Task 1: Vector Space Model over tf-idf Given the following corpus: Doc 1: "fast car highway road car" Doc 2: "car car bike fast fast" Doc 3: "road road highway fast wheel" Doc 4: "bike wheel car wheel" Calculate a vector space model over tf-idf weights for this corpus. In particular, calculate the following: 1. The document frequency df (t) of all terms, i.e. in how many documents each term occurs. 2. The inverse document frequency defined as ()- og0 whee df(t) is the df(t) document frequency of that term and N is the corpus size, i.e. the number of documents in the corpus. 3. The term frequency per document, i.e. which terms occur how many times in each document. 4. The tf-idf vectors for each document. Now, the retrieval system is faced with the query "fast fast car bike". 1. Calculate the tf-idf vector of that query 2. Calculate the cosine similarities between the query vector and all document vectors. 3. Specify the ranked document set that would be the result of the query