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[Solution Library] Customer purchase history matrix. A store keeps track of its sales of products from K different product categories to N customers over some time

Question: Customer purchase history matrix. A store keeps track of its sales of products from \(K\) different product categories to \(N\) customers over some time period, like one month. (While it doesn't matter for this problem, \(K\) might be on the order of 1000 and \(N\) might be 100000 .) The data is stored in an \(N \times K\) matrix \(C\), with \(C_{i j}\) being the total dollar purchases of product \(j\) by customer \(i\). All the entries of \(C\) are nonnegative. The matrix \(C\) is typically sparse, i.e., many of its entries are zero.

  1. What is \({{C}^{T}}\mathbf{1}\)
    (c) Give a short matrix-vector expression for the total dollar amount of all purchases, by all customers.
    (d) What does it mean if \(\left(C C^{T}\right)_{k l}=0\) ? Your answer should be simple English.
    (e) Suppose you run \(k\) -means on the rows of \(C\), with \(k=100\). How would you interpret the centroids \(z_{1}, \ldots, z_{100} ?\)
    Price: $2.99
    Solution: The downloadable solution consists of 1 pages
    Deliverable: Word Document


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