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Biomedical Signal and Image Processing
If we are to choose between the preceding PDFs, use MLE to identify the functions
that best approximate the unknown distribution.
7.7 Load the file “p_7_7.mat.” This synthetic dataset contains a set of samples generated
by an unknown distribution.
a. Assume that the data are generated by a Gaussian distribution and use
MATLAB to find its parameters.
b. Assume that the data are generated by a binomial distribution and use
MATLAB to find its parameters.
c. Assume that the data are generated by an exponential distribution and use
MATLAB to find its parameters.
d. Comparing the results of the preceding three parts, which distribution is
more likely to have produced that data?
7.8 Load the file “p_7_8.mat.” This synthetic dataset contains the input and output of
a system to be modeled using neural networks. There are two classes identified as
1 and −1. The data have been split into two sets: training and testing.
a. Use MATLAB and the training data to create a three-layer sigmoid neural
network as a classifier of the data. Assume there are two hidden neurons and
choose a suitable learning rate.
b. S imulate the trained neural network against both the training and testing data
and compare the accuracy on the neural model on these two sets.
c. Repeat parts “a” and “b” assuming ten hidden neurons in the hidden layer
and compare the results with those of part “b.”
7.9 In this problem, we are to develop a simple classifier to extract some measures
from the heartbeat signals and predict whether the person whose heartbeat is
recorded is young or elderly. Read the file p_7_9.mat. This is the same set of
data used in Problem 6.2.* This file contains 10 heartbeat signals. Ten heartbeat
time-series signals (denoted as Y1, Y2, etc.) are from five young subjects and
five elderly subjects (denoted as O1, O2, etc.).
a. Calculate the following measures for each signal: complexity, mobility, and
Higuchi fractal dimension.
b. Assuming that the distribution of all measures within the same group (old or
young) is Gaussian, use MLE to estimate these distributions.
c. Using the resulting probabilities, design a Bayesian classifier and evaluate the
performance of the resulting classifier.
REFERENCE
Goldberger, A.L., Amaral, L.A.N., Glass, L., Hausdorff, J.M., Ivanov, P.Ch., Mark, R.G.,
Mietus, J.E., Moody, G.B., Peng, C.K., and Stanley, H.E. (2000, June 13). PhysioBank,
PhysioToolkit, and PhysioNet: Components of a new research resource for complex
physiologic signals. Circulation 101(23):e215–e220. [Circulation Electronic Pages;
http://circ.ahajournals.org/cgi/content/full/101/23/e215].
* From Goldberger et al. (2000).
Biomedical Signal and Image Processing
If we are to choose between the preceding PDFs, use MLE to identify the functions
that best approximate the unknown distribution.
7.7 Load the file “p_7_7.mat.” This synthetic dataset contains a set of samples generated
by an unknown distribution.
a. Assume that the data are generated by a Gaussian distribution and use
MATLAB to find its parameters.
b. Assume that the data are generated by a binomial distribution and use
MATLAB to find its parameters.
c. Assume that the data are generated by an exponential distribution and use
MATLAB to find its parameters.
d. Comparing the results of the preceding three parts, which distribution is
more likely to have produced that data?
7.8 Load the file “p_7_8.mat.” This synthetic dataset contains the input and output of
a system to be modeled using neural networks. There are two classes identified as
1 and −1. The data have been split into two sets: training and testing.
a. Use MATLAB and the training data to create a three-layer sigmoid neural
network as a classifier of the data. Assume there are two hidden neurons and
choose a suitable learning rate.
b. S imulate the trained neural network against both the training and testing data
and compare the accuracy on the neural model on these two sets.
c. Repeat parts “a” and “b” assuming ten hidden neurons in the hidden layer
and compare the results with those of part “b.”
7.9 In this problem, we are to develop a simple classifier to extract some measures
from the heartbeat signals and predict whether the person whose heartbeat is
recorded is young or elderly. Read the file p_7_9.mat. This is the same set of
data used in Problem 6.2.* This file contains 10 heartbeat signals. Ten heartbeat
time-series signals (denoted as Y1, Y2, etc.) are from five young subjects and
five elderly subjects (denoted as O1, O2, etc.).
a. Calculate the following measures for each signal: complexity, mobility, and
Higuchi fractal dimension.
b. Assuming that the distribution of all measures within the same group (old or
young) is Gaussian, use MLE to estimate these distributions.
c. Using the resulting probabilities, design a Bayesian classifier and evaluate the
performance of the resulting classifier.
REFERENCE
Goldberger, A.L., Amaral, L.A.N., Glass, L., Hausdorff, J.M., Ivanov, P.Ch., Mark, R.G.,
Mietus, J.E., Moody, G.B., Peng, C.K., and Stanley, H.E. (2000, June 13). PhysioBank,
PhysioToolkit, and PhysioNet: Components of a new research resource for complex
physiologic signals. Circulation 101(23):e215–e220. [Circulation Electronic Pages;
http://circ.ahajournals.org/cgi/content/full/101/23/e215].
* From Goldberger et al. (2000).