Covariance matrix estimation and classification with limited training data

Hoffbeck, Joseph P.; Landgrebe, D. A.

doi:10.1109/34.506799

Cited by 273 publications

(167 citation statements)

References 2 publications

(3 reference statements)

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“…To make the above approach useful for machine learning, we still need to define a way to calculate the most convenient value for H. This can be achieved by means of the leave-one-out strategy [4,5,6]. The technique is to remove one of the training samples from X, compute SIR using the remaining samples (for a given value of H), and then compute the recognition rate of the sample that was omitted; i.e.…”

Section: The Optimal Value Of Hmentioning

confidence: 99%

Template-based Recognition of Static Sitting Postures

Zhu

Martı́nez

Tan³

2003

2003 Conference on Computer Vision and Pattern Recognition Workshop

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In this paper we introduce a generalization of FisherRao's discriminant analysis and its application in a human-computer interaction scenario: a sensing chair. Our algorithm shows to be able to successfully estimate the underlying distributions of the pressure maps data of the sensing chair. Other linear discriminant techniques, such as LDA, had been found to be inadequate for the job; typically yielding inferior results than PCA. We compare our approach to several template-based approaches and show that the new discriminant function is comparable to the best approach classifier. This is important because generally each application tends to prefer a different algorithm. Fortunately, our new algorithm is usually the top one (or comparable to the top one). In this paper we will however restrict our study tothe classification of sitting postures.

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Section: The Optimal Value Of Hmentioning

confidence: 99%

Template-based Recognition of Static Sitting Postures

Zhu

Martı́nez

Tan³

2003

2003 Conference on Computer Vision and Pattern Recognition Workshop

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“…The notation \r conforms to the Hoffbeck and Landgrebe (1996) work. It indicates that the corresponding quantity is calculated with the r-th observation from class i removed.…”

Section: The Mixture Parametermentioning

confidence: 99%

“…From replacing the true values of the mean and the covariance matrix in equation (1) by their respective estimates, the Bayes decision rule achieves optimal classification accuracy only when the number of training samples increases toward infinity (e.g., Hoffbeck and Landgrebe, 1996). In fact for p-dimensional patterns the sample covariance matrix is singular if less than 1 + p training examples from each class i are available, that is, the sample covariance matrix can not be calculated if i k is less than the dimension of the feature space.…”

Section: Maximum Probability Classifiermentioning

confidence: 99%

“…According to Hoffbeck and Landgrebe (1996), the value of the mixture parameter i w can be appropriately selected so that a best fit to the training samples is achieved. Their technique is based on the leave-one-out-likelihood (L) parameter estimation (Fukunaga, 1990).…”

Section: The Mixture Parametermentioning

confidence: 99%

“…The mixture covariance matrices are based on the Hoffbeck and Landgrebe (1996) approach and have the property of having the same rank as the pooled estimate, while allowing a different estimate for each group. Thus, the mixture estimate may result in higher accuracy.…”

Section: Introductionmentioning

confidence: 99%

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Using mixture covariance matrices to improve face and facial expression recognitions

Thomaz

Gillies

Feitosa

2003

Pattern Recognition Letters

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Abstract. In several pattern recognition problems, particularly in image recognition ones, there are often a large number of features available, but the number of training examples for each pattern is significantly less than the dimension of the feature space. This statement implies that the sample group covariance matrices often used in the Gaussian maximum probability classifier are singular. A common solution to this problem is to assume that all groups have equal covariance matrices and to use as their estimates the pooled covariance matrix calculated from the whole training set. This paper uses an alternative estimate for the sample group covariance matrices, here called the mixture covariance, given by an appropriate linear combination of the sample group and pooled covariance matrices. Experiments were carried out to evaluate the performance associated with this estimate in two biometric applications: face and facial expression. The average recognition rates obtained by using the mixture covariance matrices were higher than the usual estimates.

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A simplified MAP channel estimator for OFDM systems under Rayleigh fading

Çürük

Tanik²

2010

Trans Emerging Tel Tech

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This paper presents a simplified Maximum A Posteriori (SMAP) channel estimator to be used in orthogonal frequency division multiplexing (OFDM) systems under the Rayleigh fading assumption for the subchannels, using a parametric correlation model and assuming that the channel is frequency selective and slowly time varying. Expressions for the mean-square error (MSE) of estimations are derived to evaluate the performance of the estimator. The relation between the correlation of subchannels taps and error variance is investigated. Dependencies of the proposed estimator's performance on the correlation parameter estimation error and signal-to-noise ratios (SNR) estimation error are analysed. We provide approximations on the estimator algorithms in order to make the estimator practical. The simulations done using measured channel data show that the proposed estimator with approximations operates satisfactorily with negligible loss in performance. Finally, we investigate the symbol error rate (SER) performance of an OFDM system using quadrature phaseshift keying (QPSK) modulation, based on channel estimation modes (a) training sequence (b) decision feedback and (c) pilot subcarriers. The results have indicated that the proposed estimator performance is always better than maximum likelihood (ML) estimator, and as the subchannel correlation increases (large number of subcarriers) the performance comes very close to that of exactly known channel case. Copyright Figure 7. SER versus Doppler frequency (Hz), N = 1024, training sequence and decision directed channel estimation, Monte Carlo simulation. SIMPLIFIED MAP CHANNEL ESTIMATOR 403 of f m = 40 Hz. Thus, channel correlation is E z nk · z * ml = J 0 (2π f m (k − l) T s )

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Covariance matrix estimation and classification with limited training data

Cited by 273 publications

References 2 publications

Template-based Recognition of Static Sitting Postures

Template-based Recognition of Static Sitting Postures

Using mixture covariance matrices to improve face and facial expression recognitions

A simplified MAP channel estimator for OFDM systems under Rayleigh fading

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