Question

b) Plot the data points on the x-y plane and prepare the element-to-element distance matrix $d(x_i, x_j) = \sqrt{(x_i - x_j)^2 + (y_i - y_j)^2}$ ($i, j = 1, 2, \dots, 200$) that will be the input for the clustering algorithm. Also assume each data point carries the same weight, i.e., $p(x_i) = 1/200$ for all $i$. (2p) c) Write a code (no restriction on the program language) to implement the Blahut-Arimoto algorithm to evaluate the clustering membership probabi- lity, $p(\vec{x}|\vec{x})$, with fixed number of clusters, $N_c$, and compression-distortion tradeoff parameter, $\beta$. Your code should implement a multiple run each starting with random initial conditions. Note: Your source code should include clear comments/documentations to describe what are evaluating. I may later randomly ask a few students, especially those without clear documentations, to demonstrate how their code works. (15p) d) Run your code to construct the information curve for $N_c = 2, 3, 4$. Hint: Choose different values of $\beta$ in between 1 to 40. (6p) e) As we have already known that the correct number of clusters is 2, pro- pose a reasonable way using the quantities evaluated from your code (e.g. $I(X, \tilde{X})$, $(d(x, \tilde{x}))p(x, \tilde{x})$, the Lagrange function, etc.) and the information curves to correctly identify the number of clusters. You should clearly ex- plain your rationale and state explicitly which quantities, graphs and/or curves are used in the identification. (5p)

          b) Plot the data points on the x-y plane and prepare the element-to-element
distance matrix $d(x_i, x_j) = \sqrt{(x_i - x_j)^2 + (y_i - y_j)^2}$ ($i, j = 1, 2, \dots, 200$)
that will be the input for the clustering algorithm. Also assume each data
point carries the same weight, i.e., $p(x_i) = 1/200$ for all $i$. (2p)
c) Write a code (no restriction on the program language) to implement the
Blahut-Arimoto algorithm to evaluate the clustering membership probabi-
lity, $p(\vec{x}|\vec{x})$, with fixed number of clusters, $N_c$, and compression-distortion
tradeoff parameter, $\beta$. Your code should implement a multiple run each
starting with random initial conditions. Note: Your source code should
include clear comments/documentations to describe what are evaluating.
I may later randomly ask a few students, especially those without clear
documentations, to demonstrate how their code works. (15p)
d) Run your code to construct the information curve for $N_c = 2, 3, 4$. Hint:
Choose different values of $\beta$ in between 1 to 40. (6p)
e) As we have already known that the correct number of clusters is 2, pro-
pose a reasonable way using the quantities evaluated from your code (e.g.
$I(X, \tilde{X})$, $(d(x, \tilde{x}))p(x, \tilde{x})$, the Lagrange function, etc.) and the information
curves to correctly identify the number of clusters. You should clearly ex-
plain your rationale and state explicitly which quantities, graphs and/or
curves are used in the identification. (5p)

b) Plot the data points on the x-y plane and prepare the element-to-element
distance matrix d(xi, xj) = √((xi - xj)^2 + (yi - yj)^2) (i, j = 1, 2, …, 200)
that will be the input for the clustering algorithm. Also assume each data
point carries the same weight, i.e., p(xi) = 1/200 for all i. (2p)
c) Write a code (no restriction on the program language) to implement the
Blahut-Arimoto algorithm to evaluate the clustering membership probabi-
lity, p(x⃗|x⃗), with fixed number of clusters, Nc, and compression-distortion
tradeoff parameter, β. Your code should implement a multiple run each
starting with random initial conditions. Note: Your source code should
include clear comments/documentations to describe what are evaluating.
I may later randomly ask a few students, especially those without clear
documentations, to demonstrate how their code works. (15p)
d) Run your code to construct the information curve for Nc = 2, 3, 4. Hint:
Choose different values of β in between 1 to 40. (6p)
e) As we have already known that the correct number of clusters is 2, pro-
pose a reasonable way using the quantities evaluated from your code (e.g.
I(X, X̃), (d(x, x̃))p(x, x̃), the Lagrange function, etc.) and the information
curves to correctly identify the number of clusters. You should clearly ex-
plain your rationale and state explicitly which quantities, graphs and/or
curves are used in the identification. (5p)

Added by Charles H.

Question

Please give Ace some feedback