This letter proposes a narrowband interference-plus-noise covariance matrix (INCM) based beamformer, which is robust with sensor position errors for linear array. First, using the subspace fitting and subspace orthogonality techniques, we estimate a set of angle-related bases for the signal-plus-interference subspace (SIS) by solving a joint optimization problem. Second, we obtain the bases transition matrix between the estimated angle-related bases and the orthogonal bases consisting of the dominant eigenvectors of the sample covariance matrix (SCM). The SCM can be expressed as a function of the angle-related bases and the bases transition matrix. We construct the INCM directly from the SIS by eliminating the component of the desired signal from the angle-related bases. Simulations and experimental results show that the proposed beamformer outperforms other tested beamformers in the presence of sensor position errors.

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Self-organizing map (SOM) method combined with the empirical orthogonal function was used to reconstruct the subsurface temperature field by using sea surface data in the Northwestern Pacific Ocean. In contrast to the traditional method, SOM method can extract nonlinear relations from the data and is more suitable for nonlinear dynamics in the ocean. Error statistics show that SOM method provides reconstructions of the subsurface temperature field with the majority of relative errors below 20% at 0-1000-m depth.

This paper examines a matrix-regularized multiple kernel learning (MKL) technique based on a notion of (r,p) norms. For the problem of learning a linear combination in the support vector machine-based framework, model complexity is typically controlled using various regularization strategies on the combined kernel weights. Recent research has developed a generalized ℓp-norm MKL framework with tunable variable p(p≥1) to support controlled intrinsic sparsity. Unfortunately, this ``1-D'' vector ℓp-norm hardly exploits potentially useful information on how the base kernels ``interact.'' To allow for higher order kernel-pair relationships, we extend the ``1-D'' vector ℓp-MKL to the ``2-D'' matrix (r,p) norms (1 ≤ r,p < ∞). We develop a new formulation and an efficient optimization strategy for (r,p)-MKL with guaranteed convergence. A theoretical analysis and experiments on seven UCI data sets shed light on the superiority of (r,p)-MKL over ℓp-MKL in various scenarios.

Localized multiple kernel learning (LMKL) is an attractive strategy for combining multiple heterogeneous features with regard to their discriminative power for each individual sample. However, the learning of numerous local solutions may not scale well even for a moderately sized training set, and the independently learned local models may suffer from overfitting. Hence, in existing local methods, the distributed samples are typically assumed to share the same weights, and various unsupervised clustering methods are applied as preprocessing. In this paper, to enable the learner to discover and benefit from the underlying local coherence and diversity of the samples, we incorporate the clustering procedure into the canonical support vector machine-based LMKL framework. Then, to explore the relatedness among different samples, which has been ignored in a vector -norm analysis, we organize the cluster-specific kernel weights into a matrix and introduce a matrix-based extension of the -norm for constraint enforcement. By casting the joint optimization problem as a problem of alternating optimization, we show how the cluster structure is gradually revealed and how the matrix-regularized kernel weights are obtained. A theoretical analysis of such a regularizer is performed using a Rademacher complexity bound, and complementary empirical experiments on real-world data sets demonstrate the effectiveness of our technique.

This brief analyzes the effects of regularization variations in the localized kernel weights on the hypothesis generated by localized multiple kernel learning (LMKL) algorithms. Recent research on LMKL includes imposing different regularizations on the localized kernel weights and has led to varying formulations and solution strategies. Following the stability analysis theory as presented by Bousquet and Elisseeff, we give stability bounds based on the norm of the variation of localized kernel weights for three LMKL methods cast in the support vector machine classification framework, including vector -norm LMKL, matrix-regularized -norm LMKL, and samplewise -norm LMKL. Further comparison of these bounds helps to qualitatively reveal the performance differences produced by these regularization methods, that is, matrix-regularized LMKL achieves superior performance, followed by vector -norm LMKL and samplewise -norm LMKL. Finally, a set of experimental results on ten benchmark machine learning UCI data sets is reported and shown to empirically support our theoretical analysis.

This letter proposes a robust superdirective frequency-invariant beamforming method for circular sensor arrays. First, the beampattern is accurately transformed into an equivalent form using the property of circular arrays, and the expressions of directivity factor and white noise gain are correspondingly modified. Second, a closed-form weighting vector is accurately derived based on the minimum mean square error approximation to a desired superdirective beampattern that is expressed in a general form. When the number of elements is sufficiently large, the weighting vector can be further simplified, and the white noise gain is also modified to a concise form that is found to be an increasing function of the number of elements in the low-frequency range. Simulations and experimental results show that this method can provide a robust superdirective frequency-invariant beampattern over a wide frequency band given a suitable number of elements, and it can be readily applied to process broadband signals in practice using small circular sensor arrays.

Our objective is to train support vector machines (SVM)-based localized multiple kernel learning (LMKL), using the alternating optimization between the standard SVM solvers with the local combination of base kernels and the sample-specific kernel weights. The advantage of alternating optimization developed from the state-of-the-art MKL is the SVM-tied overall complexity and the simultaneous optimization on both the kernel weights and the classifier. Unfortunately, in LMKL, the sample-specific character makes the updating of kernel weights a difficult quadratic nonconvex problem. In this paper, starting from a new primal-dual equivalence, the canonical objective on which state-of-the-art methods are based is first decomposed into an ensemble of objectives corresponding to each sample, namely, sample-wise objectives. Then, the associated sample-wise alternating optimization method is conducted, in which the localized kernel weights can be independently obtained by solving their exclusive sample-wise objectives, either linear programming (for l1-norm) or with closed-form solutions (for lp-norm). At test time, the learnt kernel weights for the training data are deployed based on the nearest-neighbor rule. Hence, to guarantee their generality among the test part, we introduce the neighborhood information and incorporate it into the empirical loss when deriving the sample-wise objectives. Extensive experiments on four benchmark machine learning datasets and two real-world computer vision datasets demonstrate the effectiveness and efficiency of the proposed algorithm.

An approach to the optimal design of FIR broadband beamformer with frequency invariant patterns via joint optimizing the spatial and frequency responses is proposed. The beam responses are jointly optimized to satisfy some spatial and frequency domain specifications by designing a bank of FIR filters corresponding to the input channels. It minimizes the maximum error between the designed beam patterns and the desired ones over the working frequencies within the mainlobe area while guaranteeing the sidelobes and the array patterns over the stopband to be below some given threshold values. White noise gain constraint is applied to improve the robustness of the beamformer against random errors. The beam response is expressed as a linear function of the FIR filters tap weights, and the design problem is formulated as the second-order cone programming, which can be solved efficiently via the well-established interior point methods. Results of computer simulation for a twelve-element semicircular array confirm satisfactory performance of the approach proposed in this paper.

Principal component extraction is an efficient statistical tool which is applied to data compression, feature extraction, signal processing, etc. Representative algorithms in the literature can only handle real data. However, in many scenarios such as sensor array signal processing, complex data are encountered. In this paper, the complex domain generalized Hebbian algorithm (CGHA) is presented for complex principal component extraction. It extends the real domain generalized Hebbian algorithm (GHA) proposed by Sanger (1992). Convergence of CGHA is analyzed. Like GHA, CGHA can be implemented by a single-layer linear neural network with simple computation. An example is given where CGHA is utilized in direction-of-arrival estimation of multiple narrowband plane waves received by a sensor array.