Medical data mining by fuzzy modeling with selected features

Summary

Objective

Medical data is often very high dimensional. Depending upon the use, some data dimensions might be more relevant than others. In processing medical data, choosing the optimal subset of features is such important, not only to reduce the processing cost but also to improve the usefulness of the model built from the selected data. This paper presents a data mining study of medical data with fuzzy modeling methods that use feature subsets selected by some indices/methods.

Methods

Specifically, three fuzzy modeling methods including the fuzzy k-nearest neighbor algorithm, a fuzzy clustering-based modeling, and the adaptive network-based fuzzy inference system are employed. For feature selection, a total of 11 indices/methods are used. Medical data mined include the Wisconsin breast cancer dataset and the Pima Indians diabetes dataset. The classification accuracy and computational time are reported. To show how good the best performer is, the globally optimal was also found by carrying out an exhaustive testing of all possible combinations of feature subsets with three features.

Results

For the Wisconsin breast cancer dataset, the best accuracy of 97.17% was obtained, which is only 0.25% lower than that was obtained by exhaustive testing. For the Pima Indians diabetes dataset, the best accuracy of 77.65% was obtained, which is only 0.13% lower than that obtained by exhaustive testing.

Conclusion

This paper has shown that feature selection is important to mining medical data for reducing processing time and for increasing classification accuracy. However, not all combinations of feature selection and modeling methods are equally effective and the best combination is often data-dependent, as supported by the breast cancer and diabetes data analyzed in this paper.

Introduction

Early detection of medical problems such as breast cancer and diabetes is important to increase the chance of successful treatment. Such detection is often formulated as a binary classification problem. Various soft computing methods have been used for the detection of a potential medical problem. This paper specifically focuses on the use of fuzzy modeling methods because of their advantage in discovering human comprehensible knowledge, which is important to the acceptance and usability of a solution derived from the model. Consider a multiple-input single-output system, in which A₁ and C denote the predefined sets of fuzzy terms for the ith input space and the output, respectively. Assuming m input variables, the set of all possible rules constituting a fuzzy model may be presented by the Cartesian product: R:A₁ × … × A_i × … × A_m × C.

Guillaume [1] defined three necessary conditions for a set of fuzzy models to be interpretable as follows:

• The fuzzy partition must be readable, in the sense that the fuzzy sets can be interpreted as linguistic labels.

• The set of rules must be as small as possible.

• The If-part of the rules should be derived from a subset of independent variables rather than the full set.

Various methods have been proposed to learn fuzzy models but not all of them produce human interpretable models. More details can be referred to the review carried out by Liao [2]. Two methods capable of producing human interpretable models are selected for this study. More details are given in Section 2. For comparison, the fuzzy k-nearest neighbor algorithm that falls under the category of lazy learning is also used.

For high dimensional data, as often the case for medical data, an interpretable fuzzy model must use a small subset of features, not the full set. To this end, feature selection methods must be employed together with fuzzy modeling methods. Feature selection methods can be grouped into four categories: the first type encompasses feature selection algorithms built into adaptive systems for data analysis as a decision tree method; the second type of algorithms are wrapped around predictors providing them subset of features and receiving their performance feedback; the third type are algorithms independent of any predictors, filtering out features which are irrelevant or redundant and are not very useful in data analysis; and the fourth type are hybrids of filter and wrapper approaches.

The filter approach evaluates and selects feature subsets based on general characteristics of data, and some statistical analysis without employing any learning model. On the other hand, the wrapper technique involves a learning model, and uses its performance as the evaluation criterion. The wrapper approach is known to be more accurate compared to the filter approach and it is computationally more expensive as well. The hybrid approach, which is a combination of filter and wrapper technique, is designed to trade accuracy with computational speed by applying a wrapper technique to only those subsets pre-selected by a filter technique. For each category, many feature selection methods have been proposed in the past. Their usages together with fuzzy modeling methods, however, have not been studied and reported widely (refer to Section 5 for details). Hence, it is unclear which combination of feature selection and fuzzy modeling method performs better for a particular dataset. Selecting a feature selection and data mining algorithm is one of the important steps in the entire knowledge discovery process. Unfortunately, reports of such a study are still a rarity.

To fill in this gap and shed light on the performance of different combinations of feature selection and fuzzy modeling methods, a study was carried out using two popular medical-related benchmark datasets and one industrial dataset and the results are reported in this paper. Section 2 briefly describes each feature selection method and each fuzzy modeling method employed in this study. Section 3 presents the test results. Section 4 discusses the results and addresses other relevant issues. Related works concerning the use of fuzzy modeling in medical data mining are reviewed in Section 5. Finally the paper is concluded.