3.1 Key Trends in Long-Term Search Engine Usage

We first analyze the data using dimensionality reduction techniques to develop

insights about key trends. In particular, we use non-negative matrix factorization

(NNMF) [10] of the data to summarize key behavioral patterns using a small number

of basis vectors. NNMF is a method to obtain a representation of data using

non-negativity constraints. This leads to part-based representation such that the

original data can be represented as an additive combination of a small number of

basis vectors.

Formally, we construct A, an M×N matrix, where the columns represent users (N=

10,000 users) and the rows are the vector representation of 26 weeks of search engine

usage statistics. The observations we used for our initial analysis are the proportion

of queries that each user issued to each of the three search engines, thus M= 26 × 3.