Q3. Given the categorical-Gaussian model with Gaussian random variable Y of dimension D=1 and the data: Dy = {2.66, 1.89, 1.65, -3.63, -1.55} we want to cluster this data using the K-means algorithm with K = 2. In your answers to the questions below, report your numerical values correct to 2 decimal places. (a) Given initial guesses for the Gaussian means, j = {2, -3), compute the matrix of square distances Ane = (y(7) 4(7))? for n = 1, ...,5 and x= 1.2. (6 marks) (b) Given these distances, calculate the maximum a-posteriori (MAP) assignment (n) of each data point n. Calculate the complete data negative log likelihood L (Dxy). (4 marks) (c) Using the above assignments, find updated estimates of the Gaus- sian mean parameters pl. (3 marks) (d) Using these updated Gaussian parameters, re-compute the matrix of square distances and the MAP assignments for each data point. (5 marks) (e) Compute the updated negative log likelihood, and therefore, ex- plain why these last updated MAP assignments are an improvement over the previous assignments. Q3. Given the categorical-Gaussian model with Gaussian random variable Y of dimension D=1 and the data: Dy = {2.66, 1.89, 1.65, -3.63, -1.55} we want to cluster this data using the K-means algorithm with K = 2. In your answers to the questions below, report your numerical values correct to 2 decimal places. (a) Given initial guesses for the Gaussian means, j = {2, -3), compute the matrix of square distances Ane = (y(7) 4(7))? for n = 1, ...,5 and x= 1.2. (6 marks) (b) Given these distances, calculate the maximum a-posteriori (MAP) assignment (n) of each data point n. Calculate the complete data negative log likelihood L (Dxy). (4 marks) (c) Using the above assignments, find updated estimates of the Gaus- sian mean parameters pl. (3 marks) (d) Using these updated Gaussian parameters, re-compute the matrix of square distances and the MAP assignments for each data point. (5 marks) (e) Compute the updated negative log likelihood, and therefore, ex- plain why these last updated MAP assignments are an improvement over the previous assignments