The Hamming distance between two binary strings of equal length is the number of positions at which the corresponding characters differ. Expressed as a fraction, it is:

Hamming distance fraction = (Number of differing positions)/(Total number of positions)​

This gives the proportion of positions where the two strings do not match, ranging from 0 (identical strings) to 1 (completely different strings). Therefore, this hamming distance fraction is equivalent to: 

Assume point a = (1,1) and point b = (1,0). If the cosine similarity between a and another point c is 0 and the Euclidean distance between b and c is 1, what is the Euclidean distance between a and c?

Select at least one answer. Negative marking applies to this question.

What is the Euclidean distance between points a = (1,0,1,0) and b = (0,1,0,1)? Write your answer correct to 2 decimal places.

Grace and Jane were asked whether they liked hiking, fishing, cycling, or reading and which fruit out of apples or bananas, they liked the most. Grace responded yes, yes, yes, no and apples, respectively. Jane responded yes, yes, no, yes and bananas, respectively. What is the Sokal-Michener similarity index between Grace and Jane's responses? Write your answer correct to 2 decimal places.

Given that similarity-based learning requires a distance measure in the feature variable space as well as a ground-truth set of input-target mappings, is the following statement true or false?

In the case of a KNN (K=1) classifier based on the cosine similarity distance measure, the model (the KNN classifier) always predicts 0, if the query and existing nearest neighbour are the same and it predicts 1, if the query and existing nearest neighbour are different.

Assuming that the points a, b, and c respectively represent the coordinates of any three points on a two-dimensional map, is the following statement true or false?

The Euclidean distance between a and b cannot be greater than the Euclidean distance between a and c plus the Euclidean distance between b and c.

If the Russel-Rao similarity index between point a = (a1,a2,a3,a4) and point b is 0.4 and the Sokal-Michener similarity index between a and b is 0.6, what is the Jaccard similarity index between a and b? Write your answer correct to 2 decimal places.