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.
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. >
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.
15267641
Estimating Joint Probabilities from Marginal Ones
Estimating joint probabilities plays an important role in many data mining and machine learning tasks. In this paper we introduce two methods, minAB and prodAB, to estimate joint probabilities. Both methods are based on a light-weight structure, partition support. The core idea is to maintain the partition support of itemsets over logically disjoint partitions and then use it to estimate joint probabilities of item-sets of higher cardinalitiess. We present extensive mathematical analyses on both methods and compare their performances on synthetic datasets. We also demonstrate a case study of using the estimation methods in Apriori algorithm for fast association mining. Moreover, we explore the usefulness of the estimation methods in other mining/learning tasks. Experimental results show the effectiveness of the estimation methods.
5255914
Recommendation on Item Graphs
A novel scheme for item-based recommendation is proposed in this paper. In our framework, the items are described by an undirected weighted graph Q = (V,epsiv). V is the node set which is identical to the item set, and epsiv is the edge set. Associate with each edge eij isin epsiv is a weight omegaij ges 0, which represents similarity between items i and j. Without the loss of generality, we assume that any user's ratings to the items should be sufficiently smooth with respect to the intrinsic structure of the items, i.e., a user should give similar ratings to similar items. A simple algorithm is presented to achieve such a smooth solution. Encouraging experimental results are provided to show the effectiveness of our method.
17077200
A Clustering Model Based on Matrix Approximation with Applications to Cluster System Log Files
In system management applications, to perform automated analysis of the historical data across multiple components when problems occur, we need to cluster the log messages with disparate formats to automatically infer the common set of semantic situations and obtain a brief description for each situation. In this paper, we propose a clustering model where the problem of clustering is formulated as matrix approximations and the clustering objective is minimizing the approximation error between the original data matrix and the reconstructed matrix based on the cluster structures. The model explicitly characterizes the data and feature memberships and thus enables the descriptions of each cluster. We present a two-side spectral relaxation optimization procedure for the clustering model. We also establish the connections between our clustering model with existing approaches. Experimental results show the effectiveness of the proposed approach.
40685778
Hierarchical Document Classification Using Automatically Generated Hierarchy