Difference between Dimensionality Reduction and Numerosity Reduction

1. Dimensional Reduction :
It is a technique used to obtain a reduced or compressed representation of original data. It is further divided into two components:

• Feature Selection –
  It is the process of removing the irrelevant or redundant features.
• Feature Extraction –
  It is the process of transforming data into features suitable for modeling.

2. Numerosity Reduction :
It is a data reduction technique used to reduce data volume by using suitable forms of data representation. These techniques may be parametric or non-paramatric. For parametric methods, a model is used to estimate the data, so that typically only the data parameters need to be stored, instead of the actual data. Non-parametric methods for storing reduced representations of the data include histograms, clustering, and sampling.

Difference between Dimensionality Reduction and Numerosity Reduction :

Dimensionality Reduction	Numerosity Reduction
In dimensionality reduction, data encoding or data transformations are applied to obtain a reduced or compressed for of original data.	In Numerosity reduction, data volume is reduced by choosing suitable alternating forms of data representation.
It can be used to remove irrelevant or redundant attributes.	It is merely a representation technique of original data into smaller form.
In this method, some data can be lost which is irrelevant.	In this method, there is no loss of data.
Methods for dimensionality reduction are: Wavelet transformations. Principal Component Analysis.	Methods for Numerosity reduction are: Regression or log-linear model (parametric). Histograms, clusturing, sampling (non-parametric).
The components of dimensionality reduction are feature selection and feature extraction.	It has no components but methods that ensure reduction of data volume.
It leads to less misleading data and more model accuracy.	It preserves the integrity of data and the data volume is also reduced.