Random projection in dimensionality reduction: applications to image and text data
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
Similarity estimation techniques from rounding algorithms
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Mining of Massive Datasets
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Finding correlated words in large document collections is an important ingredient for text analytics. The naïve approach computes the correlations of each word against all other words and filters for highly correlated word pairs. Clearly, this quadratic method cannot be applied to real world scenarios with millions of documents and words. Our main contribution is to transform the task of finding highly correlated word pairs into a word clustering problem that is efficiently solved by locality sensitive hashing (LSH). A key insight of our new method is to note that the empirical Pearson correlation between two words is the cosine of the angle between the centered versions of their word vectors. The angle can be approximated by an LSH scheme. Although centered word vectors are not sparse, the computation of the LSH hash functions can exploit the inherent sparsity of the word data. This leads to an efficient way to detect collisions between centered word vectors having a small angle and therefore provides a fast algorithm to sample highly correlated word pairs. Our new method based on LSH improves run time complexity of the enhanced naïve algorithm. This algorithm reduces the dimensionality of the word vectors using random projection and approximates correlations by computing cosine similarity on the reduced and centered word vectors. However, this method still has quadratic run time. Our new method replaces the filtering for high correlations in the naïve algorithm with finding hash collisions, which can be done by sorting the hash values of the word vectors. We evaluate the scalability of our new algorithm to large text collections.