Dimensionality Reduction for Categorical Data

Categorical attributes are those that can take a discrete set of values, e.g., colours. This work is about compressing vectors over categorical attributes to low-dimension discrete vectors. The current hash-based methods compressing vectors over categorical attributes to low-dimension discrete vectors do not provide any guarantee on the Hamming distances between the compressed representations. Here we present FSketch to create sketches for a sparse categorical data and an estimator to estimate the pairwise Hamming distances among the uncompressed data only from their sketches. We claim that these sketches can be used in the usual data mining tasks in place of the original data without compromising the quality of the task. For that we ensure that the sketches also are categorical, sparse, and the Hamming distance estimates are reasonably precise. Both the sketch construction and the Hamming distance estimation algorithms require just a single-pass; furthermore, changes to a data point can be incorporated into its sketch in an efficient manner. The compressibility depends upon how sparse the data is and is independent of the original dimension - making our algorithm attractive for many real-life scenarios. Our claims are backed by rigorous theoretical analysis of the properties of FSketch and supplemented by extensive comparative evaluations with related algorithms on some real-world datasets. We show that FSketch is significantly faster, and the accuracy obtained by using its sketches are among the top for the standard unsupervised tasks of RMSE, clustering and similarity search.

Automated summary

This work focuses on compressing vectors over categorical attributes to low-dimension discrete vectors. Existing hash-based methods lack guarantees on the Hamming distances between compressed representations. FSketch is introduced to create sketches for sparse categorical data and estimate pairwise Hamming distances from the sketches. These sketches can be used instead of original data in data mining tasks without compromising the quality, thanks to their categorical, sparse nature and reasonably precise Hamming distance estimates. The single-pass algorithm is efficient and applicable to various real-life scenarios, as demonstrated by theoretical analysis and comparative evaluations on real-world datasets.