Abstract. The problem of automatically tuning multiple parameters for pattern recognition Support Vector Machines (SVMs) is considered. This is done by minimizing some estimates of the generalization error of SVMs using a gradient descent algorithm over the set of parameters. Usual methods for choosing parameters, based on exhaustive search become intractable as soon as the number of parameters exceeds two. Some experimental results assess the feasibility of our approach for a large number of parameters (more than 100) and demonstrate an improvement of generalization performance.

Consistency is a key property of statistical algorithms, when the data is drawn from some underlying probability distribution. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of a popular family of spectral clustering algorithms, which cluster the data with the help of eigenvectors of graph Laplacian matrices. We show that one of the two of major classes of spectral clustering (normalized clustering) converges under some very general conditions, while the other (unnormalized), is only consistent under strong additional assumptions, which, as we demonstrate, are not always satisfied in real data. We conclude that our analysis provides strong evidence for the superiority of normalized spectral clustering in practical applications. We believe that methods used in our analysis will provide a basis for future exploration of Laplacian-based methods in a statistical setting.

Future cellular systems will employ spatial multiplexing with multiple antennas at both transmitter and receiver to take advantage of large capacity gains. In such systems it will be desirable to select a subset of available transmit antennas for link initialization, link maintenance, or handoff. In this paper we present a criteria for selecting the optimal antenna subset in terms of minimum error rate, when coherent receivers, either linear or maximum likelihood (ML), are used over a slowly varying channel. For the ML receiver we propose to pick the subset whose output constellation has the largest minimum Euclidean distance. For the linear receiver we propose use of the post-processing SNRs (signal to noise ratios) of the multiplexed streams whereby the antenna subset that induces the largest minimum SNR is chosen. Simulations demonstrate that our selection algorithms also provides diversity advantage thus making subset selection useful over fading channels. I.

The purpose of this contribution is to extend some recent results on sparse representations of signals in redundant bases developed in the noise-free case to the case of noisy observations. The type of questions addressed so far is: given a (n,m)-matrix with and a vector, find a sufficient condition for to have an unique sparsest representation as a linear combination of the columns of. The answer is a bound on the number of nonzero entries of say, that guaranties that is the unique and sparsest solution of with. We consider the case where satisfies the sparsity conditions requested in the noise-free case and seek conditions on, a vector of additive noise or modeling errors, under which can be recovered from in a sense to be defined. 1.

We address the problem of designing jointly optimum linear precoder and decoder for a MIMO channel possibly with delay-spread, using a weighted minimum mean-squared error (MMSE) criterion subject to a transmit power constraint. We show that the optimum linear precoder and decoder diagonalize the MIMO channel into eigen subchannels, for any set of error weights. Furthermore, we derive the optimum linear precoder and decoder as functions of the error weights and consider specialized designs based on specific choices of error weights. We show how to obtain: 1) the maximum information rate design; 2) QoS-based design (we show how to achieve any set of relative SNRs across the subchannels); and 3) the (unweighted) MMSE and equal-error design for fixed rate systems.

This paper surveys the most important developments in multivariate ARCH-type modelling. It reviews the model specifications and inference methods, and identifies likely directions of future research.

Identity verification systems are an important part of our every day life. A typical example is the Automatic Teller Machine (ATM) which employs a simple identity verification scheme: the user is asked to enter their secret password after inserting their ATM card; if the password matches the one prescribed to the card, the user is allowed access to their bank account. This scheme suffers from a major drawback: only the validity of the combination of a certain possession (the ATM card) and certain knowledge (the password) is verified. The ATM card can be lost or stolen, and the password can be compromised. Thus new verification methods have emerged, where the password has either been replaced by, or used in addition to, biometrics such as the person's speech, face image or fingerprints. Apart from the ATM example described above, biometrics can be applied to other areas, such as telephone & internet based banking, airline reservations & check-in, as well as forensic work and law enforcement applications. Biometric systems

It is a known approach to translate propositional formulas into systems of polynomial inequalities and to consider proof systems for the latter ones. The well-studied proof systems of this kind are the Cutting Planes proof system (CP) utilizing linear inequalities and the Lovasz-Schrijver calculi (LS) utilizing quadratic inequalities. We introduce generalizations LS^d of LS that operate with polynomial inequalities of degree at most d. It turns out

A new efficient algorithm is presented for joint diagonalization of several matrices. The algorithm is based on the Frobenius-norm formulation of the joint diagonalization problem, and addresses diagonalization with a general, non-orthogonal transformation. The iterative scheme of the algorithm is based on a multiplicative update which ensures the invertibility of the diagonalizer. The algorithm 's efficiency stems from the special approximation of the cost function resulting in a sparse, block-diagonal Hessian to be used in the computation of the quasi-Newton update step. Extensive numerical simulations illustrate the performance of the algorithm and provide a comparison to other leading diagonalization methods. The results of such comparison demonstrate that the proposed algorithm is a viable alternative to existing state-of-the-art joint diagonalization algorithms.

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