Suppose you are given a set of n documents numbered 1 through n. Suppose there i

Question

Suppose you are given a set of n documents numbered 1 through n. Suppose there is a list of m words numbered 1 through m that are of interest to you. Define vectors x1through xnas follows: the jth entry of xiis the number of times the jth word appears in the ith document. You can think of xi as a summary of the information in the ith document.
I selected three articles from Wikipedia and counted the number of times the words fur, blood, bone, feather appeared in each. Here are the results:
Article fur blood bone feather Mammal 6 4 15 0 Reptile 1 5 0 3 Bird 0 7 5 43 Suppose you want to find the document that puts the most emphasis on word j.
One way of doing this is to find the i that gives the largest value of (xi · ej)/||xi||.
Do this with the word blood. Note that the document you obtain is not the one in
which the word appears the most number of times.

I think I know how to approach this question. But I don't know how to define ej. I thought it meant the vector for blood. But then the vector would only contain 3 entries and each document vector contains 4 entries. Could somebody please help me. Thank you very much. I selected three articles from Wikipedia and counted the number of times the words fur, blood, bone, feather appeared in each. Here are the results: Article fur blood bone feather Mammal 6 4 15 0 Reptile 1 5 0 3 Bird 0 7 5 43 Suppose you want to find the document that puts the most emphasis on word j.
One way of doing this is to find the i that gives the largest value of (xi · ej)/||xi||. Do this with the word blood. Note that the document you obtain is not the one in
which the word appears the most number of times.

I think I know how to approach this question. But I don't know how to define ej. I thought it meant the vector for blood. But then the vector would only contain 3 entries and each document vector contains 4 entries. Could somebody please help me. Thank you very much. Article fur blood bone feather Mammal 6 4 15 0 Reptile 1 5 0 3 Bird 0 7 5 43

Explanation / Answer

x1=(6,4,15,0) x2=(1,5,0,3) x3=(0,7,5,43) e1=(1,0,0,0) e2=(0,1,0,0) e3=(0,0,1,0) e4=(0,0,0,1)

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