Question Consider the user book-rating matrix given below. The ratings increase from 1 to 5. Absence of a rating is indicated by empty box. A new book b8

Question Consider a supermarket that contains 1000 products. In a market-basket analysis, you want to compare baskets of 2 customers C1 and C2 to find similarity in their buying behavior.

Question Given the following distance matrix, compute LOF (Local Outlier Factor) of all points, based on 2-distance neighborhood consideration (k=2). Show intermediate steps. Solution ================================================================================================== k = 2 => Second

Question Consider the below page linkage diagram among web pages A, B, C and D. As per page rank algorithm, what is the expected ranking among pages. Comment on the

Question Let be a given matrix with . If the time taken to compute the determinant of a square matrix of size j is , find upper bound on the

Question Let γ be the real root of a polynomial equation of degree 9 with integer coefficients. Construct the matrix With this information, is it possible to i)

Question Find the minimum distance from (4,2) to the parabola Solution Conceptually, this can be done by: 1) Considering the curve and finding the tangent. 2) Find normal to that

Question Prove that if A is a square matrix of size , then as if and only if Solution Norm is a value that indicates the magnitude of a matrix.

Question Given the following matrix where c and r are arbitrary real numbers and 5.5 < r ≤ 6.5, and the fact that = 3 is one of

Question Let be a non-singular matrix. If column is replaced by a and that the resulting matrix is called along with , then state the necessary and sufficient condition for