]Introduction: 1. level
Similarity analysis with staircase-functions
The mathematical background of the MY-X FREE service package can be characterized through the similarity analysis: more exact through the staircase-function (c.f. step function: more).
The similarity analysis is a part of the case-based reasoning (CBR). It is the most universal, instinctive (biological) capability of the human. It can not be really improved, still less transferred between individuals. It is due to realize more and more phenotypic knowledge in each living creature during the evolution (c.f. Konrad Lorenz). The knowledge (storing life-long) can not be transferred directly to the next generation, but well the genetic pre-conditions for them. Based on the always given cases (inputs and their consequences) the HEUREKA-feeling will be arisen in frame of the similarity analysis sooner or later. The HEUREKA-feeling means that the partial facts can be estimated (c.f. simulated, understood) through a holistic rule system (c.f. production function) on an acceptable level of fitting. Therefore near each problem-type is to manipulate successful through the similarity analysis. Inasmuch as each type of problem has certain similarity to other types, so the phenomenon 'similarity' can be quite always applied...
The core of the similarity analysis is the (mathematical/biological) description of similarity. The similarity can be defined through diverse ways. For example: The decision trees are able to build arbitrary groups from the most similar cases and to define unique (but on system level or in comparison among them: illogical) estimation function for each group. As well as decisions trees, we can generate also artificial neural networks, which can be seen as a complex, polynomial function. Neural networks (in general) are able to approximate arbitrary learning patterns, however they can produce illogical behaviour between well-known points in the n-dimensional combinatorial space.
The staircase functions of MY-X FREE try to combine the advantages of the competitive methods and to avoid their disadvantages: on the one hand they constrain the basically polynomial functions to be less random-like and to have less overfitting according to the learning patterns (c.f. to be more robust), on the other hand they make possible to derive interpretable estimations for unknown input variations (providing the capability of simulation, extrapolation, interpolation, intrapolation).
A staircase function in the similarity analysis can be defined as a set of diverse stair-constructions pro attribute, which set (in form of optimization or in form of target-based searching) such values instead of each ranking value of each attribute, which should be given the fittest estimations. A staircase function set can produce arbitrary polynomial effects, inasmuch as the developer allows them.
The combination of the stairs in the functions can be interpreted as an expert system (c.f. combinatorial space): the staircase functions reflect each learning pattern and a set of theoretical possible input variations including their estimated consequences.
The volume of an OAM (delivering the learning pattern) can be arbitrary. However the ratio of objects and attributes determine the quality of the solutions (c.f. alternative approximations, interpretability of the stairs).
The staircase function can be joined to a chain (forming potential consistent argumentations - also context free).
About the limits and possibilities of the similarity analysis:
According to Georges Cuvier (18th century, French scientist on the field of zoology and botany / Véry: Functional controlling, Raabe, 2009/): ...Functions are more important than the organs: The similarity can be detected there, where the sameness can no longer be observed...
The similarity analysis in the microbiology looks up for sameness, more exact: it calculate the grade of the sameness (according to the sequence of the genetic information units). The similarity analysis of the MY-X services creates the most similar (in extreme case: the same) outputs according to the elements of the learning pattern. As well as the most correct reflexions of the already known learning pattern, the similarity analysis is able to expand the knowledge for the consequences of quite unknown situations (e.g. deriving genetic potential vs. CBR-expectation: adaptation of consequences of the most similar, stored experience). The lowest and the highest amounts of the units in the learning pattern (verifying some model/rule) are also suspicious: namely the lowest frequency of substantiation (=1) can be seen as potential demagogy (cf. Fable of Vonnegut in the MY-X FREE News) and the highest frequency (=100%) is the embodiment of overfitting.
