42024829
Strong consistency of the contraction mapping method for frequency estimation
Some statistical properties in regard to the contraction mapping (CM) method are discussed. One of the requirements in this method is that the filter be parameterized to satisfy a certain fundamental property. The parameterization clearly depends on the normalized noise spectrum which theoretically has to be known or estimated a priori. If this information is available, one can first whiten the noise with a linear filter and then apply the CM method to the filtered data. In this way, the parameterization only needs to be done under the white noise assumption and filters like the AR(2) can be used by the CM method. In applications, however, prewhitening may not always be necessary. >
20811204
Asymptotic analysis of a fast algorithm for efficient multiple frequency estimation
Based on an asymptotic analysis of the contraction mapping (CM) method of Li and Kedem (1993), a bandwidth shrinkage rule is proposed for fast and accurate estimation of the frequencies of multiple sinusoids from noisy measurements. The CM frequency estimates are defined as the fixed points of a contractive mapping formed by the lag-one autocorrelation coefficient calculated from the output. of a parametric filter applied to the observed time series. With bandwidth parameters judiciously chosen according to the asymptotic analysis, the algorithm is shown to be able to accommodate possibly poor initial values of precision O(n/sup -1/3/) and converge to a final estimate whose accuracy is arbitrarily close to O(n/sup -3/2/), the optimal error rate for frequency estimation under the Gaussian assumption. The total computational complexity of the algorithm is shown to be O(n log n), which is comparable to that of n-point fast Fourier transform (FFT). A novelty in the asymptotic analysis is that it accommodates closely spaced frequencies by allowing not only the filter bandwidth but also the frequency separation to be functions of the sample size n. This enables an assessment of the accuracy of the frequency estimates for given bandwidths and initial values in situations where some or all of the frequencies are close to each other.
206736471
Wavelet spectrum and its characterization property for random processes
The wavelet spectrum of a random process comprises the variances of the wavelet coefficients of the process computed within each scale. This paper investigates the possibility of using the wavelet spectrum, obtained from a continuous wavelet transform (CWT), to uniquely represent the second-order statistical properties of random processes-particularly, stationary processes and long-memory nonstationary processes. As is well known, the Fourier spectrum of a stationary process is mathematically equivalent to the autocovariance function (ACF) and thus uniquely determines the second-order statistics of the process. This characterization property is shown to be possessed also by the wavelet spectrum under very mild regularity conditions that are easily satisfied by many widely used wavelets. It is also shown that under suitable regularity conditions, the characterization property remains valid for processes with stationary increments including 1/f noise.
3016046
Asymptotic analysis of a fast algorithm for efficient multiple frequency estimation
3381503
Finite-alphabet information and multivariate blind deconvolution and identification of linear systems
This article addresses the problem of estimating a multivariate linear system from its output when the input is an unobservable sequence of random vectors with finite-alphabet distribution. By explicitly utilizing the finite-alphabet property, an estimation method is proposed under the traditional inverse filtering paradigm as a generalization of a univariate method that has been studied previously. Identifiability of multivariate systems by the proposed method is proved mathematically under very mild conditions that can be satisfied even if the input is nonstationary and has both cross-channel and serial statistical dependencies. Statistical super-efficiency in estimating both parametric and nonparametric systems is also established for an alphabet-based cost function.
8716577
Blind identification and deconvolution of linear systems driven by binary random sequences
The problem of blind identification and deconvolution of linear systems with independent binary inputs is addressed. To solve the problem, a linear system is applied to the observed data and adjusted so as to produce binary outputs. It is proved that the system coincides with the inverse of the unknown system (with scale and shift ambiguities), whether it is minimum or nonminimum phase. These results are derived for nonstationary independent binary inputs of infinite or finite length. Based on these results, an identification method is proposed for parametric linear systems. It is shown that under some mild conditions, a consistent estimator of the parameter can be obtained by minimizing a binariness criterion for the output data. Unlike many other blind identification and deconvolution methods, this criterion handles nonstationary signals and does not utilize any moment information of the inputs. Three numerical examples are presented to demonstrate the effectiveness of the proposed method. >
10257142
Regularized clustering for documents
In recent years, document clustering has been receiving more and more attentions as an important and fundamental technique for unsupervised document organization, automatictopic extraction, and fast information retrieval or filtering. In this paper, we propose a novel method for clustering documents using regularization. Unlike traditional globally regularized clustering methods, our method first construct a local regularized linear label predictor for each document vector, and then combine all those local regularizers with a global smoothness regularizer. So we call our algorithm Clustering with Local and Global Regularization (CLGR). We will show that the cluster memberships of the documents can be achieved by eigenvalue decomposition of a sparse symmetric matrix, which can be efficiently solved by iterative methods. Finally our experimental evaluations on several datasets are presented to show the superiorities of CLGR over traditional document clustering methods.
13006383
Document clustering via adaptive subspace iteration
Document clustering has long been an important problem in information retrieval. In this paper, we present a new clustering algorithm ASI1 , which uses explicitly modeling of the subspace structure associated with each cluster. ASI simultaneously performs data reduction and subspace identification via an iterative alternating optimization procedure. Motivated from the optimization procedure, we then provide a novel method to determine the number of clusters. We also discuss the connections of ASI with various existential clustering approaches. Finally, extensive experimental results on real data sets show the effectiveness of ASI algorithm.
13900916
Detection of cognitive binding during ambiguous figure tasks by wavelet coherence analysis of EEG signals
It is hypothesized that the perception of an alternative image in ambiguous figures would be manifested as an increase in synchronization of EEG signals over multiple scalp sites as "cognitive binding" occurs. A statistical time-frequency analysis (STFA) approach is taken to detect cognitive binding. The STFA approach consists of an analysis filter bank that extracts useful components from the input EEG signals and certain statistical parameters at the output that characterize the synchronization patterns over multiple scalp sites. With the help of wavelet-packet filters and wavelet coherence measures, cognitive binding is detected over many frequency bands by statistical testing.
15097946
Algorithms for clustering high dimensional and distributed data
Clustering is the problem of identifying the distribution of patterns and intrinsic correlations in large data sets by partitioning the data points into similarity classes. The clustering problem has been widely studied in machine learning, databases, and statistics. This paper studies the problem of clustering high dimensional data. The paper proposes an algorithm called the CoFD algorithm, which is a non-distance based clustering algorithm for high dimensional spaces. Based on the Maximum Likelihood Principle, CoFD attempts to optimize its parameter settings to maximize the likelihood between data points and the model generated by the parameters. The distributed versions of the problem, called the D-CoFD algorithms, are also proposed. Experimental results on both synthetic and real data sets show the efficiency and effectiveness of CoFD and D-CoFD algorithms.
11749878
IFD: Iterative Feature and Data Clustering
In this paper, we propose a new clustering algorithm, IFD1, based on a cluster model of data coefficients D and feature coefficients F . The coefficients denote the degree (or weights) of the data and features associated with the clusters. Clustering is performed via an iterative optimization procedure to mutually reinforce the relationships between the coefficients. The mutually reinforcing optimization exploits the duality of the data and features and enable a simultaneous clustering of both data and features. We have shown the convergence property of the clustering algorithm and discussed its connections with various existential approaches. Extensive experimental results on both synthetic and real data sets show the effectiveness of IFD algorithm.