Fuzzy Logic provides a framework for dealing quantitatively, mathematically, and logically with semantic, ambiguous, elastic, and vague concepts. It is a well proven and well established logic of degrees.

In fuzzy logic a data point’s membership in a set is not crisp (that is, either in or out of the set), but can be specified as a degree of membership.

Fuzzy logic has a wide spectrum of applicability in expert system, neural networks, clustering, decision trees, and many forms of machine learning.

High Dimensional Visualization provides a deep insight into the structure of data by displaying key features of the data across multiple dimensions in a variety of difference formats.

Visualization exposes patterns and trends and clustering within the data that are often not obvious (as an example, scattering product sales by region by quarter or project return on investment by department by project size by project manager)

The Scianta visualization workbench provides high dimensional displays of many concurrent data streams with real-time property specifications (rotations, inversion, compression, logarithm transformations, etc.)

Fuzzy SQL extends the capabilities of the standard Structured Query Language to include filtering, selection, and joins based on the fuzzy or semantic properties of the data.

A Fuzzy SQL query returns a ranked set of records that meet the semantic intent of the query and is much more flexible and robust than traditional SQL queries.
See FS-TU-001 The FuzzySQL Tutorial for a more in depth treatment.

Automatic Cluster Detection organizes data into sets according their degrees of  similarity.
Unlike conventional cluster analysis that assigns a value to a single cluster, fuzzy clustering can assign a data point to multiple clusters with varying degrees of membership.
Automatic cluster detection and quantification finds patterns in data and then produces the if-then-else rules that turn the analysis into prediction and classification models.

Neural Networks are highly nonlinear classification machines that work in a manner analogous to a collection of artificial neurons.

A neural network learns its classifications from examples, in the same way that biological neural systems (like the brain) learn from experience. Because they learn from examples, neural networks are excellent candidates for data mining, fault prediction, problem diagnosis, and similar applications where sufficient historical examples are available.

=Calibration and Threshold Analysis combines extensive statistical analysis with machine learning and non-linear trend discovery.

Calibration discovers the normal behavior of a data stream over time and establishes an elastic (fault tolerant) threshold with the tolerance adjust for the periodic behavior of the data. This model can then be used to detect as well as predict anomalous behaviors. An adaptive feed-back loop in the calibration mechanism continuously learns the time-varying statistical properties of the data and adjusts the thresholds when necessary.

See CC-PC-001 Calibration Principles and Concepts as well as CC-UM-007 Capacity and Calibration User Manual for a more detailed treatment.

Self-Organizing Maps(SOM’s) automatically learn and expose the relationships in high dimensional collections of data. Combining computational efficiency, ease of use, and powerful pattern discovery, self-organizing maps identify common properties among data and also generate a collection of description (classification) rules.

Statistical Learning Theory comprises a closely related set of techniques for learning system behavior form the statistical characteristics of the data.
Developed by Vapnik and Chervonenkis, statistical learning theory (SLT) provides a powerful tool in building models from time-varying data. STL models can discover and quantify multiple periodicity patterns (such as seasonality trends), differentiate abrupt changes from spikes, associate confidence degrees to predictions, and work with a minimum of historical data.

Linear and Non-Linear Regression is a machine learning technique for fitting a curve to a collection of data. The algebraic formula for the curve is a model of the trend through the data and can be used to predict future values of the trend with varying degrees of certainty.

Linear regression is the most common technique and finds a straight line for the equation y = a + bx (where “y” is the dependent value and “x” is the independent variable, often time. The value “a” is the intercept, and “b” is the slope – run versus rise).

Non-linear regression models, as the name implies, model curves that fit data with underlying patterns that are not linear (such as data with seasonalities or other periodic behaviors).

Database Management combines the theoretical framework for maintaining data in an unambiguous and well-structured manner with a methodology for accessing and updating the data.
Data Exploration, in all but the simplest cases, is tied to database management concepts (as well the mechanics of commercial database management systems) as the underlying repositories that support it FuzzySQL, clustering, calibration, and visualization.

Graph Theory is a branch of mathematics dealing with the construction, analysis, and behavior of simple to complex networks.
Data Mining uses this theory to support Link and Affinity Group analysis – an extensive explorations of time-varying, location-varying, and behavior-varying connections between processes and elements.
Link analysis is also a principal technology in threat assessment and market share analysis.