**Population Algorithm (Semeion©)**

The *Population Algorithm* (hereafter referred to as *Population*) has a place in the theoretical framework of *Multi Dimensional Scaling*. Reducing the dimensionality of a dataset is a frequent problem in the analysis of data and is remarkable important, in particular, in the field of exploratory analysis. *Population* provides an opportunity to compress N records of a M-dimensional space (which we call the *Source Space*) in a subspace of Q dimensions (called the *Projected Space*), where Q<<M, maintaining the greatest possible number of existing relations contained in the original N records. *Population* is an iterative algorithm based on the calculation of a *local fitness*, the distance between two points that is considered optimal when the single differences between the matrix of the distances of the *Source Space* and the matrix of the distances of* Projected Space* are near zero.

This particular characteristic of *Population*, the ability to converge on a solution without calculating the *global fitness*, determines the speed with which it finds a solution minimizing the global error compared to other algorithms of *Multi Dimensional Scaling*, such as that of *Sammon’s map*. It is therefore particularly useful for elaborations of datasets of great dimensionality.

The *Population* program has demonstrated that it possesses a much higher quality for the resolution of the *Multi Dimensional Scaling* problem. The potential for this algorithm is considerable:

- Speed enhancement;
- Efficiency improvement;
- Simplicity of the algorithm;
- Freedom from having to calculate a specific cost function;
- The possibility of analyzing a dataset of great dimension;
- The possibility of dynamically introducing new records into the dataset during the program run;
- The possibility of choosing the dimensions of
*Projected Space*.

**References**

[1] Giulia Massini, Stefano Terzi, Paolo Massimo Buscema

**Population Algorithm: A New Method of Multi-Dimensional Scaling**

Chapter 3, pp 63-74, in W.J. Tastle (ed.), Data Mining Applications Using Artificial Adaptive Systems, DOI 10.1007/978-1-4614-4223-3_1, Springer Science+Business Media New York 2013