Project Report: Analysis of JL Transform Implementations

Most of the scientific research today has become data-intensive [1]. Vast amounts of data are being collected from different sources by researchers in all the areas we can imagine, ranging from basic sciences like nuclear physics (Large Hadron Collider is a recent example), astronomy, biology to more applied areas like web mining, natural language processing, biomedical applications, etc. This huge amount of data (both structured and unstructured) presents a big challenge in terms of finding ways to do efficient dimensionality reduction (what is ‘efficient’, is dictated by the application) to achieve one or more of the these goals being able to visualize data effectively, looking for interesting patterns in the data, reduce the computational power needed to process the data without compromising much on the end goal, and sometimes to provide the computer algorithms with only relevant information so they are not confused by irrelevant information, and there may be many others depending on the application. The most popular way of doing dimensionality reduction during the past few decades has been the principle component analysis (PCA). PCA attempts to reduce the dimensionality of data such that the mean square error between original and reconstructed data (from lower ranked representation) is minimized. PCA, however, does not provide any guarantees on preserving the local structures present in the data (like pairwise distances, others). Although, given sufficient samples of un-noisy data, PCA does a decent job in dimensionality reduction