Random Projections Algorithm

A Random Projections Algorithm is a dimensionality reduction algorithm that ...

• • …
• Counter-Example(s):
  • Latent Semantic Analysis Algorithm.
  • Latent Dirichlet Allocation Algorithm.
  • Hierarchical Dirichlet Process Algorithm.
• AKA: Random Projections.

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References

2016

• https://pypi.python.org/pypi/gensim/0.13.1
  • QUOTE: … Efficient multicore implementations of popular algorithms, such as online Latent Semantic Analysis (LSA/LSI/SVD), Latent Dirichlet Allocation (LDA), Random Projections (RP), Hierarchical Dirichlet Process (HDP) or word2vec deep learning.

2002

• (Fodor, 2002) ⇒ Imola K. Fodor. (2002). “A Survey of Dimension Reduction Techniques." LLNL technical report, UCRL ID-148494
  • The method of random projections is a simple yet powerful dimension reduction technique that uses random projection matrices to project the data into lower dimensional spaces [47, 32, 33, 35]. The original data X 2 Rp is transformed to the lower dimensional S 2 Rk, with k ¿ p, via
    • S = RX; (55)
  • where the columns of R are realizations of independent and identically distributed (i.i.d.) zero-mean normal variables, scaled to have unit length. The method was proposed in the context of clustering text documents, where the initial dimension p can be on the order of 6000, and the ¯nal dimension k is still relatively large, on the order of 100. Under such circumstances, even PCA, the simplest alternative linear dimension reduction technique, can be computationally too expensive. Random projections are applied as a data pre-processing step, then, the resulting lower dimensional data is clustered. It has been shown empirically that results with the random projection method are comparable with results obtained with PCA, and take a fraction of the time PCA requires [33, 35].

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