Auto CM Hyper Composition

Auto CM Hyper Composition

The Hyper Composition Auto Contractive Map (CM-HC) is an algorithm able to synthesize in only one matrix variables and records (coordinates and points).

Let us image a matrix M, where the Rows (P)={A,B,C,D} and the Columns(N)={α,β,γ}.

Usually a complete multivariate analysis of the matrix M is possible, using Principal Component Analysis (PCA), or an Auto-Associative Neural Networks (AANN). In both cases we have to choose if we want to map the N variables, using the records as coordinates in a P dimensional space, or if we want to transpose the matrix MT, in order to map the P records using the variables as coordinates in the a N dimensional space.

To realize both the mappings simultaneously is impossible, because it is not possible to measure the similarity of variables and records among them using a shared metric. It should be analogous to pretend to dress a glove in the same moment in which this glove is dressed by the same hand that is dressing. It seems to be a problem of self circularity.

Hyper Composition Auto Contractive Map (CM-HC) is a procedure able to provide a positive answer to this apparent paradox.

An Example: The Rooms dataset ( 50 variables and 6 records – the value is the probability of an object to be present in a room).