Consider the data points in the table, taken from a 4- W X Y Z dimensional space. Perform the following tasks for the 21 points of this dataset. P1 12 5 7 1. Use any calculator, Matlab/R type of toolbox, or your P2 3 2 own small computer program for the following tasks. 7 3 Include a screenshot of the Matlab code or your P3 1 O program code used by you. P4 3 14 6 a. (9) Using Manhattan distance, find the three P5 6 10 14 2 closest and the three farthest points from the point P10. Report these closest/farthest P6 10 12 points, their coordinates, and their distances P7 12 17 9 2 from P10. Show your complete calculations for only one pair of data points. P8 4 2 b. (9) Using Cosine similarity, find the three Pg 2 20 2 2 closest and the three farthest points from the point P10. Report these closest/farthest P10 6 5 1 points, their coordinates and their distances P11 5 14 11 2 from P10. Show your complete calculations for only one pair of data points. P12 6 15 20 2 (7) Standardize the values of every variable P13 15 11 using linear transformation. For each variable P14 8 11 1 now the values should be in the range [0. . .1]. Take any four data points form this table and P15 2 12 1 compute all pair-wise distances for both cases, P16 16 5 that is, before normalization and after normalization. List the point-pairs in P17 1 17 O decreasing order of their pair-wise distances P18 7 3 2 for both cases. Is the ordering the same or it 2 has changed? Comment on why any changes P19 4 14 3 in the rank ordering may have occurred. P20 5 16 12 2 2. (20) Use Minkowski distance formula and compute P21 1 13 7 1 the distance between points P7 and P8 for the cases of "r" taking the values, 1, 2, 3, 4, 5, 6, and 10. Report the distance values obtained. Discuss the effect of changing the value of "r" as you see in your results. 3. Perform the following steps in the context of Mahalanobis distance: a. (5) Compute and show the covariance matrix "C" of this data set. You can use a toolbox such as Matlab to compute this matrix. b. (5) Find and show the inverse of the matrix C and call it C-inv. Use Matlab type of toolbox to compute the inverse