradient type methods. The strategy we use here is to reformulate the robust counterpart of the uncertain SVM problem as a saddle point problem and employ a special gradient scheme which works directly on the convex-concave saddle function. The algorithm is a simplified version of a general scheme due to Juditski and Nemirovski (2011). It achieves an O(1/T-2) reduction of the initial error after T iterations. A comprehensive empirical study on both synthetic data and real-world protein structure data sets show that the proposed formulations achieve the desired robustness, and the saddle point based algorithm outperforms the IP method significantly.

Fast Likelihood Computation in Speech Recognition using Matrices

Acoustic modeling using mixtures of multivariate Gaussians is the prevalent approach for many speech processing problems. Computing likelihoods against a large set of Gaussians is required as a part of many speech processing systems and it is the computationally dominant phase for Large Vocabulary Continuous Speech Recognition (LVCSR) systems. We express the likelihood computation as a multiplication of matrices representing augmented feature vectors and Gaussian parameters. The computational gain of this approach over traditional methods is by exploiting the structure of these matrices and efficient implementation of their multiplication. In particular, we explore direct low-rank approximation of the Gaussian parameter matrix and indirect derivation of low-rank factors of the Gaussian parameter matrix by optimum approximation of the likelihood matrix. We show that both the methods lead to similar speedups but the latter leads to far lesser impact on the recognition accuracy. Experiments on 1,138 work vocabulary RM1 task and 6,224 word vocabulary TIMIT task using Sphinx 3.7 system show that, for a typical case the matrix multiplication based approach leads to overall speedup of 46 % on RM1 task and 115 % for TIMIT task. Our low-rank approximation methods provide a way for trading off recognition accuracy for a further increase in computational performance extending overall speedups up to 61 % for RM1 and 119 % for TIMIT for an increase of word error rate (WER) from 3.2 to 3.5 % for RM1 and for no increase in WER for TIMIT. We also express pairwise Euclidean distance computation phase in Dynamic Time Warping (DTW) in terms of matrix multiplication leading to saving of approximately of computational operations. In our experiments using efficient implementation of matrix multiplication, this leads to a speedup of 5.6 in computing the pairwise Euclidean distances and overall speedup up to 3.25 for DTW.

Field extension code based dispersion matrices for coherently detected space-time shift keying

Motivated by the recent Coherent Space-Time Shift Keying (CSTSK) philosophy, we construct new dispersion matrices for rotationally invariant PSK signaling sets. Given a specific PSK signal constellation, the dispersion matrices of the existing CSTSK scheme were chosen by maximizing the mutual information over randomly generated sets of dispersion matrices. In this contribution we propose a general method for constructing a set of structured dispersion matrices for arbitrary PSK signaling sets using Field Extension (FE) codes and then study the attainable Symbol Error Rate (SER) performance of some example constructions. We demonstrate that the proposed dispersion scheme is capable of outperforming the existing dispersion arrangement at medium to high SNRs.

Structured Dispersion Matrices From Division Algebra Codes for Space-Time Shift Keying

We propose a novel method of constructing Dispersion Matrices (DM) for Coherent Space-Time Shift Keying (CSTSK) relying on arbitrary PSK signal sets by exploiting codes from division algebras. We show that classic codes from Cyclic Division Algebras (CDA) may be interpreted as DMs conceived for PSK signal sets. Hence various benefits of CDA codes such as their ability to achieve full diversity are inherited by CSTSK. We demonstrate that the proposed CDA based DMs are capable of achieving a lower symbol error ratio than the existing DMs generated using the capacity as their optimization objective function for both perfect and imperfect channel estimation.

Segmental relaxations and crystallization-induced phase separation in PVDF/PMMA blends in the presence of surface-functionalized multiwall carbon nanotubes

Crystallization-induced phase separation and segmental relaxations in poly(vinylidene fluoride)/poly(methyl methacrylate) (PVDF/PMMA) blends was systematically investigated by melt-rheology and broadband dielectric spectroscopy in the presence of multiwall carbon nanotubes (MWNTs). Different functionalized MWNTs (amine, -NH2; acid, -COOH) were incorporated in the blends by melt-mixing above the melting temperature of PVDF, where the blends are miscible, and the crystallization induced phase separation was probed in situ by shear rheology. Interestingly, only -NH2 functionalized MWNTs (a-MWNTs) aided in the formation of beta-phase (trans-trans) crystals in PVDF, whereas both the neat blends and the blends with -COOH functionalized MWNTs (c-MWNTs) showed only alpha-phase (trans-gauche-trans-gauche') crystals as inferred from wide-angle X-ray diffraction (WXRD) and Fourier transform infrared (FTIR). Furthermore, blends with only a-MWNTs facilitated in heterogeneous nucleation in the blends manifesting in an increase in the calorimetric crystallization temperature and hence, augmented the theologically determined crystallintion induced phase separation temperature. The dielectric relaxations associated with the crystalline phase of PVDF (alpha(c)) was completely absent in the blends with a-MWNTs in contrast to neat blends and the blends with c-MWNTs in the dielectric loss spectra. The relaxations in the blends investigated here appeared to follow Havriliak-Negami (HN) empirical equations, and, more interestingly, the dynamic heterogeneity in the system could be mapped by an extra relaxation at higher frequency at the crystallization-induced phase separation temperature. The mean relaxation time (tau(HN)) was evaluated and observed to be delayed in the presence of MWNTs in the blends, more prominently in the case of blends with a-MWNTs. The latter also showed a significant increase in the dielectric relaxation strength (Delta epsilon). Electron microscopy and selective etching was used to confirm the localization of MWNTs in the amorphous phases of the interspherulitic regions as observed from scanning electron microscopy (SEM). The evolved crystalline morphology, during crystallization-induced phase separation, was observed to have a strong influence on the charge transport processes in the blends. These observations were further supported by the specific interactions (like dipole induced dipole interaction) between a-MWNTs and PVDF, as inferred from FTIR, and the differences in the crystalline morphology as observed from WXRD and polarized optical microscopy (POM).

Burst error correction using partial fourier matrices and block sparse representation

There is a strong relation between sparse signal recovery and error control coding. It is known that burst errors are block sparse in nature. So, here we attempt to solve burst error correction problem using block sparse signal recovery methods. We construct partial Fourier based encoding and decoding matrices using results on difference sets. These constructions offer guaranteed and efficient error correction when used in conjunction with reconstruction algorithms which exploit block sparsity.

Lipschitz Correspondence between Metric Measure Spaces and Random Distance Matrices

Given a metric space with a Borel probability measure, for each integer N, we obtain a probability distribution on N x N distance matrices by considering the distances between pairs of points in a sample consisting of N points chosen independently from the metric space with respect to the given measure. We show that this gives an asymptotically bi-Lipschitz relation between metric measure spaces and the corresponding distance matrices. This is an effective version of a result of Vershik that metric measure spaces are determined by associated distributions on infinite random matrices.

Nonlinear optical second harmonic generation in ZnS quantum dots and observation on optical properties of ZnS/PMMA nanocomposites

ZnS quantum dots (QDs) of different sizes are synthesized by a simple chemical co-precipitation method at room temperature, by varying pH value of the reaction mixture. Samples are characterized by an X-ray diffractometer, transmission electron microscope, energy-dispersive X-ray analysis, etc. Linear optical properties, including UV-visible absorption and photoluminescence emission characteristics, of as-prepared QDs are measured. Size dependent nonlinear optical property, such as second harmonic generation (SHG) of 1064 nm Nd:YAG laser fundamental radiation in the synthesized ZnS QDs, is reported for the first time, to the best of our knowledge, by using the standard Kurtz-Perry powder method. In not to study the possibility of the synthesized ZnS QDs in different device applications ZnS/PMMA (polymethylmethacrylate) nanocomposites are also synthesized. The presence of weak chemical interaction between the polymer matrix and ZnS QDs is confirmed by Fourier transform infrared spectroscopy. Thermal properties of the nanocomposites are studied by differential scanning calorimetry and thermo-gravimetric analysis techniques, which show that the composites are stable up to similar to 300 degrees C temperature. (C) 2013 Elsevier B.V. All rights reserved.

Cooperativity and Structural Relaxations in PVDF/PMMA Blends in the Presence of MWNTs: An Assessment through SAXS and Dielectric Spectroscopy

Intermolecular cooperativity and structural relaxations in PVDF/PMMA blends were studied in this work with respect to different surface modified (amine, similar to NH2; carboxyl acid, similar to COOH and pristine) multiwalled nanotubes (MWNTs) at 1 wt % near blend's T-g and in the vicinity of demixing using dielectric spectroscopy, SAXS, DSC, and WAXD. Intermolecular cooperativity at T-g and configurational entropy was addressed in the framework of cooperative rearranging region (CRR) at T-g. Because of specific interactions between PVDF and NH2-MWNTs, the local composition fluctuates at its average value resulting in a broad T-g. The scale of cooperativity (xi(CRR)) and the number of segments in the cooperative volume (N-CRR) is comparatively smaller in the blends with NH2-MWNTs. This clearly suggests that the number of segments cooperatively relaxing is reduced in the blends due to specific interactions leading to more heterogeneity. The configurational entropy at T-g, as derived from Vogel-Fulcher and Adam-Gibbs analysis, was reduced in the blends in presence of MWNTs manifesting in entropic penalty of the chains. The crystallite size and the amorphous miscibility was evaluated using SAXS and was observed to be strongly contingent on the surface functional groups on MWNTs. Three distinct relaxations-alpha(c) due to relaxations in the crystalline phase of PVDF, alpha(m) indicating the amorphous miscibility in PVDF/PMMA blends, and alpha beta concerning the segmental dynamics of PMMA-were observed in the blends in the temperature range T-g < T < T-c. The dynamics as well as the nature of relaxations were observed to be dependent the surface functionality on the MWNTs. The dielectric permittivity was also enhanced in presence of MWNTs, especially with NH2-MWNTs, with minimal losses. The influence of the MWNTs on the spherulite size and crystalline morphology of the blends was also confirmed by POM and SEM.