Research On The Methods Of Mining New Patterns Based On The Formal Context Of Small Samples

Small sample problems exist in all kinds of many disciplines research. Thecharacteristics of small sample data mainly display in the small sample size and highsample dimension. However, due to some sample in the research field is the small sampledata. And there are vast amounts of data in some research contents, but to explore thesmall sample data can retry related problem solution from another view, orprovide a morebroad perspective for related research. Then, based on the two features of small sampledata, we can increase the sample size, or reduce the dimension of sample data to solve theproblem of small sample.From the research perspective of increasing the sample size, the basic researchcontent of this article is the formal context and its properties in formal concept analysistheory, and provides detailed descriptions for attribute mathematical concepts and abstractattribute characteristics. And based on the definition and characteristics of attributes,explore the two possible patterns discovery methods which regard partial order attributestructure as the research carrier, that is possible pattern principle based on strictmathematical treatises and the prefix substitution isomorphism replacement method basedon the relationship between simple attributes.Form a complete research train of thought for finding possible patterns from smallsample formal context. Extract small sample data attributes and objects, structure thesmall sample formal context, to form the hierarchical optimization formal context,structure partial order attribute diagram of the hierarchical optimization formal context,using the model directed graph or prefix replacement method to discover new possiblepatterns, recovery the new possible patterns to the existing attribute partial order diagram,then rely on the expert knowledge to discriminant the practical significance of newpossible patterns in professional background.Based on the possible patterns finding method of small sample, it can discoveringnew patterns effectively, greatly increase the quantity of samples, to generate a certainnumber of virtual data, but also can effectively restore the missing data from samll sample, such as combining with the authoritative judgments of experts in the research field, whichcan be used to find more possible patterns and to provide a creative thinking forknowledge discovery.