What GAMLS Is

What GAMLS Is

1. maximum likelihood principles,
2. fuzzy probability,
3. a particular n-dimensional model utilized to achieve a solution,
4. the ability to cluster without training (unsupervised clustering),
5. the ability to initialize a clustering run using a training set (supervised clustering),
6. the ability to cluster using a large number of variables (>15),
7. the ability to cluster using a large number of modes (>15),
8. the ability to cluster using datasets with much missing data,
9. the ability to cluster many wells within the same run (multi-well clustering),
10. the ability to predict missing parameters in "Test" wells based on the clustering statistics of "Model" wells.

GAMLS develops a generalized multi-dimensional solution that results in a unique n-dimensional relationship for each mode.

GAMLS is a system for performing multivariate analyses on large, complex datasets. It uses maximum likelihood principles, it incorporates fuzzy probability, and it has a neural-like component - that is, it learns as it attains a solution. However, GAMLS is not a neural net, per se; that is, a training set is not required, and if used, the training set serves only to initialize the system prior to iteration to a solution. Although GAMLS is not strictly a neural net, it can be compared in some ways to neural nets, because neither GAMLS nor neural nets fall within what can be termed a "parametric" approach to solving a problem.

Parametric vs. Nonparametric

According to Mendenhall (1967, pp. 294-295):

Parametric hypotheses are those concerned with the population parameters. Nonparametric hypotheses do not involve the population parameters but are concerned with the form of the population frequency distribution.

...it has become common to classify statistical methods for either nonparametric hypotheses or populations of unknown distributional form as nonparametric methods...

Nonparametric statistical procedures apply not only to data that are difficult to quantify. They are particularly useful in making inferences in situations where serious doubt exists about the assumptions underlying standard methodology.

Put simply, a parametric approach is one wherein particular equations are known or developed that gives the mathematical relationship among the variables. That is, a model is known or developed, and that model is used to mathematically describe the system.

For systems that are extremely complex (highly nonlinear), or for which the relationship among the variables is not known, neural nets sometimes have been used to arrive at a "solution" when otherwise the problem might have been considered intractable.

Neural Nets

Neural nets can be broadly classified as a type of mathematical analysis in which a solution to a problem (e.g., a large numerical dataset) is obtained by first providing the answer (the training set) and then, given certain rules which must be followed, asking the "net" to find the best way to associate the dataset with the answer. The solution, i.e., the association, is found by a form of parallel processing wherein all data is simultaneously linked to the answer by a "web" or "net" along which information flows, both forward and backward. The intersections of information flow are the synapses. To each synapse is assigned, during the solution process, a weight, i.e., a numerical value equivalent to the importance of that synapse, the values of which change as iteration towards a solution occurs. An electrical analogy is that the synapses act like capacitors, and the weights are somewhat like the capacitance values; the nodes that let information flow freely are essentially given more weight, and thus are more important to the information flow and the solution. This analysis process is believed to function somewhat like a brain, hence the expression "neural net".

All neural nets are not the same. However, most neural nets operate via "teaching" or "training" using a dataset. That is, a "training set" (answers to a given dataset) is presented, and the program is instructed to "find" the best path for getting from the dataset to the answers. Once trained, this path can be used by the neural net to find an appropriate solution to a second dataset for which the answers are not known.

GAMLS

GAMLS:

1. does not require training to perform a clustering analysis;
2. if training is used, all depths are used, not just a few;
3. can efficiently utilize datasets with much missing data;
4. learns very quickly; and
5. is very effective for complicated real-world problems. In addition, GAMLS can also account for known geological properties or behaviors of rock types and has within its structure the ability to fuse deterministic or probabilistic information from other sources (e.g., other sensors, geologist opinions......). [Note: This "expert opinion" facet has not yet been implemented into GAMLS.]

GAMLS derives its name from the maximum likelihood system by which it works. However, it could also be termed a model-based neural system (to separate it from neural nets, we abstain from the word "net"). The mathematical framework of GAMLS, termed MLANS (Maximum Likelihood Adaptive Neural System), is described in Perlovsky and McManus (1991). MLANS has previously been used in pattern recognition problems such as missile tracking and discrimination (Perlovsky, 1992, 1994a, 1994b).

MLANS is a neural system that combines a priori knowledge, adaptivity, and fuzzy logic. Also, it can process both numerical and symbolic information. Finally, MLANS performance has been demonstrated to approach the information-theoretic performance limits:

1. the Bayes error in classification and association accuracy (Fukunaga, 1990), and
2. the Cramer-Rao bound on learning efficiency or speed (Cramer, 1963).

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