PCA in Autocorrelation Space

The use of higher order autocorrelations as features for pattern classification has been usually restricted to second or third orders due to high computational costs. Since the autocorrelation space is a high dimensional space we are interested in reducing the dimensionality of feature vectors for the benefit of the pattern classification task. An established technique is Principal Component Analysis (PCA) which, however, cannot be applied directly in the autocorrelation space. In this paper we develop a new method for performing PCA in autocorrelation space, without explicitly computing the autocorrelations. The connections with the nonlinear PCA and possible extensions are also discussed

A New Kind of Finance

Finance has benefited from the Wolfram's NKS approach but it can and will benefit even more in the future, and the gains from the influence may actually be concentrated among practitioners who unintentionally employ those principles as a group.Comment: 13 pages; Forthcoming in "Irreducibility and Computational Equivalence: 10 Years After Wolfram's A New Kind of Science," Hector Zenil, ed., Springer Verlag, 201

The development of a convergence diagnostic for Markov Chain Monte Carlo estimation

The development and investigation of a convergence diagnostic for Markov Chain Monte Carlo (MCMC) posterior distributions is presented in this paper. The current method is an adaptation of an existing convergence diagnostic based on the Cumulative Sum (CUSUM, Page 1954; Yu & Mykland, 1998; Brooks, 1998c) procedure. The diagnostic under development is seen to be an improvement over the technique upon which it is based because it offers a simple way to remove one of the two major assumptions made by the previous method, namely that the shape of the distribution under consideration is symmetric. Results are mixed, but there is some evidence to indicate that the new technique is sensitive to the degree of autocorrelation present and the stability of the chains. Also, the new diagnostic behaves differently than three existing convergence diagnostics

Automatic Modulation Classification of Common Communication and Pulse Compression Radar Waveforms using Cyclic Features

This research develops a feature-based MAP classification system and applies it to classify several common pulse compression radar and communication modulations. All signal parameters are treated as unknown to the classifier system except SNR and the signal carrier frequency. The features are derived from estimated duty cycle, cyclic spectral correlation, and cyclic cumulants. The modulations considered in this research are BPSK, QPSK, 16-QAM, 64-QAM, 8-PSK, and 16-PSK communication modulations, as well as Barker coded, Barker coded, Barker coded, Frank coded, Px49 coded, and LFM pulse compression modulations. Simulations show that average correct signal modulation type classification %C 90% is achieved for SNR 9dB, average signal modulation family classification %C 90% is achieved for SNR 1dB, and an average communication versus pulse compression radar modulation classification %C 90% is achieved for SNR -4dB. Also, it is shown that the classification cation performance using selected input features is sensitive to signal bandwidth but not to carrier frequency. Mismatched bandwidth between training and testing signals caused degraded classification cation of %C 10% - 14% over the simulated SNR range