Nonlinear Synergetics

Data Mining: the nontrivial extraction of implicit, previously unknown, and potentially useful information from data ⁽¹⁾

Business has lots of incoming data but what does it mean? How can the data be used for economic gain? What should one do to use the data to advantage?

The most frequent users of data mining today are found in the financial, marketing and communications sectors, yet other industries, such as agriculture and animal science, are beginning to find meaningful answers from detailed data analysis. These companies - dealing both with consumers and business-to-business transactions - use data mining to find hidden trends and buying patterns. The data intelligence comes from factors that can be locally controlled, such as price, sales tactics and geographic strategies, as well as from marketplace dynamics, such as the competitive landscape and economic conditions. Data mining can be open-ended, finding dominant data trends on a broad scale, or can be keyed to specific variables that a company may wish to study.

Data mining engineers typically choose between a handful of methodologies such as data visualization, rule induction and genetic algorithms. However the most productive method today for successful data mining is the use of artificial neural networks: Nonlinear predictive models that learn through training and resemble biological neural networks in structure.

Neural networks are nonlinear statistical data modeling or decision making tools. They can be used to model complex relationships between inputs and outputs or to find patterns in data. ⁽²⁾

In pursuits as diverse as physics, banking, investing, engineering and medicine, artificial neural networks have been increasingly employed in recent years to find answers to complex problems that previously were out of reach via standard linear multivariable methods. Issues of classification, prediction and trend identification can be uniquely addressed via neural networks, a highly refined yet marvelously simple methodology that copies nature itself.

Artificial neural networks are sophisticated nonlinear modelling devices that are easily able to handle a large number of variables and can handle extremely complex functions which are inherent within the data relationships. They teach themselves as they work, learning by example directly from the data itself! Neural networks begin to approach the massive parallel processing techniques used by the human brain. They are the architectural model for the supercomputers of tomorrow.

Nonlinear Synergetics methodology addresses both the Regression and Classification prediction tasks of Neural Network modelling. The Nonlinear Synergetics toolbox includes two multivariable regression methods, based on the Probabilistic Neural Network (PNN). The first method is matrix based. As such, it is a fast evaluation tool that looks at a basic initial model of the data to determine relevance of potential modelling. It determines whether an effective and useful model can be made from the data. The second is a more sophisticated technique using full nonlinear programming to obtain a finer solution with better generalization; i.e. the model can be more accurate with less data. Both of our methods can employ hundreds of variables so that indeed, very extensive models can be built if needed. (Many problems however fall into the range of much less than 100 variables.)

Further, with many other systems, only very large data sets could be relied upon to provide meaningful results. By employing the process of "optimal jittering" - which adds just the sufficient level of artificial noise on top of the original inputs during training of the model, and in so doing makes the best of the information that is inherent in the data. Normally data is split down and statistical results follow from what can be called classical "cross validation techniques". However, when data is limited, the results are also limited because it is hard to split a very small "pie" into the many pieces needed to make valid statisitical results. Simply, there is not enough data to obtain the necessary estimation of variance, and the whole model is a house of cards which must fall apart. Final answers are much too fuzzy for proper interpretation and prediction.

The Nonlinear Synergetics method employs a proprietary technology that delivers a useable, statistically reliable result even when the number of training cases is small. This may be the case for some critical data- a sort of Murphy's Law in which what may be critical to a company may rely on small amounts of data yet there is a belief or avenue practiced by the company wherein the approach taken may depend more on intuition than practical basis. Nonlinear Synergetics can deal with small data sets, given the data is good and true³, to obtain verification of intuitive-based decisions.

¹W. Frawley and G. Piatetsky-Shapiro and C. Matheus (Fall 1992). "Knowledge Discovery in Databases: An Overview". AI Magazine: pp. 213-228. ISSN 0738-4602
²Wikipedia
³We note an important caverat herein that if the small data set contains poor estimators of the inherent generative model and/or a sufficient amount of outliers, then almost all methods will fail to give results that can be trusted.