Assessing a feature's trustworthiness and two approaches to feature selection
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Improvements in technology have led to a relentless deluge of information that current data mining approaches have trouble dealing with. An extreme example of this is a problem domain that is referred to as“non-classical”. Non-classical problems fail to fulfill the requirements of statistical theory: that the number of instances in the sample set be much greater than the number of dimensions. Non-classical problems are mainly characterized by many dimensions (or features) and few noise-affected samples. Microarray technology provides one source of non-classical problems, which typically produces data sets with a dimensionality exceeding ten thousand and containing just a few hundred instances. A risk with such a data set is building a model that is significantly influenced by coincidental correlations between the inputs (or the model’s features) and the output. A classical strategy for managing this risk is reducing the dimensionality without significantly affecting the correlation between the remaining features and the model’s output. However this strategy does not explicitly consider the impact of poor data quality (or noise) and having few data samples. In order to actively manage noise—a feature selection strategy is needed that not only considers the correlation between the features and the output, but also the quality of the features. It is proposed that feature quality, or simply the feature’s “trustworthiness”, should be incorporated within feature selection. As the trustworthiness of a feature increases, it is expected that the ability to accurately extract the underlying structure of the data will also increase. Another characteristic of non-classical problems is significant feature redundancy (where information provided within one dimension is also present in one or other dimensions). This research postulates that the use of feature trustworthiness and redundancy provides an opportunity to actively reduce the noise associated with the selected feature set, while still finding features that are well correlated with the model’s output. Two fundamental contributions are provided by this thesis: the notion of feature “trustworthiness” and how trustworthiness can be integrated within feature selection. Trustworthiness provides a flexible approach for evaluating the quality of a feature’s sample data and in certain cases, the quality of the test data. This flexibility encourages the use of prior knowledge about the specific problem and in particular, how the quality of the data is best estimated. Traditionally feature selection implicitly assumes that every instance of data, supplied by preprocessing, has the same quality. Trustworthiness also provides an opportunity for incorporating a measure of the changes applied to the data set as a result of data cleaning. Using an area of computational learning, a theoretical justification was constructed that showed the difficulty of building an accurate model for a non-classical problem. The justification showed how a modest data quality problem can result in insufficient sample data to permit successful learning. It also showed how selecting less noisy data, or sufficiently trustworthy features, can enable successful learning using the available data points. This thesis presents two methodologies that incorporate a measure of data quality within feature selection: one methodology only uses training data, while the other also incorporates test data while evaluating feature trustworthiness. The two methodologies are contrasted with each other and with a traditional feature selection methodology, which does not consider data quality. A number of data sets were used to test these methodologies, with the main data sets being: synthetic data, childhood leukaemia and chronic fatigue syndrome. In most cases the three feature selection methodologies achieved similar accuracy however there were clear differences in the features selected by each. Using heat maps to visualize the clarity of the separation of the class labels by the selected features—showed dramatic differences. The two methodologies that incorporate trustworthiness provided a clearer separation, while the traditional methodology was substantially inferior and appeared to be heavily influenced by artifacts. Using Gene Set Enrichment Analysis (GSEA), a widely used resource for evaluating the biological meaningfulness of gene sets (Subramanian, Tamayo, Mootha, Mukherjee, Ebert, Gillette, Paulovich, Pomeroy, Golub, Lander, and Mesirov, 2005), showed that the two proposed methodologies selected genes that were more biologically meaningful than those selected by a traditional feature selection methodology. The experiments also evaluated the sensitivity of trustworthiness to differences in the data set. By evaluating the trustworthiness of every feature, it was shown that considerable changes occurred across data folds. This result agrees with findings in the literature, such as (Ein-Dor, Kela, Getz, Givol, and Domany, 2005) and provides one explanation for the difficulty of modeling non-classical problems.
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