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39
Estimating the number of endmembers in hyperspectral images using the normal compositional model and a hierarchical Bayesian algorithm
 Department of Electrical Engineering and Computer Science, University of Michigan, Ann
, 1984
"... Abstract—This paper studies a semisupervised Bayesian unmixing algorithm for hyperspectral images. This algorithm is based on the normal compositional model recently introduced by Eismann and Stein. The normal compositional model assumes that each pixel of the image is modeled as a linear combinati ..."
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Abstract—This paper studies a semisupervised Bayesian unmixing algorithm for hyperspectral images. This algorithm is based on the normal compositional model recently introduced by Eismann and Stein. The normal compositional model assumes that each pixel of the image is modeled as a linear combination of an unknown number of pure materials, called endmembers. However, contrary to the classical linear mixing model, these endmembers are supposed to be random in order to model uncertainties regarding their knowledge. This paper proposes to estimate the mixture coefficients of the Normal Compositional Model (referred to as abundances) as well as their number using a reversible jump Bayesian algorithm. The performance of the proposed methodology is evaluated thanks to simulations conducted on synthetic and real AVIRIS images. Index Terms—Bayesian inference, hyperspectral images, Monte Carlo methods, normal compositional model, reversible jump,
Comparison of model order selection techniques for highresolution parameter estimation algorithms
 in Proc. 54th International Scientific Colloquium (IWK
, 2009
"... In sensor array processing it is often required to know the number of signals received by an antenna array, since in practice only a limited number of observations is available. Robust techniques for the estimation of the model order are needed. In this paper, we propose general application rules fo ..."
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Cited by 7 (1 self)
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In sensor array processing it is often required to know the number of signals received by an antenna array, since in practice only a limited number of observations is available. Robust techniques for the estimation of the model order are needed. In this paper, we propose general application rules for the most recent model order selection techniques in the literature considering different onedimensional scenarios. Other important contributions are a more general and improved form of the modified exponential fitting test (MEFT) and extensions of other known model order selection techniques for the case that the number of sensors is greater than the number of snapshots.
Source enumeration via MDL criterion based on linear shrinkage estimation of noise subspace covariance matrix
 IEEE Trans. Signal Process. 2013
"... Abstract—Numerous methodologies have been investigated for source enumeration in samplestarving environments. For those having their root in the framework of random matrix theory, the involved distribution of the sample eigenvalues is required. Instead of relying on the eigenvalue distribution, thi ..."
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Abstract—Numerous methodologies have been investigated for source enumeration in samplestarving environments. For those having their root in the framework of random matrix theory, the involved distribution of the sample eigenvalues is required. Instead of relying on the eigenvalue distribution, this work devises a linear shrinkage based minimum description length (LSMDL) criterion by utilizing the identity covariance matrix structure of noise subspace components. With linear shrinkage and Gaussian assumption of the observations, an accurate estimator for the covariance matrix of the noise subspace components is derived. The eigenvalues obtained from the estimator turn out to be a linear function of the corresponding sample eigenvalues, enabling the LSMDL criterion to accurately detect the source number without incurring significantly additional computational load. Furthermore, the strong consistency of the LSMDL criterion for and is proved, where and are the antenna number and snapshot number, respectively. Simulation results are included for illustrating the effectiveness of the proposed criterion. Index Terms—Linear shrinkage, minimum description length, sample covariance matrix, source enumeration. I.
Theoretical analysis and comparison of several criteria on linear model dimension reduction
 Independent Component Analysis and Signal Separation. Lecture Notes in Computer Science
"... Abstract. Detecting the dimension of the latent subspace of a linear model, such as Factor Analysis, is a wellknown model selection problem. The common approach is a twophase implementation with the help of an information criterion. Aiming at a theoretical analysis and comparison of different crit ..."
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Abstract. Detecting the dimension of the latent subspace of a linear model, such as Factor Analysis, is a wellknown model selection problem. The common approach is a twophase implementation with the help of an information criterion. Aiming at a theoretical analysis and comparison of different criteria, we formulate a tool to obtain an order of their approximate underestimationtendencies, i.e., AIC, BIC/MDL, CAIC, BYYFA(a), from weak to strong under mild conditions, by studying a key statistic and a crucial but unknown indicator set. We also find that DNLL favors cases with slightly dispersed signal and noise eigenvalues. Simulations agree with the theoretical results, and also indicate the advantage of BYYFA(b) in the cases of small sample size and large noise. 1
ESTIMATION OF THE NUMBER OF FACTORS, POSSIBLY EQUAL, IN THE HIGHDIMENSIONAL CASE
, 2013
"... Abstract. Estimation of the number of factors in a factor model is an important problem in many areas such as economics or signal processing. Most of classical approaches assume a large sample size n whereas the dimension p of the observations is kept small. In this paper, we consider the case of hi ..."
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Abstract. Estimation of the number of factors in a factor model is an important problem in many areas such as economics or signal processing. Most of classical approaches assume a large sample size n whereas the dimension p of the observations is kept small. In this paper, we consider the case of high dimension, where p is large compared to n. The approach is based on recent results of random matrix theory. We extend our previous results to a more difficult situation when some factors are equal, and compare our algorithm to an existing benchmark method. 1.
A theoretical investigation of several model selection criteria for . . .
 PATTERN RECOGNITION LETTERS
, 2012
"... ..."
An investigation of several typical model selection criteria for detecting the number of signals
 FRONT. ELECTR. ELECTRON. ENG. CHINA 2011, 6(2): 245–255
, 2011
"... Based on the problem of detecting the number of signals, this paper provides a systematic empirical investigation on model selection performances of several classical criteria and recently developed methods (including Akaike’s information criterion (AIC), Schwarz’s Bayesian information criterion, B ..."
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Based on the problem of detecting the number of signals, this paper provides a systematic empirical investigation on model selection performances of several classical criteria and recently developed methods (including Akaike’s information criterion (AIC), Schwarz’s Bayesian information criterion, Bozdogan’s consistent AIC, HannanQuinn information criterion, Minka’s (MK) principal component analysis (PCA) criterion, Kritchman & Nadler’s hypothesis tests (KN), Perry & Wolfe’s minimax rank estimation thresholding algorithm (MM), and Bayesian YingYang (BYY) harmony learning), by varying signaltonoise ratio (SNR) and training sample size N. A family of model selection indifference curves is defined by the contour lines of model selection accuracies, such that we can examine the joint effect of N and SNR rather than merely the effect of either of SNR and N with the other fixed as usually done in the literature. The indifference curves visually reveal that all methods demonstrate relative advantages obviously within a region of moderate N and SNR. Moreover, the importance of studying this region is also confirmed by an alternative reference criterion by maximizing the testing likelihood. It has been shown via extensive simulations that AIC and BYY harmony learning, as well as MK, KN, and MM, are relatively more robust than the others against decreasing N and SNR, and BYY is superior for a small sample size.
Optshrink: An algorithm for improved lowrank signal matrix denoising by optimal, datadriven singular value shrinkage
 ISSN 00189448. doi: 10.1109/TIT.2014.2311661. URL http://dx.doi.org/ 10.1109/TIT.2014.2311661
, 2014
"... Abstract. The truncated singular value decomposition (SVD) of the measurement matrix is the optimal solution to the representation problem of how to best approximate a noisy measurement matrix using a lowrank matrix. Here, we consider the (unobservable) denoising problem of how to best approximate ..."
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Abstract. The truncated singular value decomposition (SVD) of the measurement matrix is the optimal solution to the representation problem of how to best approximate a noisy measurement matrix using a lowrank matrix. Here, we consider the (unobservable) denoising problem of how to best approximate a lowrank signal matrix buried in noise by optimal (re)weighting of the singular vectors of the measurement matrix. We exploit recent results from random matrix theory to exactly characterize the large matrix limit of the optimal weighting coefficients and show that they can be computed directly from data for a large class of noise models that includes the i.i.d. Gaussian noise case. Our analysis brings into sharp focus the shrinkageandthresholding form of the optimal weights, the nonconvex nature of the associated shrinkage function (on the singular values) and explains why matrix regularization via singular value thresholding with convex penalty functions (such as the nuclear norm) will always be suboptimal. We validate our theoretical predictions with numerical simulations, develop an implementable algorithm (OptShrink) that realizes the predicted performance gains and show how our methods can be used to improve estimation in the setting where the measured matrix has missing entries. 1.
Bayesian information criterion for source enumeration in largescale adaptive antenna array
 IEEE TRANS. VEH. TECHNOL
, 2015
"... Subspacebased highresolution algorithms for directionofarrival estimation have been developed for largescale adaptive antenna arrays. However, its prerequisite step, namely, source enumeration, has not yet been addressed. In this work, a new approach is devised in the framework of Bayesian info ..."
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Subspacebased highresolution algorithms for directionofarrival estimation have been developed for largescale adaptive antenna arrays. However, its prerequisite step, namely, source enumeration, has not yet been addressed. In this work, a new approach is devised in the framework of Bayesian information criterion (BIC) to provide reliable detection of the signal source number for the general asymptotic regime where m;n! 1 and m=n! c 2 (0;1) with m and n being the numbers of antennas and snapshots, respectively. In particular, the a posteriori probability is determined by correctly calculating the loglikelihood and penalty functions for the general asymptotic case. By means of the maximum a posteriori probability, we are capable of effectively finding the signal number. Accurate closedform expression for the probability of missed detection is also derived for the proposed BIC variant. In addition, the probability of falsealarm for the BIC detector is proved to converge to zero as m;n! 1 and m=n! c. Simulation results are included to demonstrate the superiority of the proposed detection approach over stateoftheart schemes and corroborate our theoretical calculations.
Improved blind automatic malicious activity detection in honeypot data,” ICoFCS
, 2012
"... Abstract—This paper presents the modified exponential fitting test for automatically identifying malicious activities in honeypot data based on state of the art model order selection schemes. Model order selection (MOS) schemes are frequently applied in several signal processing applications, such a ..."
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Abstract—This paper presents the modified exponential fitting test for automatically identifying malicious activities in honeypot data based on state of the art model order selection schemes. Model order selection (MOS) schemes are frequently applied in several signal processing applications, such as RADAR, SONAR, communications, channel modeling, medical imaging, and parameters estimation of dominant multipath components from MIMO channel measurements. "In this paper, we apply MOS schemes for the identification of malicious activity in honeypots." The proposed blind automatic techniques are efficient and need neither previous training nor knowledge of attack signatures for detecting malicious activities. In order to achieve such results an innovative approach is considered which models network traffic data as signals and noise allowing the application of signal processing methods. The model order selection schemes are adapted to process network data, showing that the Modified Exponential Fitting Test achieves the best performance and reliability in detecting attacks. The efficiency and accuracy of the theoretical results are tested on real data collected at a honeypot system located at the network border of a large banking institution in Latin America. I.