3. (This exercise is a variation of Exercise 2.8 in Chapter 2 of the textbook) C

Question

3. (This exercise is a variation of Exercise 2.8 in Chapter 2 of the textbook) Consider the data as 2-D data points. Given a new data point x (1.4, 1.6) as a query, rank the database points based on the cosine similarity measure A2 x1 1.51.7 1.9 1.6 1.8 1.2 1.5 X2 2 X 1.5 In other words, find the cosine similarity for each data point and sort in decreasing order Similarity Closest Second closest Third closest Fourth closest Farthest Vector 4. (This exercise is a variation of Exercise 3.3 in Chapter 3 of the textbook) Using the data set given in Exercise 1 of this assignment, use smoothing by bin means to smooth this data, using a bin depth of 3 Round results to two decimal places Bins Smoothed by Bin Means

Explanation / Answer

We have given new data point X = c(1.4, 1.6)

Also we have given data set,

A1 A2

X1 1.5 1.7

X 2 2 1.9

X3 1.6 1.8

X4 1.2 1.5

X5 1.5 1

Now we compute a distance of each data point in given data set from the new data point X = c(1.4,1.6) using euclidian distance formula.

i.e. distance of X from X1 is sqrt((1.5-1.4)^2 + (1.7-1.6)^2) = 0.1414

distance of X from X2 is sqrt((2-1.4)^2 + (1.9-1.6)^2) = 0.6708

distance of X from X3 is sqrt((1.6-1.4)^2 + (1.8-1.6)^2) = 0.2828

distance of X from X4 is sqrt((1.2-1.4)^2 + (1.5-1.6)^2) = 0.2236

distance of X from X5 is sqrt((1.5-1.4)^2 + (1-1.6)^2) = 0.6083

Hence cosine similarity for each data point is,

Similarity Vector

Closest X1

Second CLosest X4

Third Closest X3

Fourth Closest X5

Fifth CLosest X2

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