Progressive Random Indexing: Dimensionality Reduction Preserving Local Network Dependencies.

The vector space model is undoubtedly among the most popular data representation models used in the processing of large networks. Unfortunately, the vector space model suffers from the so-called curse of dimensionality, a phenomenon where data become extremely sparse due to an exponential growth of the data space volume caused by a large number of dimensions. Thus, dimensionality reduction techniques are necessary to make large networks represented in the vector space model available for analysis and processing. Most dimensionality reduction techniques tend to focus on principal components present in the data, effectively disregarding local relationships that may exist between objects. This behavior is a significant drawback of current dimensionality reduction techniques, because these local relationships are crucial for maintaining high accuracy in many network analysis tasks, such as link prediction or community detection. To rectify the aforementioned drawback, we propose Progressive Random Indexing, a new dimensionality reduction technique. Built upon Reflective Random Indexing, our method significantly reduces the dimensionality of the vector space model while retaining all important local relationships between objects. The key element of the Progressive Random Indexing technique is the use of the gain value at each reflection step, which determines how much information about local relationships should be included in the space of reduced dimensionality. Our experiments indicate that when applied to large real-world networks (Facebook social network, MovieLens movie recommendations), Progressive Random Indexing outperforms state-of-the-art methods in link prediction tasks.