Fuzzy Logic In Data Mining

[Annemie]

FuzzyLogic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1, instead of just the traditional values of true or false. It is used to deal with imprecise or uncertain information and is a mathematical method for representing vagueness and uncertainty in decision-making.

Fuzzy Logic is based on the idea that in many cases, the concept of true or false is too restrictive, and that there are many shades of gray in between. It allows for partial truths, where a statement can be partially true or false, rather than fully true or false.

The fundamental concept of Fuzzy Logic is the membership function, which defines the degree of membership of an input value to a certain set or category. The membership function is a mapping from an input value to a membership degree between 0 and 1, where 0 represents non-membership and 1 represents full membership.

Fuzzy Logic is implemented using Fuzzy Rules, which are if-then statements that express the relationship between input variables and output variables in a fuzzy way. The output of a Fuzzy Logic system is a fuzzy set, which is a set of membership degrees for each possible output value.

In summary, Fuzzy Logic is a mathematical method for representing vagueness and uncertainty in decision-making, it allows for partial truths, and it is used in a wide range of applications. It is based on the concept of membership function and the implementation is done using Fuzzy rules.

In the boolean system truth value, 1.0 represents the absolute truth value and 0.0 represents the absolute false value. But in the fuzzy system, there is no logic for the absolute truth and absolute false value. But in fuzzy logic, there is an intermediate value too present which is partially true and partially false.

Definition: A graph that defines how each point in the input space is mapped to membership value between 0 and 1. Input space is often referred to as the universe of discourse or universal set (u), which contains all the possible elements of concern in each particular application.

In standard logic, every statement must have an absolute value: true or false. In fuzzy logic, truth values are replaced by degrees of "membership" from 0 to 1, where 1 is absolutely true and 0 is absolutely false.

Data mining is the process of identifying significant relationships in large sets of data, a field that overlaps with statistics, machine learning, and computer science. Fuzzy logic is a set of rules that can be used to reach logical conclusions from fuzzy sets of data. Since data mining is often applied to imprecise measurements, fuzzy logic is a useful way of determining relevant relationships from this kind of data.

Fuzzy logic is often grouped together with machine learning, but they are not the same thing. Machine learning refers to computational systems that mimic human cognition, by iteratively adapting algorithms to solve complex problems. Fuzzy logic is a set of rules and functions that can operate on imprecise data sets, but the algorithms still need to be coded by humans. Both areas have applications in artificial intelligence and complex problem-solving.

An artificial neural network is a computational system designed to imitate the problem-solving procedures of a human-like nervous system. This is distinct from fuzzy logic, a set of rules designed to reach conclusions from imprecise data. Both have applications in computer science, but they are distinct fields.

Predictive understanding of cell signaling network operation based on general prior knowledge but consistent with empirical data in a specific environmental context is a current challenge in computational biology. Recent work has demonstrated that Boolean logic can be used to create context-specific network models by training proteomic pathway maps to dedicated biochemical data; however, the Boolean formalism is restricted to characterizing protein species as either fully active or inactive. To advance beyond this limitation, we propose a novel form of fuzzy logic sufficiently flexible to model quantitative data but also sufficiently simple to efficiently construct models by training pathway maps on dedicated experimental measurements. Our new approach, termed constrained fuzzy logic (cFL), converts a prior knowledge network (obtained from literature or interactome databases) into a computable model that describes graded values of protein activation across multiple pathways. We train a cFL-converted network to experimental data describing hepatocytic protein activation by inflammatory cytokines and demonstrate the application of the resultant trained models for three important purposes: (a) generating experimentally testable biological hypotheses concerning pathway crosstalk, (b) establishing capability for quantitative prediction of protein activity, and (c) prediction and understanding of the cytokine release phenotypic response. Our methodology systematically and quantitatively trains a protein pathway map summarizing curated literature to context-specific biochemical data. This process generates a computable model yielding successful prediction of new test data and offering biological insight into complex datasets that are difficult to fully analyze by intuition alone.

Over the past few years, many methods have been developed to construct large-scale networks from the literature or databases of genetic and physical interactions. With the advent of high-throughput biochemical methods, it is also possible to measure the states and activities of many proteins in these biochemical networks under different conditions of cellular stimulation and perturbation. Here we use constrained fuzzy logic to systematically compare interaction networks to experimental data. This systematic comparison elucidates interactions that were theoretically possible but not actually operating in the biological system of interest, as well as data that was not described by interactions in the prior knowledge network, pointing to a need to increase our knowledge in specific parts of the network. Furthermore, the result of this comparison is a trained, quantitative model that can be used to make a priori quantitative predictions about how the cellular protein network will respond in conditions not initially tested.

Copyright: 2011 Morris et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

One way to accomplish this is to apply traditional fuzzy logic [FL], as demonstrated previously in modeling continuous input-output relationships to encode a complex signaling network [31], [32]. In the realm of control theory, FL modeling is an established technique for predicting the outputs of complex industrial processes when the influences of inputs cannot be characterized precisely [33], [34], [35]. A central feature of FL is that it accounts for graded values of process states using a virtually unlimited repertoire of relationships between model species or components. However, for past application to biochemical signaling networks, the flexibility of conventional FL modeling necessitated that the network topology be fixed prior to either manual [31] or computational [32] parameter fitting, rendering a formal training of network topology to experimental data infeasible.

However, our goal is to train models on quantitative biological data that are inevitably incomplete in the sense that (i) measurements are not obtained under all possible conditions and (ii) available data are not sufficient to constrain both the topology and quantitative parameters of the underlying networks. Accordingly, we sought to develop a fuzzy logic system that minimizes the number of parameters to avoid over-fitting and simplifies the logic structure to facilitate model interpretability. Because we aim to represent relationships among proteins in enzymatic cascades, mathematical relationships should be biologically relevant. We therefore use a simple Sugeno fuzzy logic gate with a defined form (see Text S1) based on transfer functions (mathematical functions describing the relationship between input and output node values) that approximate the Hill functions of classical enzymology.

In some cases, use of a normalized function is too restrictive for practical application. For example, if model inputs are purely binary (values of either zero or one), the output of a normalized function would also be zero or one, making it impossible for a cFL gate to achieve intermediate states of activation. Accordingly, our cFL method allows for alternative transfer functions. For example, although the method is not limited to binary model inputs, the ligand inputs of our current work are binary (either present or not). If we used normalized transfer functions to relate these model inputs to downstream outputs, all model species would also be either zero or one. Thus, for these transfer functions, we used a constant multiplied by the binary ligand input value (see Materials & Methods).

In practice, available experimental data is usually insufficient to fully constrain both the parameters and topology of the cFL models, and CellNOpt-cFL recovers many models that describe the data equally well. Due to this typical absence of firm structural and parametric identifiability [29], [49], [50], we examine families of models that fit the data equally well rather than attempting to identify a single global best fit. Specifically, we examine interactions in the PKN that were either retained or consistently removed by training. We also use individual models to predict input-output characteristics. This treatment allows us to calculate both an average prediction as well as a standard deviation, which we show below can be useful for discrediting inaccurate predictions.

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