Description
Problem 1 For the K-means clustering problem, when the binary indicators (responsibilities) ๐ a e fi ed f k=1, 2, , K a d =1, 2, , N, de i e f he cl e ce e ๐ฆ , k=1, 2, , K, ch ha he following objective function J is minimized:
Problem 2 Iris.xls contains 150 data samples of three Iris categories, labeled by outcome values 0, 1, and 2. Each data sample has four attributes: sepal length, sepal width, petal length, and petal width.
Implement the K-means clustering algorithm to group the samples into K=3 clusters. Randomly choose three samples as the initial cluster centers. Calculate the objective function value J as defined in Problem 1 after the assignment step in each iteration. Exit the iterations if the following criterion is met: ๐ฝ Iter 1 ๐ฝ Iter ฮต, where ฮต 10 , and Iter is the iteration number. Plot the objective function value J versus the iteration number Iter. Comment on the result. Attach the code at the end of the homework.
Problem 3 Assume a data sample ๐ฑ โ โ comes from one of two classes, ๐ถ1 and ๐ถ . Use logistic regression to do classification.
- Write the math expression of the logistic regression output, and the criterion used for the final classification.
- How many parameters (weights) need to be calculated/trained in this method?
Problem 4 Assume a data sample ๐ฑ โ โ comes from one of ๐พ classes, ๐ถ1, ๐ถ , ย ย ย ย ย ย , ๐ถ . Use logistic regression to do classification.
- Write the math expression of the logistic regression output, and the criterion used for the final classification.
- How many parameters (weights) need to be calculated/trained in this method?
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