In the vector space model, the input query and the documents in the collection are represented as vectors in V-dimensional space, where V denotes the size of the indexed vocabulary (i.e., the number of unique terms in the collection). Given a query, documents are scored (and ranked) based on their vector-space similarity to the query. In class, we talked about two vector space similarity measures: (1) the inner product and (2) the cosine similarity. The goal of this question is to understand their differences Suppose we have a collection of 8 documents (denoted as D. Ds below). Answer the following questions. Assume a binary text representationa vectors value for a particular dimension (i.e., a particular index term) equals 1 if the term appears at least once and 0 otherwise. Note: Please show your work for full credit Di: jack and jill went up the hill D2: to fetch a pail of water . D3: jack fell down and broke his crown .Di: and jill came tumbling after Ds: up jack got and home did trot . De: as fast as he could caper o D7: to old dame dob who patched his nob . D: with vinegar and brown paper (1) Given a query-vector q and a document-vector d, the inner product (i.e, the score given to document d for query q) is given by, inner-product(g, d) = (g * d.) Using the inner product, what is the score given to each document Di... Ds in response to the query 'jack'? (2) Given a query-vector q and a document-vector d, the cosine similarity (i.e, the score given to document d for query q) is given by, CosSim(q, Using the cosine similarity, what is the score given to each document Di... D8 in response to the query 'jack'? (3) For this particular query, scoring documents Di... D8 using the inner-product and the cosine similarity would result in equal rankings (HINT: if theyre not, you made a mistake). Why? (4) Give an example of a query for which scoring documents Di... D8 using the inner-product and the cosine similarity would result in different rankings (5) The vector space model has the flexibility that it can accommodate different term-weighting schemes. Different term-weighting schemes make different assumptions about which terms are most important. Compute TF-IDF for terms in Di. Use Di... Ds to compute corpus statistics such as dfi In the vector space model, the input query and the documents in the collection are represented as vectors in V-dimensional space, where V denotes the size of the indexed vocabulary (i.e., the number of unique terms in the collection). Given a query, documents are scored (and ranked) based on their vector-space similarity to the query. In class, we talked about two vector space similarity measures: (1) the inner product and (2) the cosine similarity. The goal of this question is to understand their differences Suppose we have a collection of 8 documents (denoted as D. Ds below). Answer the following questions. Assume a binary text representationa vectors value for a particular dimension (i.e., a particular index term) equals 1 if the term appears at least once and 0 otherwise. Note: Please show your work for full credit Di: jack and jill went up the hill D2: to fetch a pail of water . D3: jack fell down and broke his crown .Di: and jill came tumbling after Ds: up jack got and home did trot . De: as fast as he could caper o D7: to old dame dob who patched his nob . D: with vinegar and brown paper (1) Given a query-vector q and a document-vector d, the inner product (i.e, the score given to document d for query q) is given by, inner-product(g, d) = (g * d.) Using the inner product, what is the score given to each document Di... Ds in response to the query 'jack'? (2) Given a query-vector q and a document-vector d, the cosine similarity (i.e, the score given to document d for query q) is given by, CosSim(q, Using the cosine similarity, what is the score given to each document Di... D8 in response to the query 'jack'? (3) For this particular query, scoring documents Di... D8 using the inner-product and the cosine similarity would result in equal rankings (HINT: if theyre not, you made a mistake). Why? (4) Give an example of a query for which scoring documents Di... D8 using the inner-product and the cosine similarity would result in different rankings (5) The vector space model has the flexibility that it can accommodate different term-weighting schemes. Different term-weighting schemes make different assumptions about which terms are most important. Compute TF-IDF for terms in Di. Use Di... Ds to compute corpus statistics such as dfi
