Dimensionality Reduction

Definition

From database perspective, dimensionality reduction (DR) is to map the original high-dimensional data into a lower dimensional representation that captures the content in the original data, according to some criterion. Formally, given a data point P = {p₁, p₂,...,p_D} in D- dimensional space, DR is to find a d-dimensional subspace, where d < D, such that P is represented by a d-dimensional point by projecting P into the d-dimensional subspace.

Key Points

Advances in data collection and storage capabilities have led to an information overload in most sciences. Many new and emerging data types, such as multimedia, time series, biological sequence, have been studied extensively in the past and present new challenges in data analysis and management due to their high dimensionality of data space. One known phenomenon of “dimensionality curse” leads traditional data access methods to fail [3]. High-dimensional datasets present many mathematical challenges as well as some...