Grouping a few sets of normally distributed voxels of SPECT volumes in discrimination between Alzheimer dementia and controls.

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Abstract

It is widely accepted and can be easily verified that any specific voxel in a class of brain single photon emission computed tomography (SPECT) volumes is of a univariate normal distribution. In this research, we conjecture that all the voxels in a class of SPECT volumes are also approximately of a multivariate normal (MVN) distribution from which in terms of the Bayes errors of statistics, an optimal classifier can be designed using quadratic discriminant functions (QDFs). However, the number of training volumes needed for deriving the covariance matrix of an MVN distribution increases quadratically with respect to the number of voxels such that practically the MVN distributions cannot be modeled. To overcome this, we selected a reduced number of voxels and put them into groups based on the P values of two-sided t tests or a greedy algorithm of discrimination between two classes of volumes. We also tried the same approach on the 3D Haar wavelet coefficients which were obtained from the discrete wavelet transform of the voxels. Experiments showed that the accuracies of QDFs, linear discriminant functions (LDFs), and support vector machines (SVMs) were not significantly different in discrimination between Alzheimer's and normal controls verifying that the proposed MVNs effectively model the discrimination information. Moreover, the proposed QDF classifier obtained satisfactory performance.

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Single photon emission computed tomography
Normal Distribution
Normal distribution
Single-Photon Emission-Computed Tomography
Alzheimer Disease
Classifiers
Wavelet Analysis
Discrete wavelet transforms
Covariance matrix
Support vector machines
Brain
Statistics
Research
Experiments

All Science Journal Classification (ASJC) codes

  • Computer Vision and Pattern Recognition
  • Signal Processing
  • Biomedical Engineering
  • Health Informatics

Cite this

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title = "Grouping a few sets of normally distributed voxels of SPECT volumes in discrimination between Alzheimer dementia and controls.",
abstract = "It is widely accepted and can be easily verified that any specific voxel in a class of brain single photon emission computed tomography (SPECT) volumes is of a univariate normal distribution. In this research, we conjecture that all the voxels in a class of SPECT volumes are also approximately of a multivariate normal (MVN) distribution from which in terms of the Bayes errors of statistics, an optimal classifier can be designed using quadratic discriminant functions (QDFs). However, the number of training volumes needed for deriving the covariance matrix of an MVN distribution increases quadratically with respect to the number of voxels such that practically the MVN distributions cannot be modeled. To overcome this, we selected a reduced number of voxels and put them into groups based on the P values of two-sided t tests or a greedy algorithm of discrimination between two classes of volumes. We also tried the same approach on the 3D Haar wavelet coefficients which were obtained from the discrete wavelet transform of the voxels. Experiments showed that the accuracies of QDFs, linear discriminant functions (LDFs), and support vector machines (SVMs) were not significantly different in discrimination between Alzheimer's and normal controls verifying that the proposed MVNs effectively model the discrimination information. Moreover, the proposed QDF classifier obtained satisfactory performance.",
author = "Yin, {Tang Kai} and Chiu, {Nan Tsing} and Pai, {Ming Chyi}",
year = "2010",
language = "English",
pages = "6126--6129",
journal = "Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings",
issn = "1557-170X",
publisher = "Institute of Electrical and Electronics Engineers Inc.",

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T1 - Grouping a few sets of normally distributed voxels of SPECT volumes in discrimination between Alzheimer dementia and controls.

AU - Yin, Tang Kai

AU - Chiu, Nan Tsing

AU - Pai, Ming Chyi

PY - 2010

Y1 - 2010

N2 - It is widely accepted and can be easily verified that any specific voxel in a class of brain single photon emission computed tomography (SPECT) volumes is of a univariate normal distribution. In this research, we conjecture that all the voxels in a class of SPECT volumes are also approximately of a multivariate normal (MVN) distribution from which in terms of the Bayes errors of statistics, an optimal classifier can be designed using quadratic discriminant functions (QDFs). However, the number of training volumes needed for deriving the covariance matrix of an MVN distribution increases quadratically with respect to the number of voxels such that practically the MVN distributions cannot be modeled. To overcome this, we selected a reduced number of voxels and put them into groups based on the P values of two-sided t tests or a greedy algorithm of discrimination between two classes of volumes. We also tried the same approach on the 3D Haar wavelet coefficients which were obtained from the discrete wavelet transform of the voxels. Experiments showed that the accuracies of QDFs, linear discriminant functions (LDFs), and support vector machines (SVMs) were not significantly different in discrimination between Alzheimer's and normal controls verifying that the proposed MVNs effectively model the discrimination information. Moreover, the proposed QDF classifier obtained satisfactory performance.

AB - It is widely accepted and can be easily verified that any specific voxel in a class of brain single photon emission computed tomography (SPECT) volumes is of a univariate normal distribution. In this research, we conjecture that all the voxels in a class of SPECT volumes are also approximately of a multivariate normal (MVN) distribution from which in terms of the Bayes errors of statistics, an optimal classifier can be designed using quadratic discriminant functions (QDFs). However, the number of training volumes needed for deriving the covariance matrix of an MVN distribution increases quadratically with respect to the number of voxels such that practically the MVN distributions cannot be modeled. To overcome this, we selected a reduced number of voxels and put them into groups based on the P values of two-sided t tests or a greedy algorithm of discrimination between two classes of volumes. We also tried the same approach on the 3D Haar wavelet coefficients which were obtained from the discrete wavelet transform of the voxels. Experiments showed that the accuracies of QDFs, linear discriminant functions (LDFs), and support vector machines (SVMs) were not significantly different in discrimination between Alzheimer's and normal controls verifying that the proposed MVNs effectively model the discrimination information. Moreover, the proposed QDF classifier obtained satisfactory performance.

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