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Multidimensional scaling (MDS) refers to a class of dimensionality reduction techniques, which represent entities as points in a low-dimensional space so that the interpoint distances approximate the initial pairwise dissimilarities between entities as closely as possible. The traditional methods for solving MDS are susceptible to outliers. Here, a unified framework is proposed, where the MDS is treated as maximization of a correntropy criterion, which is solved by half-quadratic optimization in either multiplicative or additive forms. By doing so, MDS can cope with an initial dissimilarity matrix contaminated with outliers because the correntropy criterion is closely related to $M$-estimators. Three novel algorithms are derived. Their performances are assessed experimentally against three state-of-the-art MDS techniques, namely the scaling by majorizing a complicated function, the robust Euclidean embedding, and the robust MDS under the same conditions. The experimental results indicate that the proposed algorithms perform substantially better than the aforementioned competing techniques. [ABSTRACT FROM PUBLISHER]

A stepped-frequency (SF) waveform is effective in achieving high-range resolution (HRR) in modern radars. In this paper, we determine various fundamental limits of the SF waveform regarding the ambiguity, stability, and accuracy of stationary target profiling and the velocity compensation accuracy for moving targets. The investigation reveals that by using the information contained in both the phase and envelope of the echo signal, SF radars can achieve HRR profiles without ambiguity under a looser criterion and can compensate the range shift caused by a target's radial velocity. The results of this paper can aid in SF waveform design and in the development of processing algorithms for HRR profiling and velocity compensation. [ABSTRACT FROM PUBLISHER]

Recently, the information potential (IP) of order \alpha, defined as the argument of the log in the \alpha-order Renyi entropy, has been successfully used as an information theoretic criterion for supervised adaptive system training. In this paper, we use the survival function (or equivalently the distribution function) of an absolute value transformed random variable to define a new information potential, named the survival information potential (SIP). Compared with the IP, the SIP has some advantages, such as validity in a wide range of distributions, robustness, and the simplicity in computation. The properties of SIP and a simple formula for computing the empirical SIP are given in the paper. Finally, the SIP criterion is applied in adaptive system training, and simulation examples on FIR adaptive filtering, kernel adaptive filtering, and time delay neural networks (TDNNs) training are presented to demonstrate the performance. [ABSTRACT FROM PUBLISHER]

Proposes the extended least square (XLS) criterion for differentiating measurement errors from model errors. Details on the pseudo-linear model; Application of the XLS; Conclusion.

Recent work by Ding and Kay has demonstrated that the Bayesian information criterion (BIC) is an inconsistent estimator of model order in nested model selection as the noise variance \tau^\ast\rightarrow 0. Unfortunately, Ding and Kay have erroneously concluded that the minimum description length (MDL) principle also leads to inconsistent estimates of model order in this setting by equating BIC with MDL. This correspondence shows that only the earlier MDL criterion based on asymptotic assumptions has this problem, and proves that the new MDL linear regression criteria based on normalized maximum likelihood and Bayesian mixture codes satisfy the notion of consistency as \tau^\ast\rightarrow 0. The main result may be used as a basis to easily establish similar consistency results for other closely related information theoretic regression criteria. [ABSTRACT FROM PUBLISHER]