Vector Space Model (VSM)

citation : Pro Deep Learning with Tensorflow

In NLP information-retrieval systems, a document is generally represented as simply a vector of the count of the words it contains. For retrieving documents similar to a specific document either the cosine of the angle or the dot product between the document and other documents is computed. The cosine of the angle between two vectors gives a similarity measure based on the similarity between their vector compositions. To illustrate this fact, let us look at two vectors x, y $\in$

[\begin{align} & \phi(x,y) = \phi \left(\sum_{i=1}^n x_ie_i, \sum_{j=1}^n y_je_j \right) = \sum_{i=1}^n \sum_{j=1}^n x_i y_j \phi(e_i, e_j) =
& (x_1, \ldots, x_n) \left( $$\begin{array}{ccc} \phi(e_1, e_1) & \cdots & \phi(e_1, e_n) \vdots & \ddots & \vdots \phi(e_n, e_1) & \cdots & \phi(e_n, e_n) \end{array}$$ \right) \left( $$\begin{array}{c} y_1 \vdots y_n \end{array}$$ \right) \end{align}]