The Vector Space Model solves this problem by introducing vectors of index items each assigned with weights. The weights are ranged from positive (if matched completely or to some extent) to negative (if unmatched or completely oppositely matched) if documents are present. Term Frequency - Inverse Document Frequency (tf-idf) is one of the most popular techniques where weights are terms (e.g. words, keywords, phrases etc.) and dimensions is number of words inside corpus.