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Assignment 1 Vertebral Column Data Set
1. In this exercise, you will work with Vertebral Column Data Set that you
can download from the following link:
http://archive.ics.uci.edu/ml/datasets/Vertebral+Column
a. Once you have downloaded the data, you will prepare a descriptive
summary of the data. The summary should describe the followings in a
tabular form:
i. Means for all features (attributes) for both normal and
abnormal classes
ii. Standard deviations for all features for each class
iii. Medians for all features for each class.
b. Next generate scatter plots for all feature pairs
c. Based on (a) and (b), express your opinion about how well the two
classes are separated.
2. This exercise is designed to make you familiar with multivariate normal
distribution generation and using the generated data.
a. Generate 100 3-dimensional vectors that come from a normal
distribution with mean vector as [1 2 1]t and 3x3 covariance matrix as
[4 0.8 -0.3; 0.8 2 0.6; -0.3 0.6 5]
b. Make scatter plots of x1 vs x2, x1 vs x3, and x2 vs x3. Explain
whatever relationships you can gather from these plots
c. Pick any pair of generated vectors and calculate the Euclidean and
Mahalanobis distances between that pair.
3. Consider the following five-dimensional records consisting of attributes 1
to 5.:
Suppose we are interested in reducing the five-dimensional records to two
CSI 5810 (Assignment # 1)
dimensions by means of the principal component analysis. List the
eigenvalues and eigenvectors obtained via PCA. Determine the reduced
representation for all of the records, and plot the reduced representation in
form of scatter plot. Reconstruct the original data and compute the
reconstruction error.
4. Apply PCA to Vertebral Column Data Set and reduce the data to two
dimensions [The class labels are not used in PCA]. List all eigenvalues and
make a scatter plot of the transformed data. Show transformed normal and
abnormal data points in different colors or shapes.
5. Repeat Exercise #3 using t-SNE visualization method. Perform visualization
with two perplexity values, 10 and 50. Comment on the results obtained.
can download from the following link:
http://archive.ics.uci.edu/ml/datasets/Vertebral+Column
a. Once you have downloaded the data, you will prepare a descriptive
summary of the data. The summary should describe the followings in a
tabular form:
i. Means for all features (attributes) for both normal and
abnormal classes
ii. Standard deviations for all features for each class
iii. Medians for all features for each class.
b. Next generate scatter plots for all feature pairs
c. Based on (a) and (b), express your opinion about how well the two
classes are separated.
2. This exercise is designed to make you familiar with multivariate normal
distribution generation and using the generated data.
a. Generate 100 3-dimensional vectors that come from a normal
distribution with mean vector as [1 2 1]t and 3x3 covariance matrix as
[4 0.8 -0.3; 0.8 2 0.6; -0.3 0.6 5]
b. Make scatter plots of x1 vs x2, x1 vs x3, and x2 vs x3. Explain
whatever relationships you can gather from these plots
c. Pick any pair of generated vectors and calculate the Euclidean and
Mahalanobis distances between that pair.
3. Consider the following five-dimensional records consisting of attributes 1
to 5.:
Suppose we are interested in reducing the five-dimensional records to two
CSI 5810 (Assignment # 1)
dimensions by means of the principal component analysis. List the
eigenvalues and eigenvectors obtained via PCA. Determine the reduced
representation for all of the records, and plot the reduced representation in
form of scatter plot. Reconstruct the original data and compute the
reconstruction error.
4. Apply PCA to Vertebral Column Data Set and reduce the data to two
dimensions [The class labels are not used in PCA]. List all eigenvalues and
make a scatter plot of the transformed data. Show transformed normal and
abnormal data points in different colors or shapes.
5. Repeat Exercise #3 using t-SNE visualization method. Perform visualization
with two perplexity values, 10 and 50. Comment on the results obtained.
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