[PS-2.2] Sparsification based on sampeled unary sub-vectors

Cardoso, &. 1, 2 , Sacramento, J. 1, 2 & Wichert, A. . 1, 2

1 Universidade Técnica de Lisboa
2 INESC-ID Lisboa

In this work we investigate the sparsification method for efficient information retrieval using the associative memory.
A unary representation of a number h would require binary vector of length d=log2 h+1. However if we represent the number h unary we are required h position. A binary number of length d is represented by a unary number of 2^d positions which is exponential in the size of input.
A binary vector x of dimension t is split into f distinct sub vectors of dimension p=dim(t/f). The binary sub vectors of dimension p=dim(t/f) are represented as unary vectors of dimension 2^p.
The resulting binary vector is composed out of the unary vectors and has the dimension f * 2^p.
Such a binary sparse vector could correspond to set of c sensors at different positions. At a position one and only one sensor is activated. For f positions and c sensors a state would be represented by binary vector of the dimension f*c with f ones.
An example of such unary coding is the MTC model of the visual system [1], it is a less complex description of the pattern recognition capabilities of the Neocognitron. Each layer represents a set of features. A binary vector in which the positions represent different features at different positions on the image describes it. The input image is tiled with a squared mask M of size j * j in which a corresponding category of a feature is determined. Each feature is determined through the use of the elements in each squared mask. The categories can be learned by a simple clustering algorithm such as K-Means [1] that represents the distribution of the data.

[1] Cardoso, A, Wichert A.: Neocognitron and the Map Transformation Cascade, Neural Networks, 23 (1): 74-88, 2010