Estimating the Information Potential with the Fast Gauss Transform

Han, Seungju; Rao, S.S.; Prı́ncipe, José C.

doi:10.1007/11679363_11

Cited by 10 publications

(10 citation statements)

References 8 publications

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“…Therefore, we define the test statistic , where (18) where the constant (19) The resulting classification rule therefore becomes , . We name the classifier we have derived the Laplacian classifier, because of the connection to the Laplacian matrix and its eigenspectrum (see also Section V-A).…”

Section: New Classification Rulementioning

confidence: 99%

“…Let be the outlier, and let denote its weight. The test statistic, (18), for class , with the outlier appended, is thus given by (23) The normalizing constant is expressed by the denominator of this expression. Let .…”

Section: Robustness Against Outliersmentioning

confidence: 99%

“…This reduces the training phase complexity to , . Another possibility is to evaluate the kernel expansions with less computational complexity using the fast Gauss transform [17], as demonstrated on a similar problem in [18]. This reduces the complexity to per data dimension, where is the number of clusters used in the approximation and is the truncation order.…”

Section: New Classification Rulementioning

confidence: 99%

See 2 more Smart Citations

The Laplacian Classifier

Jenssen

Erdoğmuş²,

Prı́ncipe³

et al. 2007

IEEE Trans. Signal Process.

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We develop a novel classifier in a kernel feature space related to the eigenspectrum of the Laplacian data matrix. The classification cost function measures the angle between class mean vectors in the kernel feature space, and is derived from an information theoretic divergence measure using Parzen windowing. The classification rule is expressed in terms of a weighted kernel expansion. The weighting associated with a data point is inversely proportional to the probability density at that point, emphasizing the least probable regions. No optimization is needed to determine the weighting scheme, as opposed to the support vector machine. The connection to Parzen windowing also provides a theoretical criterion for kernel size selection, reducing the need for computationally demanding cross-validation. We show that the new classifier performs better than the Parzen window Bayes classifier, and in many cases comparable to the support vector machine, at a computationally lower cost.

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Section: New Classification Rulementioning

confidence: 99%

Section: Robustness Against Outliersmentioning

confidence: 99%

Section: New Classification Rulementioning

confidence: 99%

See 1 more Smart Citation

The Laplacian Classifier

Jenssen

Erdoğmuş²,

Prı́ncipe³

et al. 2007

IEEE Trans. Signal Process.

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show abstract

“…Although there are double summations in the correntropy coefficient, the computational complexity can be reduced to using the fast-Gauss transform [35]. However, the "narrowed" autocorrelation function increases computational complexity by including more delay terms.…”

Section: Pda Based On Correntropymentioning

confidence: 99%

A Pitch Detector Based on a Generalized Correlation Function

Prı́ncipe

2008

IEEE Trans. Audio Speech Lang. Process.

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Abstract-This paper proposes a novel pitch determination algorithm (PDA) based on the newly introduced concept of a generalized correlation function called correntropy. Correntropy is a positive definite kernel function which implicitly transforms the original signal into a high-dimensional reproducing kernel Hilbert space (RKHS) in a nonlinear way, and calculates very efficiently the generalized correlation in that RKHS. By incorporating the kernel function, correntropy is able to utilize higher order statistics to enhance the resolution of pitch estimation. The proposed PDA computes the summary of correntropy functions from the outputs of an equivalent rectangular bandwidth (ERB) filter bank. We present simulations on pitch determination for a single vowel, double vowels, and a benchmark database test. Simulations show that correntropy exhibits much better resolution than conventional autocorrelation in pitch determination and outperforms other PDAs in the benchmark database test.Index Terms-Correntropy, pitch determination, reproducing kernel Hilbert space (RKHS).

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“…Of course the computation of each entry of the matrix, the correntropy between components increases with the square of the number of samples. New fast techniques O(N ) to compute each entry have been developed [3].…”

Section: Simulationsmentioning

confidence: 99%

Nonlinear Component Analysis Based on Correntropy

Xu¹,

Pokharel²,

Paiva³

et al.

The 2006 IEEE International Joint Conference on Neural Network Proceedings

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Abstract-In this paper, we propose a new nonlinear principal component analysis based on a generalized correlation function which we call correntropy. The data is nonlinearly transformed to a feature space, and the principal directions are found by eigen-decomposition of the correntropy matrix, which has the same dimension as the standard covariance matrix for the original input data. The correntropy matrix characterizes the nonlinear correlations between the data. With the correntropy function, one can efficiently compute the principal components in the feature space by projecting the transformed data onto those principal directions. We give the derivation of the new method and present simulation results.

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Estimating the Information Potential with the Fast Gauss Transform

Cited by 10 publications

References 8 publications

The Laplacian Classifier

The Laplacian Classifier

A Pitch Detector Based on a Generalized Correlation Function

Nonlinear Component Analysis Based on Correntropy

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