Question

(a) Briefly describe the learning procedure of principal component analysis (PCA) algorithm. What is the meaning of the 1st principal component? (3 marks) (b) Given a dataset (as shown below) consisting of five instances and five predictor variables - X1, X2, X3, X4 and X5, calculate the processed dataset whose mean equals zero. You will need to provide a step-by-step solution. (2 marks) X1 X2 X3 X4 X5 Instance_1 -2.10 5.10 -5.10 4.30 -4.90 Instance_2 1.90 -8.30 -3.20 1.90 3.90 Instance_3 -2.70 -7.10 -7.80 3.80 -3.30 Instance_4 -1.70 3.20 9.10 2.10 7.20 Instance_5 6.30 -8.30 -5.20 2.30 -5.70 (c) Calculate the transformed dataset using the 1st and 2nd principal component values, i.e. PC_1 and PC_2. You will need to provide a step-by-step solution. (5 marks) PC_1 = (0.18, -0.51, -0.68, 0.03, -0.49) PC_2 = (0.32, -0.74, 0.27, -0.16, 0.50)

          (a) Briefly describe the learning procedure of principal component analysis (PCA) algorithm. What is the meaning of the 1st principal component?
(3 marks)
(b) Given a dataset (as shown below) consisting of five instances and five predictor variables - X1, X2, X3, X4 and X5, calculate the processed dataset whose mean equals zero. You will need to provide a step-by-step solution.
(2 marks)
X1	X2	X3	X4	X5
Instance_1	-2.10	5.10	-5.10	4.30	-4.90
Instance_2	1.90	-8.30	-3.20	1.90	3.90
Instance_3	-2.70	-7.10	-7.80	3.80	-3.30
Instance_4	-1.70	3.20	9.10	2.10	7.20
Instance_5	6.30	-8.30	-5.20	2.30	-5.70
(c) Calculate the transformed dataset using the 1st and 2nd principal component values, i.e. PC_1 and PC_2. You will need to provide a step-by-step solution. (5 marks)
PC_1 = (0.18, -0.51, -0.68, 0.03, -0.49)
PC_2 = (0.32, -0.74, 0.27, -0.16, 0.50)

(a) Briefly describe the learning procedure of principal component analysis (PCA) algorithm. What is the meaning of the 1st principal component?
(3 marks)
(b) Given a dataset (as shown below) consisting of five instances and five predictor variables - X1, X2, X3, X4 and X5, calculate the processed dataset whose mean equals zero. You will need to provide a step-by-step solution.
(2 marks)
X1 X2 X3 X4 X5
Instance1 -2.10 5.10 -5.10 4.30 -4.90
Instance2 1.90 -8.30 -3.20 1.90 3.90
Instance3 -2.70 -7.10 -7.80 3.80 -3.30
Instance4 -1.70 3.20 9.10 2.10 7.20
Instance5 6.30 -8.30 -5.20 2.30 -5.70
(c) Calculate the transformed dataset using the 1st and 2nd principal component values, i.e. PC1 and PC2. You will need to provide a step-by-step solution. (5 marks)
PC1 = (0.18, -0.51, -0.68, 0.03, -0.49)
PC2 = (0.32, -0.74, 0.27, -0.16, 0.50)

Added by Joseph H.

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