Data Mining Practical Machine Learning Tools and Techniques

An overview of the self-organizing map algorithm, on which the papers in this issue are based, is presented in this article.

The Self-Organizing Map

1. Basic Concepts. 2. Nonparametric Methods. 3. Parametric Methods for Rational Spectra. 4. Parametric Methods for Line Spectra. 5. Filter Bank Methods. 6. Spatial Methods. Appendix A: Linear Algebra and Matrix Analysis Tools. Appendix B: Cramer-Rao Bound Tools. Appendix C: Model Order Selection Tools. Appendix D: Answers to Selected Exercises. Bibliography. References Grouped by Subject. Subject Index.

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Spectral analysis of signals

The performance of the MUSIC and ML methods is studied, and their statistical efficiency is analyzed. The Cramer-Rao bound (CRB) for the estimation problems is derived, and some useful properties of the CRB covariance matrix are established. The relationship between the MUSIC and ML estimators is investigated as well. A numerical study is reported of the statistical efficiency of the MUSIC estimator for the problem of finding the directions of two plane waves using a uniform linear array. An exact description of the results is included. >

MUSIC, maximum likelihood, and Cramer-Rao bound

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

This paper is motivated by sensing and wireless communication, where data compression or dimension reduction may be used to reduce the required communication bandwidth. High-dimensional measurements are converted into low-dimensional representations through linear compression. Our aim is to compress a noisy sensor measurement, allowing for the fact that the compressed measurement will then be transmitted over a noisy channel. We give the closed-form expression for the optimal compression matrix that minimizes the trace or determinant of the error covariance matrix. We show that the solutions share a common architecture consisting of a canonical coordinate transformation, scaling by coefficients which account for canonical correlations and channel noise variance, followed by a coordinate transformation into the sub-dominant invariant subspace of the channel noise. Furthermore, we explore the design problem with respect to more general criteria and provide a unified factorization for the corresponding optimal compression matrix. A necessary condition is obtained for the optimal compression.

Optimum Compression of a Noisy Measurement for Transmission Over a Noisy Channel

: The objective of this program is to define a very general class of iterative subspace Wiener filters. Within this class, identify two interesting subclasses: conjugate direction Wiener filters and multistage Wiener filters, and to study their equivalencies.

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Algebraic Equivalence of Conjugate Direction and Multistage Wiener Filters

Maximum-likelihood estimates for the levels of the mean value function and the covariance function of a Gaussian random process are investigated. The stability of these estimates is examined as the actual covariance function of the process deviates from the form assumed in the estimators. It is found that the time-bandwidth product for stationary processes represents an upper bound on the number of estimator terms that can be safely used when estimating with uncertainty about the process covariance function. This result is consistent with other interpretations of the time-bandwidth product and tempers the conclusion that, in principle, an infinite number of estimator terms can be used to obtain a perfect estimate of the covariance level. In practice, the estimate of the level can never be perfect, and the accuracy of the estimate depends on the observation interval. Finally, conditions are established to ensure asymptotic stability of the estimates and physical interpretations are presented.

Stability of Parameter Estimates for a Gaussian Process

Exact likelihood for stationary vector autoregressive moving average process

We present simple methods for constructing radar waveforms whose ambiguity functions are free of sidelobes inside a desired range or Doppler interval. We exploit the time-frequency duality between pulse amplitude modulation (PAM) and orthogonal frequency division multiplexing (OFDM) to sequence Golay complementary codes across time or frequency and clear out range/Doppler sidelobes. Proper sequencing of complementary codes in time (PAM design) enables the annihilation of range sidelobes along a desired Doppler interval. The dual design, i.e., OFDM signaling of complementary codes, enables the annihilation of Doppler sidelobes along a desired range interval. The two designs can be used sequentially to bring weak targets out of the sidelobes of nearby strong reflectors inside a range-Doppler interval of interest.

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Louis L. Scharf

Papers

Optimum Compression of a Noisy Measurement for Transmission Over a Noisy Channel

Algebraic Equivalence of Conjugate Direction and Multistage Wiener Filters

Stability of Parameter Estimates for a Gaussian Process

Exact likelihood for stationary vector autoregressive moving average process

Sidelobe suppression in a desired range/doppler interval