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B.Sasikala

, IJRIT 46 International Journal of Research in Information Technology (IJRIT) International Journal of Research in Information Technology (IJRIT) International Journal of Research in Information Technology (IJRIT) International Journal of Research in Information Technology (IJRIT)

www.ijrit.comwww.ijrit.com www.ijrit.comwww.ijrit.com ISSN 2001-5569

An Improved Feature Subset Selection with Correlation Measure using Clustering Technique

1B.Sasikala, 2M.Kalaiselvi

1PG Student, Department of CSE Vivekananda College of Technology for Women Tiruchengode, Tamil Nadu, India sasipathi.b@gmail.com

2Assistant Professor,Department of CSE Vivekananda College of Technology for Women Tiruchengode, Tamil Nadu, India kalaiselvi.mayilsami@gmail.com

Abstract

Clustering techniques are used to partition the transaction data values. Vector based similarity models are suitable for low dimensional data values. High dimensional data values are clustered using subspace clustering method.

Feature selection involves identifying a subset of the most useful features that produces compatible results as the original set of features. In this paper the clustering technique are used to improve the feature subset selection with correlation measure. Based on these criteria, a fast clustering based feature selection algorithm, FAST, is proposed and experimentally evaluated in this paper. A feature selection algorithm is constructed with the consideration of efficiency and effectiveness factor. The efficiency concerns the time required to find a subset of features. The effectiveness is related to the quality of the subset of features. Fast clustering-based feature selection algorithm (FAST) is used to cluster the high dimensional data. The feature selection process is improved with correlation measures. Redundant feature filtering mechanism is used to filter the similar features and also the custom threshold is used to improve the clustering accuracy.

Index Terms

-

Feature clustering, Feature subset selection, redundant filtering, filter method.

I. Introduction

Feature subset selection is an effective way for reducing dimensionality, increasing learning accuracy, removing irrelevant and redundant data, and improving result comprehensibility [5],[11]. The main aim of feature selection (FS) is to determine the relevant feature in the high dimensional data. Usually FS algorithms involve heuristic or random search strategies in an attempt to avoid this prohibitive complexity. They can be divided into four broad categories: the embedded, filter, and hybrid approaches.

The wrapper methods use the predictive accuracy of a predetermined learning algorithm to determine the goodness of the selected subsets. The embedded methods incorporate feature selection as a part of the training

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process and are usually specific to given leaning algorithms.[23].The wrapper methods are computationally expensive and tend to over fit on training sets[13],[14].The filter methods are independent of learning algorithm with good generality. The filter methods, in addition to the generality, are usually a good choice when the number of features is very large. [20]. The general graph theoretic clustering is simple: compute a neighborhood graph of instances, then delete any edge in the graph that is much longer/shorter (according to some criterion) than its neighbors. In cluster analysis, graph-theoretic methods have been well studied and used in many applications. In our study, we apply graph-theoretic clustering methods to the features. Based on the minimum spanning tree (MST) method, we propose a Fast clustering- bAsed feature Selection algoriThm (FAST). We adopt the MST based clustering algorithms, because they do not assume that data points are grouped around centers or separated by a regular geometric curve and have been widely used in practice. The FAST algorithm works in two steps. In the first step, features are divided into clusters by using graph-theoretic clustering methods. In the second step, the most representative feature that is strongly related to target classes is selected from each cluster and to form the final subset of features.

Features in different clusters are relatively independent; the clustering based strategy of FAST has a high probability of producing a subset of producing a subset of useful and independent features. In this work, we introduce a novel concept predominant correlation, and propose a fast filter method which can identify relevant features as well as redundancy among relevant features without pairwise correlation analysis. In section 2, we describe the related works. In section 3, we present the new feature subset selection algorithm FAST. In section 4, we report extensive experimental results to support FAST algorithm. Finally, in section 5, we evaluate the efficiency and effectiveness of this algorithm via extension experiments on various real world dataset comparing with other representative feature selection algorithm. In section 6, we conclude our work with some possible extension.

2. Related work

Feature selection is frequently used as a preprocessing step to machine learning. Feature subset selection can be viewed as the process of identifying and removing many irrelevant and redundant features. This is because: (i) irrelevant features do not contribute to the predictive accuracy [13], and (ii) redundant features do not rebound to getting a better predictor for that they provide mostly information which is already present in other features.

Hierarchical clustering has been adopted in word selection in the context of text classification [19],[23].Distributed clustering has been used to cluster words into groups based either on their participation in particular grammatical relations with other words by Lee et al[24].Distributed clustering of words are in nature, and result in sub optimal word clusters and high dimensional cost Kumar et al [18].

II Existing System

3. Feature Subset Selection Algorithm

3.1 Framework and Definitions

In this section we discuss about how to find the relevant features from the high dimensional data. The irrelevant features and redundant features are severely affect the accuracy of the learning a machines.[11][21].Feature subset selection algorithm are able to identify and remove the irrelevant and redundant information. Moreover, “good feature subsets contains features highly correlated with (predictive of) the class, yet uncorrelated with (not predictive of) each other.”

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Feature subset selection can be viewed as the process of classifying and removing as many unrelated and completed features as possible. Feature selection methods are used to identify the key features from a data collection. Irrelevant feature identification and redundant feature filtering methods are used in the feature selection process. Correlation similarity measures are used for the relationship analysis. Fast clustering method is used to perform data clustering with feature selection process. Minimum Spanning Tree is used to construct the tree with transaction values.

Redundant Filtering Mechanism

Fig 1: Framework of the proposed feature subset selection algorithm.

The feature selection process is improved with a set of correlation measures. Dynamic feature intervals can be used to distinguish features. Redundant feature filtering mechanism is used to filter the similar features. Custom threshold is improved with clustering accuracy. The graph based clustering algorithm is designed with MST.

Feature selection process is enhanced with dynamic threshold values. Mutual information measures how much the distribution of the feature values and target classes differ from statistical independence. This is a nonlinear estimation of correlation between feature values and target classes.

The symmetric uncertainty is defined as follows 2*Gain (X|Y)

SU (X, Y) =

H(X) + H(Y) (1) Where,

1) H(X) is the entropy of a discrete random variable X. Suppose p(x) is the prior probabilities for all values of X,H(X) is defined by

H(X) = - ∑ p(x) log2 p(x) (2) x ∈ 

Data Set

Data preprocess

Irrelevant Feature

Removal

Feature Selection

Minimum Spanning

Tree

Tree Partition

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2) Gain (X|Y) is the amount by which the entropy of Y decreases. It reflects the additional information about

Y provided by X and is called the information gain which is given by H(X) -H (X|Y)

Gain (X|Y) =

H(Y) -H (Y|X) (3)

Where H (X|Y) is the conditional entropy which quantifies the remaining entropy (i.e. uncertainty) a random variable X given that the value of another random variable Y is known. Suppose p(x) is the prior probabilities for all values of X and p (x|y) is the posterior probabilities of X given the values of Y, H (X|Y) is defined by

H (X|Y) = - ∑ p(y) ∑ p(x|y) log2 p(x|y) (4) y∈  x∈ 

Information gain is a symmetrical measure. That is the amount of information gained about X after observing Y is equal to the amount of information gained about Y after observing X. This ensures that the order of two variables (e.g.,(X,Y) or (Y|X)) will not affect the value of the measure.

Definition 1(T-Relevance) The relevance between any pair of feature Fi F and the target concept C is referred to as the T-Relevance of Fi and C denoted by SU(Fi, C).

Definition 2(F-Correlation) The correlation between any pair of feature Fi and Fj (Fi, Fj ∈ F Ʌ I ≠j) is called the F- Correlation of Fi and Fj, and denoted by SU (Fi, Fj).

Definition 3(F-Redundancy) Let S= {F1,F2,…Fi,

…, Fk< |F|} be a cluster of features. If ∃ Fj ∈ S,SU(Fj, C)> SU(Fi, C) SU(Fi, Fj)> SU(Fi, C) is always corrected for each Fi S(i j),then Fi are redundant features with respect to the given Fj (i.e each Fi is a F-Redundancy)

According to the above definitions, feature subset selection can be the process that identifies and retains the strong T-Relevance features and selects R- Features from feature clusters. The behind heuristics are that

1) Irrelevant features have no/weak correlation with target concept;

2) Redundant features are assembled in a cluster and a representative feature can be taken out of the cluster.

III Proposed System

4. Correlation Based Filter Approach

In this section, we discuss how to evaluate the goodness of features for classification. In general, a feature is good if it is relevant to the class concept but is not redundant to any of the other relevant features. If we adopt the correlation between two variables as a goodness measure, the above definition becomes that a feature is good if it is highly correlated to the class but not highly correlated to any other features. In other words, if the correlation between a feature and the class is high enough to make it relevant to (or predictive of) the class and the correlation between it and any other relevant features does not reach a level so that it can be predicted by any of the other relevant features, it will be regarded as a good feature for the classification task.

There exist broadly two approaches to measure the correlation between two random variables. One is based on classical linear correlation and the other is based on information theory. Under the first approach the most well-

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known measure is linear correlation coefficient. There are several benefits of choosing linear correlation as a feature goodness measure for classification.

First, it helps removes feature with near zero linear correlation to the class. Second, it helps to reduce redundancy among selected features. It is known that if data is linearly separable if all but one of a group of linearly dependent features is removed. However it is not safe to always assume linear correlations that are not linear in nature. Another limitation is that the calculation requires all features contain numerical values.

To overcome these shortcomings, in our solution we adopt the other approach and choose a correlation measure based on the information theoretical concept of entropy, a measure of the uncertainty of a random variable. Using symmetrical uncertainty (SU) as the goodness measure, we are now ready to develop a procedure to select good features for classification based on correlation analysis of features for (including the class). This involves two aspects (1) how to decide whether a feature is relevant to the class or not; and (2) how to decide whether such a relevant feature is redundant or not when considering it with other relevant features.

The answer to the first question can be using a user defined threshold SU value, as the method used by many other feature weighting algorithms (e.g., Relief). More specifically, suppose a dataset S contains N features and C class. Let SUic denote the SU value that measures the correlation between a feature Fi and class C (named C- correlation), then a subset S’ of relevant features can be decided by a threshold SU value .The answer to the second question is more complicated because it may involve analysis of pairwise correlation between all features (named F- correlation), which results in time complexity of 0(N2) associated with the number of features N for most existing algorithms.

Since F-correlation is also captured by SU values, in order to decide whether a relevant feature is redundant or not, we need to find a reasonable way to decide the threshold level for F-correlations as well. In other words, we need to decide whether the level of correlation between two features in S’ is high enough to cause redundancy so that one of them may be removed from S’. In the context of a set of relevant features S’ already identified for the class concept, when we try to determine the highly correlated features for a given feature Fi and the class concept, SU I,c as a reference. Therefore, even the correlation between this feature and the class concept is larger than some threshold value and therefore making this feature relevant to the class concept, this correlation is by no means predominant.

Definition 4: (Predominant Feature). A feature is predominant to the class, if its correlation to the class is predominant or can become predominant after removing its redundant peers. According to the above definitions, a feature is good if it is predominant in predicting the class concept, and feature selection for classification s a process that identifies all predominant features and remove redundant ones among all relevant features, without having to identify all the redundant peers for every feature in S’, and thus avoids pairwise analysis of F-correlation between all relevant features.

5. Empirical Study

In this section, we empirically evaluate the efficiency and effectiveness of our method by comparing with feature selection algorithms. For the purpose of evaluating the performance and effectiveness of our proposed FAST algorithm, verifying whether or not the method is potentially useful in practice, and allowing other researchers to confirm our results, 35 publicly available dataset were used.

We describe experimental setup in section 5.1, discuss the experimental procedure in section 5.2 and discuss the result and analysis in 5.3 discusses the experimental producers.

5.1 Experimental Setup

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The efficiency of a feature selection algorithm can be directly measured by its running time over various data sets .For real world data, we often do not have such prior knowledge about the optimal subset, so we use the predictive accuracy on the selected subset of feature. To evaluate the performance of our proposed FAST algorithm and compare it with other feature selection algorithms in a fair and reasonable way, we set up our experimental study as follows.

In terms of the above criteria, we limit our comparison to the filter model as FCBF is a filter algorithm designed for high dimensional data. We choose representative algorithms from both approaches (i.e., individual evaluation and subset evaluation). One algorithm, from individual evaluation, is Relief- F (Robnik-Sikonja and Kononenko, 2003) which searches for nearest neighbors of instances of different classes and weights. Another algorithm, from subset evaluation, is a variation of CFS (Hall, 2000), denoted by CFS-SF (Sequential Forward).Sequential forward selection is used in CFS-SF as initial experiments show CFS_SF runs much faster to produce similar results than CFS. In addition to feature selection algorithms, we use the learning algorithm C4.5 (Quinlan.1993), to evaluate the predictive accuracy on the selected subset of features. All these selected algorithms are from Weka’s collection (Witten and Frank, 2000).

The proposed algorithm is compared with five different types of representative feature selection algorithms. They are (i) FCBF, (ii) Relief-F, (iii) CFS, (IV) Consist and (v) FOCUS-SF respectively. FCBF and Relief –F evaluate feature individually. For FCBF, in the experiments, we set the relevance threshold to be the SU value of the ranked feature for each dataset. Relief –F searches for nearest neighbors of instances of different classes and weights features according to how well they differentiate instances of different classes. The other three feature selection algorithms are based on subset evaluation. CFS exploits best-first search based on the evaluation of as subset that contains features highly correlated with the target concept, yet uncorrelated with each other. The feature selection method searches for the minimal subset that separates classes as consistently as the full set can under best-first search strategy. FOCUS-SF has some evaluation strategy as consist, but it examines all subsets of features.

5.2 Experimental Procedures

In order to make the best use of the data and obtain stable results, (M=5)*(N=10) cross validation strategy is used.

That is, for each dataset, each classification algorithm, the 10-fold cross validation is repeated M=5 times, with each time the order of the instances of the dataset being randomized. Randomizing the order of the inputs can help diminish the order effects. In the experiment, for each feature subset selection algorithm, we obtain M×N feature subset and the corresponding runtime time with each dataset .For each classification algorithm, we obtain M×N classification accuracy for each feature selection algorithm and each dataset.

The Friedman test [24] can be used to compare k algorithms over N datasets by ranking each algorithm on each set separately. The algorithm obtained the best performance gets the rank of 11, the second best ranks 2, and so on.

Then the average ranks of all algorithms on all data sets are calculated and compared. The Nemenyi test [21]

compares classifiers in a pairwise manner. According to this test, the performances of two classifiers are significantly different if the distance of the average ranks exceed the critical distances. It is known that if data is linearly separable if all but one of a group of linearly dependent features is removed. However it is not safe to always assume linear correlations that are not linear in nature. Using symmetrical uncertainty (SU) as the goodness measure, we are now ready to develop a procedure to select good features for classification based on correlation analysis of features for (including the class).Another limitation is that the calculation requires all features contain numerical values.

Procedure Experimental Process

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1

M=5, N=10

2 DATA = {D1, D2, .., D35}

3 Learner= {NB, C4.5, IBI, RIPPER}

4 Feature Selector = {FAST, FCBF, Relief, CFS, Consist, FOCUS-SF}

5 for each data ∈ DATA do 6 for each times ∈ [1, N] do

7 randomize instance order for data 8 generate N bins from the randomized data 9 for each fold ∈ [1, N] do

10 Test data=bin [fold]

11 training data=data – Test Data 12 for each selector ∈ feature selectors do 13 (Subset, Time) = selector (Training Data) 14 Training Data’ = select Subset from Training 15 Test Data’=select subset from test data 16 for each Learner ∈ Learners do 17 classifier=learners (Training Data’) 18 accuracy=apply classifier to Test Data’

5.3 Result and Analysis

In this section we present the experimental results in terms of the proportion of selected features, the time to obtain the feature subset, the classification accuracy.

Generally all the six algorithms achieve significant reduction of dimensionality by selecting only a small portion of the original features. Fast on average obtains the best proportion of selected features.

In order to further explore feature selection algorithms whose reduction rates have statistically significant differences, we performed a Nemenyi test.The results indicate that the proportion of selected features of FAST is statistically smaller than those of Relief-F, CFS andFCBF, and there is no consistent evidence to indicate statistical difference between FAST, Consist, and FOCUS-SF, respectively.

5.3.1Runtime

Table 1: Runtime (in ms) of the six feature selection algorithms

Dataset FAST FCBF CFS Relief Consist FOCUS-SF

Chess 105 60 345 12660 1990 653

Coil 1472 716 938 13918 3227 660

Elephant 866 875 1483 30416 53845 1282

Arrhy 783 312 905 1072 3492 1098

Colon 166 115 821 744 1360 2940

Ar10p 706 458 736 7945 1624 1032

Pie10p 678 1223 1224 3874 57934 960

Oh0.wc 5283 5990 6650 7636 3568 4689

Oh10.wc 5549 6033 1034 4898 4149 8446

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B-cell1 160 248 9345 5652 4882 3421

b-cell2 626 1618 4524 4166 5102 1273

b-cell3 635 2168 3415 5102 2914 8446

Average 3573 4671 5456 4580 7490 5227

Win/draw/

loss

- 22/0/3 31/0/1 20/0/6 35/0/0 34/0/1

Generally the individual evaluation based feature selection algorithms of FAST, FCBF and Relief are much faster than the subset evaluation based algorithms of CFS, Consist and FOCUS-SF.FAST is consistently faster than all other algorithms. The runtime of FAST is only 0.1 % of that of CFS 2.4 % of that of Consist, 2.8 % of that of FOCUS-SF, 7.8% of that of Relief, and 76.5% of that of FCBF, respectively. The Win/Draw/Loss records show that FAST outperforms other algorithms as well.

From the analysis above we can know that FAST performs very well on the microarray data. The reason lies in both the characteristics of the dataset itself and the property of the proposed algorithm. Microarray data has the nature of the large number of features (genes) but small sample size, which can cause “curse of dimensionality” and over- fitting of the training data [22]. For the purpose of exploring the relationship between feature selection algorithms and data types, i.e. which algorithm are more suitable for which types of data, we rank the six feature selection algorithms according to the classification accuracy of the feature selection method. Therefore, selecting a small number of discriminative genes from thousands of genes is essential for successful sample classification [21], [24].

Our proposed FAST effectively filters out a mass of irrelevant features in the first step. This reduces the possibility of improperly bringing the irrelevant features into the subsequent analysis. Then in the second step FAST removes redundant features by using the redundant filtering mechanism. Our proposed FAST also requires a parameter that is the threshold of feature relevance. Different values might end with different classification results.

6. Conclusion

In this paper, we propose a novel concept of predominant correlation, introduce an efficient way of analyzing feature redundancy, and design a fast correlation based filter approach and clustering based feature subset selection algorithm for high dimensional data. The algorithm involves (i) removing irrelevant features,(ii) constructing a minimum spanning tree from relative ones, and(iii) partitioning the MST and selecting representative features. We compared the performance of the proposed algorithm with those of the five feature selection algorithm FCBF, CFS, Relief, Consist, and FOCUS-SF. The above experimental results suggest that the feature selection for classification on high dimensional data are efficiently achieving the high degree of dimensionality reduction and enhance classification accuracy with predominant correlation features.

For the future work, we plan to enhance the correlation measure to improves the searching efficiency will modify the Fast algorithm.

References

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[18] Scherf M. and Brauer W., Feature Selection By Means Of A Feature Weighting Approach, Technical Report FKI-221-97, Institute Fur Informatics, and Technics Universidad Munched 1997.

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References

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