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Feature Subset Selection: a Correlation Based Filter Approach

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Feature Subset Selection: a Correlation Based Filter Approach Feature Subset Selection: A Correlation Based Filter Approach Mark A. Hall, Lloyd A. Smith ([mhall, las]@cs.waikato.ac.nz) Department of Computer Science, University of Waikato, Hamilton, New Zealand. Abstract features, and evaluates its effectiveness with three common Recent work has shown that feature subset selection can have a ML algorithms. positive affect on the performance of machine learning algorithms. Some algorithms can be slowed or their performance 2. Feature Selection: Filters and Wrappers In ML, feature selectors can be characterised by their tie with irrelevant or redundant to the learning task. Feature subset the induction algorithm that ultimately learns from the selection, then, is a method for enhancing the performance of reduced data. One paradigm, dubbed the Filter [Kohavi and learning algorithms, reducing the hypothesis search space, and, in some cases, reducing the storage requirement. This paper John, 1996], operates independent of any induction describes a feature subset selector that uses a correlation based before induction takes place. Some filter methods strive for evaluates its effectiveness with three common ML algorithms: a decision tree inducer (C4.5), a naive Bayes classifier, and an combination of values for a feature subset is associated with instance based learner (IB1). Experiments using a number of a single class label [Almuallim and Deitterich, 1991]. Other standard data sets drawn from real and artificial domains are filter methods rank features according to a relevancy score presented. Feature subset selection gave significant [Kira and Rendell, 1992; Holmes and Nevill-Manning,1995] improvement for all three algorithms; C4.5 generated smaller Another school of thought argues that the bias of a decision trees. particular induction algorithm should be taken into account 1. Introduction when selecting features. This method, dubbed the Wrapper [Kohavi and John, 1996], uses the induction algorithm along with a statistical re-sampling technique such as cross- easy and storing it is relatively inexpensive. Unfortunately, validation (CV) to evaluate feature subsets. as the amount of machine readable information increases, the Often, the strengths of the wrapper approach advocated by ability to understand and make use of it does not keep pace its proponents are hailed as weaknesses by the filter camp and with this growth. Traditional statistical analysis is time vice versa. For example, wrappers often achieve better results consuming as each hypothesis must be formulated and tested than filters due to fact that they are tuned to the specific individually. Moreover, it requires a background in interaction between an induction algorithm and its training mathematics in order to understand the results. Machine data. However, they are much slower than filters as they learning (ML) aims to automate the process of information must repeatedly call the induction algorithm and must be re- discovery and be of use to people from a wide range of run when a different induction algorithm is used. backgrounds. The feature selector described in this paper is a filter. The ML programs often make assumptions or apply heuristics author believes that filters will ultimately be feasible in cases that trade some accuracy of the resulting model for speed of execution, and comprehensibility of the result. While these may be a large number of features. assumptions and heuristics are reasonable and often yield Filter Wrapper Training Training redundant and irrelevant data data opposite of their intended effect: slowed execution, less understandable results, and much reduced accuracy. FS FS In the typical supervised machine learning task, data is Search Search represented as a table of examples or instances. Each instance feature estimated feature heuristic set accuracy is described by a fixed number of measurements or features set "goodness" Feature evaluation along with a label that denotes the category (class) the Feature cross val, hold out evaluation instance belongs to. Feature selectors are algorithms that are ML Algorithm applied to the data before it reaches an ML program. Their aim is to reduce the dimensionality of the data by removing Final feature set Final feature set the irrelevant and redundant information; thus allowing the ML ML ML program to operate more effectively. Algorithm Algorithm This paper describes a feature selector that uses a Figure 1: Filter and wrapper feature selectors. correlation based heuristic to determine the usefulness of an indication of how predictive of the class a group of 2.1 Search features are; the denominator of how much redundancy there Most feature selection algorithms perform a search through is among them. The heuristic goodness measure should filter the space of feature subsets. Since the size of this space is out irrelevant features as they will be poor predictors of the exponential in the number of features, an exhaustive search is class. Redundant features should be ignored as they will be usually intractable. Greedy hill climbing search strategies highly correlated with one or more of the other features. such as forward selection and backward elimination [Kittler, 1978] are often applied to search the feature subset space in 3.1 Feature Correlations reasonable time. Although simple, these searches often yield By and large most classification tasks in ML involve learning to distinguish between nominal class values, but sophisticated AI search strategies such as Best First search may involve features that are ordinal or continuous. A and Beam search [Rich and Knight, 1991]. measure based on conditional entropy [Press et al., 1988] is Greedy hill climbing expands the current node and moves used to measure correlations between features and the class, to the child with the highest evaluation. Nodes are expanded and between features. Continuous features are first converted by applying search space operators to them (add or delete a to nominal by binning. If X and Y are discrete random single feature for forward selection and backward Elimination variables with respective ranges Rx and Ry , Equations 2 and respectively). 3 give the entropy of Y before and after observing X. Table 1: Hill climbing search H(Y) = p(y)log( p(y)) (2) 1. Let s start state. y Ry 2. Expand s by applying search operators. ( ) = ( ) ( ) ( ) 3. Evaluate each child t of s. H Y X p x p y x log( p y x ) (3) x Rx y Ry 4. Let s© child t with highest evaluation e(t). 5. If e(s© ) > e(s) then s s© , go to step 2. Y on X. This measure is sometimes called the uncertainty 6. Return s. coefficient of Y [Press et al., 1988]. Forward selection starts with an empty set of features; H(Y) H(Y X) ( ) = Backward elimination starts with a full set of features. C Y X ( ) (4) Forward selection will terminate when no child node is better H Y than its parent, while backward elimination will continue to This measure lies between 0 and 1. A value of 0 indicates delete features as long as a child is not worse than its parent. that X and Y have no association; the value 1 indicates that Forward selection and backward elimination are the used knowledge of X completely predicts Y. in the experiments described in section 4. 4. Experimental Methodology 3. CFS: Correlation-based Feature In order to determine whether CFS is of use to common ML Selection algorithms, a series of experiments was run using the Like the majority of feature selection programs, CFS uses a following ML algorithms (with and without feature search algorithm along with a function to evaluate the merit selection) on a number of standard data sets drawn from real of feature subsets. The heuristic by which CFS measures the and artificial domains. IB1: An instance based learner. Classifies a new usefulness of individual features for predicting the class label instance by comparing it with a data base of along with the level of intercorrelation among them. The instances seen during training. The class of the hypothesis on which the heuristic is based can be stated: most similar training instance is assigned to the Good feature subsets contain features highly correlated new instance. (predictive of) with the class, yet uncorrelated with (not Naive Bayes: A bayesian classifier that assumes predictive of) each other. independence between features in order to simplify the calculation of conditional probabilities. Equation 1 formalises the heuristic. C4.5: A decision tree inducer. Builds a decision tree kr for the training data in a greedy fashion by always = ci testing features that provide the most gain in Gs (1) + information. Leaves in the tree correspond to k k(k 1)rii© classifications. k is the number of features in the subset; rci is the mean 4.1 Domains feature correlation with the class, and rii© is the average feature intercorrelation. Data sets from seven natural domains and three artificial Equation 1 is borrowed from test theory [Ghiselli, 1964], domains were drawn from the UCI repository of machine where it is used to measure the reliability of a test consisting learning databases. These data sets were chosen because of the of summed items from the reliability of the individual items. prevalence of nominal features and their predominance in the literature. Three additional artificial domains were borrowed been standardised. The numerator can be thought of as giving from work by Langley and Sage [1994]. They each have 3 relevant features to which a further 27 irrelevant features have improves the performance of IB1 on 3 of natural domains and been added. These boolean domains exhibit an increasing 3 of the artificial domains. Performance is significantly level of feature interaction. It is expected that CFS will have degraded on 2 of the natural and 3 of the artificial domains. difficulty dealing with domains with high levels of feature CFS has successfully removed the 27 irrelevant attributes interaction.
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