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tinybig.compression

This module provides the "data compression functions" that can be used to build the RPN model within the tinyBIG toolkit.

Data Compression Function

Different from the "data expansion functions", the data compression functions aim to compress input data batch from high-dimensional space into lower-dimensional spaces.

Formally, given the underlying data distribution mapping \(f: {R}^m \to {R}^n\) to be learned, the data compression function \(\kappa\) projects input data into a new space shown as follows:

\[ \kappa: {R}^m \to {R}^{D}, \]

where the target dimension vector space dimension \(D\) is determined when defining \(\kappa\).

In practice, the function \(\kappa\) can either expand or compress the input to a higher- or lower-dimensional space. The corresponding function, \(\kappa\), can also be referred to as the data expansion function (if \(D > m\)) and data compression function (if \(D < m\)), respectively. Collectively, these can be unified under the term "data transformation functions".

To differentiate from the dimension notation \(D\) of the expansion functions, we will use the lower-case dimension notation \(d\) for compression functions implemented in this module instead.

Classes in this Module

This module contains the following categories of compression functions:

  • Basic compression functions
  • Geometric compression functions (based on the cuboid, cylinder and sphere patch shapes)
  • Metric based compression functions
  • Feature selection based compression functions
  • Dimension reduction based compression functions
  • Manifold based compression functions
  • Probabilistic compression functions
  • Extended and Nested compression functions

Organization of this Module

Data Expansion/Transformation

Basic Compressions

Metric based Compressions

Geometric based Compressions

Feature Selection based Compressions

Dimension Reduction based Compressions

Manifold based Compressions

Naive Probabilistic Compressions

Combinatorial Probabilistic Compressions

Nested and Extended Compressions