In recent years, a variety of nonlinear dimensionality reduction techniques have been proposed that aim to address the limitations of traditional techniques such as PCA and classical scaling. The paper presents a review and systematic comparison of these techniques. The performances of the nonlinear techniques are investigated on artificial and natural tasks. The results of the experiments reveal that nonlinear techniques perform well on selected artificial tasks, but that this strong performance does not necessarily extend to real-world tasks. The paper explains these results by identifying weaknesses of current nonlinear techniques, and suggests how the performance of nonlinear dimensionality reduction techniques may be improved.

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Dimensionality Reduction: A Comparative Review

We explore the effect of dimensionality on the nearest neighbor problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as dimensionality increases, the distance to the nearest data point approaches the distance to the farthest data point. To provide a practical perspective, we present empirical results on both real and synthetic data sets that demonstrate that this effect can occur for as few as 10-15 dimensions. These results should not be interpreted to mean that high-dimensional indexing is never meaningful; we illustrate this point by identifying some high-dimensional workloads for which this effect does not occur. However, our results do emphasize that the methodology used almost universally in the database literature to evaluate high-dimensional indexing techniques is flawed, and should be modified. In particular, most such techniques proposed in the literature are not evaluated versus simple linear scan, and are evaluated over workloads for which nearest neighbor is not meaningful. Often, even the reported experiments, when analyzed carefully, show that linear scan would outperform the techniques being proposed on the workloads studied in high (10-15) dimensionality!.

When is nearest neighbor meaningful

Inspired by recent advances in multiple-input multiple-output (MIMO) communications, this proposal introduces the statistical MIMO radar concept To the authors' knowledge, this is the first time that the statistical MIMO is being proposed for radar The fundamental difference between statistical MIMO and other radar array systems is that the latter seek to maximize the coherent processing gain, while statistical MIMO radar capitalizes on the diversity of target scattering to improve radar performance Coherent processing is made possible by highly correlated signals at the receiver array, whereas in statistical MIMO radar, the signals received by the array elements are uncorrelated Radar targets generally consist of many small elemental scatterers that are fused by the radar waveform and the processing at the receiver, to result in echoes with fluctuating amplitude and phase It is well known that in conventional radar, slow fluctuations of the target radar cross section (RCS) result in target fades that degrade radar performance By spacing the antenna elements at the transmitter and at the receiver such that the target angular spread is manifested, the MIMO radar can exploit the spatial diversity of target scatterers opening the way to a variety of new techniques that can improve radar performance This paper focuses on the application of the target spatial diversity to improve detection performance The optimal detector in the Neyman–Pearson sense is developed and analyzed for the statistical MIMO radar It is shown that the optimal detector consists of noncoherent processing of the receiver sensors' outputs and that for cases of practical interest, detection performance is superior to that obtained through coherent processing An optimal detector invariant to the signal and noise levels is also developed and analyzed In this case as well, statistical MIMO radar provides great improvements over other types of array radars

Spatial Diversity in Radars&#8212;Models and Detection Performance

Wireless location refers to the geographic coordinates of a mobile subscriber in cellular or wireless local area network (WLAN) environments. Wireless location finding has emerged as an essential public safety feature of cellular systems in response to an order issued by the Federal Communications Commission (FCC) in 1996. The FCC mandate aims to solve a serious public safety problem caused by the fact that, at present, a large proportion of all 911 calls originate from mobile phones, the location of which cannot be determined with the existing technology. However, many difficulties intrinsic to the wireless environment make meeting the FCC objective challenging. These challenges include channel fading, low signal-to-noise ratios (SNRs), multiuser interference, and multipath conditions. In addition to emergency services, there are many other applications for wireless location technology, including monitoring and tracking for security reasons, location sensitive billing, fraud protection, asset tracking, fleet management, intelligent transportation systems, mobile yellow pages, and even cellular system design and management. This article provides an overview of wireless location challenges and techniques with a special focus on network-based technologies and applications.

Network-based wireless location: challenges faced in developing techniques for accurate wireless location information

This chapter introduces the subject of statistical pattern recognition (SPR). It starts by considering how features are defined and emphasizes that the nearest neighbor algorithm achieves error rates comparable with those of an ideal Bayes’ classifier. The concepts of an optimal number of features, representativeness of the training data, and the need to avoid overfitting to the training data are stressed. The chapter shows that methods such as the support vector machine and artificial neural networks are subject to these same training limitations, although each has its advantages. For neural networks, the multilayer perceptron architecture and back-propagation algorithm are described. The chapter distinguishes between supervised and unsupervised learning, demonstrating the advantages of the latter and showing how methods such as clustering and principal components analysis fit into the SPR framework. The chapter also defines the receiver operating characteristic, which allows an optimum balance between false positives and false negatives to be achieved.

Raviv Raich

Papers

Efficient Graph-based Signal Motif Discovery with Performance Bounds