High relevancy low redundancy vague set based feature selection method for telecom dataset

Abstract

The prompt enhancement of Telecom turned to be a vibrant and economical industry, which comprises an intrinsically great perspective for customer churn, requiring exact churn prediction models. In recent times, there has been phenomenal responsiveness in the development of feature selection methods for a large number of datasets. Through this research work, a High Relevancy and Low Redundancy (HRLR) approach by consuming Vague Set (VS) has proposed for selecting the subset of features from the features set. This proposed method is based on the Minimum Redundancy and Maximum Relevancy (MRMR) approach by using Vague Set. The proposed HRLR-VS method is based on the filtered approach feature selection, where the features are selected only when the measure of feature-class relevancy is maximized and a measure of feature-feature redundancy is minimized. The collaboration of similarity measures and ranking algorithms are prepared by utilizing the vital notions of Vague Sets information energies by Information Gain, Gain Ratio, and Chi-Square methods. The projected approach has been employed with the Particle Swarm Optimization for probing the best feature subset. Further, it measures the efficacy of the projected approach HRHL-VS for telecommunication dataset. The performance metrics like Accuracy, Kappa Statistics, True Positive Rate, Precision, F-Measure, Recall, MAE, RRSE, RMSE and RAE are considered in this paper for evaluating the proposed HRLR-VS method. The proposed HRRL-VS method has compared with existing literature approaches like mRMR and FCBF. From the result obtained in this paper, the proposed HRLR-VS method better results in all aspects for selecting the feature subset in telecommunication dataset.

Keywords

Feature Selection Vague Set Information Gain Gain Ratio Chi-Square Particle Swarm Optimization Euclidean Distance Cosine Similarity Pearson’s Correlation Coefficient

1 Introduction

The researchers in the present world face some elusive problems which clue us to inoculate the vagueness to the problems. The concept of Vague Set (VS) is proposed by Torra [1] which is the extension of fuzzy sets. VSs are exemplified by the various causes of uncertainty or various opinions of experts is the biggest advantage. By employing VS, the scholars cogitate the several characteristics of uncertainty. The telecommunication industry has gone through tremendous changes over the last few decades such as addition of new services, technological advancements and increased competition due to deregulation. Customer churn moving from individual service provider to neighboring opponent in the business is a developing problem for many server-based enterprises and especially for the telecommunication business [2]. It is an example of the vital problem for project supervisors because missing a consumer is a low-cost chance for opponents to get consumers. It has summarized that the different cost with the procurement of new consumers in ten eras added for an industry as compared to maintaining the current consumer. Maintaining present customers’ heads resulted in significant improvement in businesses and diminished purchasing cost. These factors made us finally concentrate on customer churn prediction as an essential part of imperative decision making in telecom organizations and outlining the process that is the primary aim of Customer Relationship Management (CRM) [3]. The effect of this ever increasing problem has paved way for the growth of many predictive mechanisms that help some necessary tasks in the classification process and predictive modeling.

The development of high-dimensional data that are publically available on the internet in past several ages supports diverse machine learning applications for evolution in investigation. Since, machine learning methods have inherent difficulties in dealing with the critical amount of input attributes, attract researchers for developing an alternate methods and exploring algorithms. To use machine learning methods expeditiously, preprocessing of the input is necessary.

Feature selection [4] is an example of the common prominent and frequent techniques in data preprocessing and has converted a crucial part of the machine learning method it has also distinguished as attribute selection, variable subset or variable selection in statistics and machine learning. It is the process of identifying relevant and eliminating irrelevant, redundant or noisy features. This method rushes up data mining algorithms, improves predictive accuracy and understandability. Irrelevant features are those that provide no valuable knowledge, and irrelevant features present no further information than the presently selected features. In supervised inductive learning, feature selection performs a collection of candidate features utilizing one of the three strategies 5:

The specific dimension of the subset of attributes that optimizes the measure of valuation.

The little dimension of the subset that provides a critical limitation on the measures of evaluation.

In general, the subset with the best confinement between the evaluation measure and size

The rest of the paper organization as follows, section 2 depicts the preliminaries of Vague Set, Feature Selection techniques and Similarity measures. Section 3 represents the related works done in the field of churn customer prediction in the telecommunication industry. Section 4 presents the High Relevant Low Redundant Vague set-based feature selection for considering only the high relevant and low redundant features in the Telecommunication dataset. Section 5 depicts the Experiments which consists of Dataset description. Section 6 represents the result and discussion of the proposed HRLR-VS and existing feature selection techniques. Section 7 highlights of this research work summary

2 Preliminaries of vague set, feature selection and similarity measure

The proposed HRLR-VS feature selection algorithm practices Merit value, Similarity measure, Filter algorithms, and Vague sets for finding the HRLR feature subsets.

2.1 Vague set

Illustration 1: Let A be a universe of discourse by Equation (2.1). A finite subset of [0,1] is obtained when a Vague Set (VS) X on A is represented by a h_x (a), only when A is applied. $X = {< a, h_{x} (a) > | a \in A}$ (2.1) where h_x (a) is represents the possible conditions set between the [0,1] interval. Certainly, h_x (a) is coined as the Vague Set.

Illustration 2: Given a VS h, the h’s upper and lower limit are demarcated by: h^- (a) = low h (a) is the lower limit whereas h⁺ (a) = high h (a) is the upper limit.

Illustration 3: <a, h_x (a) > |a_j ∈ A, j = 1, 2,. . . , m is considered as VS {< h_x (a) , a > a_j ∈ A, j = 1, 2,. . . , m}, the IE of X is described by Equation (2.2): ${IE}_{VS} (X) = \sum_{j = 1}^{m} (\frac{1}{d_{j}} \sum_{k = j}^{d_{j}} h_{x σ (k)}^{2} (a_{j}))$ (2.2) where m is the cardinality of hte A (Universe of Disclosure), the membership condition is presented by d_j and h_xσ(k) (a_j) is the k^th element of j^th A members toward VS.

Illustration 4: Consider two distinctive VSs X and Y, the correlation among the X and Y are represented in the Equation (2.3): $C_{VS} (X, Y) = \sum_{j = 1}^{m} (\frac{1}{d_{j}} h_{X σ (k)} (a_{j}) h_{Y σ (k)} (a_{j}))$ (2.3) The parameters used in this equation is same as in the previous Equation (2.2).

Illustration 5: X and Y are the two distinctive VSs, the correlation coefficient (CC) among X and Y is depicted by Equation (2.4): $P_{VS} (X, Y) = \frac{C_{VS} (X, Y)}{[C_{VS} (X, X)]^{\frac{1}{2}} [C_{VS} (Y, Y)]^{\frac{1}{2}}}$ (2.4)P_VS (X, Y) = $\frac{\sum_{j = 1}^{m} (\frac{1}{d_{j}} h_{X σ (k)} (a_{j}) h_{Y σ (k)} (a_{j}))}{[\sum_{j = 1}^{m} (\frac{1}{d_{j}} \sum_{k = j}^{d_{j}} h_{X σ (k)}^{2} (a_{j})]^{\frac{1}{2}} [\sum_{j = 1}^{m} (\frac{1}{d_{j}} \sum_{k = j}^{d_{j}} h_{Y σ (k)}^{2} (a_{j}))]^{\frac{1}{2}}}$ where it must satisfy the following circumstances:

CC matrix is symmetrical when P_VS (X, Y) = P_VS (Y, X).

[0, 1] is the interval for CC and it is given by 0 ≤ P_VS (X, Y) ≤1: implies that all correlation coefficients must be in the interval of [0, 1].

X and Y are equal, then the high value of CC is received when P_VS (X, Y) =1 if X = Y

The exploration of the ranking algorithms like Gain Ratio, Information Gain and Chi-Square feature selection approaches are practiced in the proposed methodology are represented here.

2.2 Information gain feature selection method

Entropy is generally worked in the information theory measure, which symbolizes the clarity of the subjective collection of examples [6]. It is in the establishment of Gain Ratio, Information Gain, Symmetrical Uncertainty (SU). The entropy criterion is considered through the measure of the system’s randomness. The entropy of Y is depicted in the Equation (2.5): $H (Y) = \sum_{y \in Y} p (y) {log}_{2} (p (y))$ (2.5) where p (y|X) is the marginal probability density function for the random variable Y. If the experiential values of Y in the training dataset S are apportioned according to the values of a second feature X, and the entropy of Y with reference to the partitions prompted by X is less than the entropy of Y prior to partitioning, then there is an association between the features Y and X. The entropy of Y after observing X is in the Equation (2.6) then: $H (X | Y) = \sum_{x \in X} p (x) \sum_{y \in Y} p (y | x) {log}_{2} (p (y | x))$ (2.6) where p (y|x) is the conditional probability of y given x. The given entropy is the criterion of impurity in a training set S, we can state the measure which reflects further information about Y provided by X that epitomizes the quantity by which, the entropy of Y decreases. This measure is acknowledged as IG. It is given by the Equation (2.7) $IG = H (Y) - H (Y | X) = H (X) - H (X | Y)$ (2.7) IG [8, 9] is a symmetrical measure and it is given by Equation (2.7). The information gained about Y after detecting X is equal to the information gained about X after observing Y. A weakness of the IG criterion is that it is predisposed in approval of features with further values even when they are not more informative.

2.3 Gain ratio feature selection method

The Gain Ratio [7] is the non-symmetrical measure that is presented to pay back on the bias of the Information Gain (IG) [8]. GR is given by Equation (2.8) $GR = \frac{InformationGain (IG))}{H (X)}$ (2.8) Information Gain (IG) is a symmetrical measure. $IG = H (Y) - H (Y | X) = H (X) - H (X | Y) (2.9)$ (2.9) The information gained about Y after observing X is alike to the information gained about X after observing Y in the Equation (2.9). There, a weakness of the IG criterion is that it is biased in favor of features with more values even when they are not more informative. As in the above Equation (2.9) presents, when the variable Y has to be predicted, then regularize the IG by distributing the entropy of X, and vice versa. Owing to this normalization, the GR values constantly fall in the range [0, 1]. A value of GR = 1 specifies that the knowledge of X totally forecasts Y, and GR = 0 means that there is no relation between Y and X. In opposition to IG, the GR favor variables with lesser values.

2.4 Chi-square feature selection method

Feature Selection via chi square χ² test [7] is another, regularly used technique. Chi-squared attribute evaluation assesses the value of a feature by calculating the value of the chi-squared statistic with reverence to the class. The preliminary hypothesis H₀ is the assumption that the two features are distinct, and it is tested by chi-squared formula in the equation (2.10): $χ^{2} = \sum_{i = 1}^{r} \sum_{j = 1}^{c} (\frac{O_{ij} - E ij}{E ij})^{2}$ (2.10) where O_ij is the observed frequency and E_ij is the expected (theoretical) frequency, proclaimed by the null hypothesis. The greater the value of χ², the greater the evidence against the hypothesis H₀. The following three Similarity Measures (SMs) are utilized with the proposed HRLR-VS feature selection method. The u^th and v^th columns of a dataset is given by the two vectors A and B. In the dataset, those columns are customarily known as the u^th and v^th features.

2.5 Euclidean distance

The major comparison measure calculates the resemblances among the u^th and v^th features is known as Inverse of Euclidean Distance (IED). The Equation (2.11) is represented as: $S 1_{uv} = \frac{1}{Euclidean (A, B)} = \frac{1}{(| | A - B | |_{2})}$ (2.11) In the above equation, the same length of A and B is the considered two vectors.

2.6 Pearson’s correlation coefficient

The PCC [9] calculation for the given u^th and v^th features are represented by the below given by the Equation (2.12) $S 1_{uv} = | \frac{\sum_{j = 1}^{m} (a_{j} - \bar{A}) (b_{j} - \bar{B})}{\sqrt{\sum_{j = 1}^{m} (a_{j} - \bar{A})^{2}} \sqrt{\sum_{j = 1}^{m} (b_{j} - \bar{B})^{2}}} |$ (2.12) where same size of two feature vectors A and B are considered, and a_j represents A’s element j_th, and vector’s element arithmetic mean is $\bar{A}$ . Similarly, b_j depicts the B’s element j_th, and vector’s element average is denoted by $\bar{B}$ .

2.7 Cosine similarity

The CS calculation among the features is given by the below Equation (2.13) $S 3_{uv} = \frac{\sum_{j = 1}^{m} (a_{j}) (b_{j})}{\sqrt{\sum_{j = 1}^{m} (a_{j})^{2}} \sqrt{\sum_{j = 1}^{m} (b_{j})^{2}}}$ (2.13) where same size of two feature vectors A and B are considered; also, the element j^th of A’s and B’s are represented by a_j and b_j.

2.8 Merit value calculation

Hall et.al [11] proposed the merit. The experts projected a strategy to find the redundancy among the features and relevancy among class labels and features are represented by the Equation (2.14): $merit \leftarrow \frac{iX \bar{FCRL}}{\sqrt{i + i (i - 1) \bar{FF ¯ RD}}}$ (2.14) In the above equation, the number of features is presented by k, and FCRL exploses the relevancy. Moreover, FFRD displays the redundancy. Using the Equation (2.12), the maximum merit value has obtained only when the redundant feature has eliminated and relevancy feature is extracted. Accordingly, in this merit, both the high relevancy and low redundancy are considered.

3 Related works

Ding, Chris, and Hanchuan Peng [12] introduced the Minimum Redundancy – Maximum Relevance feature selection framework for the accurate classification of phenotypes in the microarray datasets. This paper presented that through the filter feature selection approach the redundancy was reduced explicitly. Yu, Lei, and Huan Liu [13] proposed the Fast Correlation-Based Filter method for identifying the relevant attributes as well as the redundancy among the relevant attributes without pairwise correlation analysis Vijaya, J., E. Sivasankar, and S. Gayathri [14] introduced a hybrid model with ensemble techniques which are used to enhance the classification. The clustering techniques like Possibility Fuzzy C Means (PFCM), Possibility C Means, and Fuzzy C Means are used for clustering the customers into groups. The ensemble models like Random Subspace, Bagging and Boosting are utilized for building themodels.

Stripling, Eugen, et al [15] used a Genetic Algorithm in the training model that maximizes the Expected Maximum Profit Measure for Customer Churn (EMPC) was developed to obtain the most profitable churn model. The author demonstrated a classifier called ProfLogit, which is similar to the lasso-regularized logistic model.

Ahmed, Ammar AQ, and D. Maheswari [16] presented an ensemble stacking integrated uplifting-based schemes for predicting the churners in the telecom. This model developed by the high correlation levels. Óskarsdóttir, María, et al [17] suggested a similarity forest-based classification method for eliciting the call networks time series data for establishing the dynamic behavior of the customer. The proposed method with one-nearest neighbor performed better for the classification of time series.

De Caigny, Arno, Kristof Coussement, and Koen W. De Bock [18] introduced a new hybrid algorithm called Logit Leaf Model (LLM) for improving the classification of the customer churn data. The proposed algorithm compared with the random forests, decision trees, logistic model and logistic regression models.

Yu, Ruiyun, et al [19] proposed the algorithm called PBCCP which is based on the Particle Swarm Optimization and Back Propagation network. It is used for optimizing the thresholds and weights of the BP NN and to improve the accuracy of the customer churn prediction.

Jamalian, Elham, and Rahim Foukerdi [20] in this paper introduced a novel hybrid Data Mining method which composed of feature selection and classification for classifying the churn customers in telecommunication. The authors used Principle Component Analysis (PCA) for the feature selection process whereas C5.0 and LOLIMOT (Linear Tree Model) algorithms are utilized for the classification.

Faris, Hossam [21] suggested an intelligent model which combines the Feed forward Neural Network (FNN) and Particle Swarm Optimization for the prediction of churn customer in the telecommunication industry. In this paper, PSO utilized to optimize the weight and structure of the NN which simultaneously improve the prediction power.

Even if some of the earlier stated techniques exhibit advancements by forecast accuracy, these developments derived at the rate of intricacy and interpretability of the method. In contrast, the most preceding functions highlight on the forecast power of their methods, without generous adequate consideration to the issue of recognizing the most instructive variables that disturb the blend ofclients.

4 High relevancy low redundancy vague set (HRLR-VS) based feature selection method

The proposed HRLR-VS algorithm consists of three major classifications. Firstly, it has considered the features redundancy by engendering the VSs established on proportional measures. The subsequent portion processes its dependence between the class labels and features to feature selection methods. Finally, the process follows an appropriate subset of features by a Particle Swarm Optimization searching method. The HRLR-VS has three main parts: They are

By provoking the Ranking Vague Sets (R-VSs), the relation between the class labels and the features are considered.

By using the Similarity Vague Sets (S-VSs), the association between the features is taken into consideration.

Using PSO search method for finding the best subset of features by executing the proposed relevance and redundancy algorithms.

Through the PSO search method, S-VSs are created in every round. The step by step procedure for HRLR-VS is described in ensuing algorithm. As a result, in the first line of HRLR-VS is the empty subset for adding the features iteratively.

Fig.1

Proposed Framework for High Relevant and Low Redundant Vague Set (HRLR-VS) based Feature Selection.

Table 1

Terms and its description in the proposed DUPP-HRLR-VS feature selection algorithm

Term	Description
s	Dataset size: This variable represents the quantity of features in the original dataset
FR-VS	VSs which is created by ranking of feature selection methods
S-VS	The VS which is engendered by SM
FS	Feature set of the selected features
FCRL	The features and class labels relevancy is represented with this variable in the proposed algorithm. It is the s x 1vector which gives the IE of FR-VS as the relevancy ratio of every attributes to the class labels.
MM	It is an array and it is the variable represents the highest value
FML	It is an array, the list of a value that attains highest value
m	Used to counts the features starting 1 to s
mer_file	It is the array to store the merit values in each round.
num_arr	It is used to store the nominated attributes in each round.
t	It is used to counts the features from 1 to s
FFRD	It is the representation of attributes redundancy by features itself. It is also a s x 1 vector that discloses associations between the attributes
i	Number of attributes
mer	The merit represents the assessment value for FS
list	List is the directory of supreme mer_file
FS_fin	It is the concluding nominated attributes subset
VSE	Vague Set Element: It is an array that contains the membership values of attributes
canF	It is the variable contains the candidate feature that desires to be estimated
FS_temp	It is the variable which holds FS and canF for additional computations
PP	Possible pair of attributes in FS_temp
: S1u,v	It is the representation of Inverse of Euclidean Distance among attributes u and v
S2u,v	It is the representation of Pearson Correlation among attributes u and v
S3u,v	It is the representation of Cosine Similarity among attributes u and v

Proposed HRLR-VS Feature Selection Algorithm

Input: Telecommunication Churn Customer Dataset

Output: Nominated Feature Subset

Step 1: Start

Step 2: FS ← {}

Step 3: Calling the function1 FCRL for generating the R-VSs and calculating their information energies.

Step 4: Finding the feature with maximum value in FCRL and storing it in MM and finding its list and holding it in FML. [MM, FML] ← maxFCRL

Step 5: m ← 1.

Initializing the variable n

Step 6: FS ← FS ∪ FML. Assigning the feature which achieves maximum value in FCRL is added to FS.

Step 7: mer¯file (m)← MM ; Saving the value of the selected feature to mer¯ file.

Step 8: num¯arr {m} ← FS. Saving FS in the m^th of num ← arr

Step 9: While (m < s). This loop is used to generate s feature subset candidates

Step 9.1: forj ← 1tos. This loop finds the best feature in order to add the subset.

Step 9.2: Call the function2 called FFRD. This function is used to generate the S-VSs among FS and the j^th feature and calculate their information energies.

Step 9.3: Calculation of Merit $mer (j) \leftarrow \frac{iXFCRL}{\sqrt{i + i (i - 1)} FFRD}$

Step 9.4: endfor

Step 10: mer (FS)← ∞. The merit value for existed features in SF considered as a large negative value to avoid selecting redundant features.

Step 11: [MM, FML] ← max (mer). Finding the feature with maximum value in merit and storing it in MM and finding its index and holding it inFML.

Step 12: FS ← FS ∪ {FML }. Adding the above features to the feature¯subset

Step 13: m ← m + 1. Increment the value of m

Step 14: num¯arr {m } ← FS. Saving the FS in the m^th row of num¯arr

Step 15: mer¯file (m) ← MM. Saving the correspond value to the selected feature to mer¯file.

Step 16: endwhile

Step 17: list ← max (mer¯file). Finding the best features subset that obtains best merit.

Step 18: FS¯fin ← num¯arr (list). Retrieving the corresponding features subset from num¯arr.

Step 19: Returns Features¯subset

Step 20: End Then in the subsequent line of the proposed HRLR-VS feature selection algorithm, the function1 FCRL is known to engender R-VSs and the IE which represents the relevancy.

Function 1: FCRL - The Pseudo-code of calculating the FCRL (Generating R-VSs and Calculating the Information Energies of R-VSs)

Suppose a dtaset with three attributes like A1, A2, and A3, is assumed. The computation for generating R-VSs by: $\begin{matrix} \overset{´}{R} - {VS}_{n} \\ = {< A_{n}, h_{r_{n}} (A_{n}) > | A_{n} \in A; n = 1, 2, . . ., s} \end{matrix}$ where R-VSs is the n^th VS computed by the n^th feature ranking score. A_n specifies the n^th attribute and A contains all feature A = {A₁, A₂,. . . , A_n,. . . , A_s }. h_{r
_n} (A_n) = {IG (A_n) , GR (A_n) , CS (A_n) } is a set of VSE. IG (A_n) , GR (A_n) , CS (A_n) is the n^th attribute value by IG, GR and CS methods. The following equation gives the computation for IE of R-VS_n. ${IE}_{VS} (R - {VS}_{n}) = \frac{1}{3} \sum_{k = 1}^{3} h_{R - {VS}_{n} σ (k)}^{2} A (n)$ $= \frac{1}{3} (IG (A_{n})^{2} + GR (A_{n})^{2} + CS (A_{n})^{2})$ The value of IE_VS (R - VS_n) substitutes the n^th element of FCRL vector. $FCRL (n) \leftarrow {IE}_{VS} (R - {VS}_{n})$

Input: Telecommunication Churn Customer Dataset

Output: FCRL

Step 1: for n ← s

Step 2: h_{R-VS_n} ← {IG (n) , GR (n) , CS (n) }. Calculating the information Gain (IG), Gain Ratio (GR) and Chi-Square (CS) scores for n^th features and assigning them as Vague Set Element (VSE) of R-VSs.

Step 3: $FCRL (n) \leftarrow \frac{1}{3} (IG (A_{n})^{2} + GR (A_{n})^{2} + CS (A_{n})^{2})$ . Calculating the information energies of above VS and saving its value in FCRL.

Step 4: endfor

Step 5: Return FCRL

Step 6: End

After engendering the FCRL, the selection of attribute with high FCRL takes place. This key attribute known as FML and MM represents its merit value. FML is taken to the FS and for making the concluding decision, mer¯arr stores the MM. MM with high value is stored in num¯arr is measured with the intention of keep the FS in every action. By a merit, the best attribute hasnominated.

Function2: FFRD: The pseudo-code for calculating the FFRD (generating S-VSs and calculatin the Information Energies of R-VSs)

For computing the FFRD, produce a candidate attribute (c^th attribute as canF) and S-VSs between attributes in FS. And to augment the canF to FS and FS¯temp is used to hold these attributes. Formerly, it creates all the possible mixtures of the current features in FS¯temp. The IE of all attributes are computed by IED, PCC and CS for generating the S-VSs. Finally, this function gives FFRD that contains the attributes relationship.

Input: Telecommunication Churn Customer Dataset

Output: FS and a candidate feature (canF)

Step 1: FS¯temp ← FS ∪ canF. Adding the candidate feature canF to FS.

Step 2: PP ← FS¯temp. Generate all possible pairs combination of canF.

Step 3: Initialize cnt ← 1

Step 4: for each pair, pair(u,v) in PP

Step 5: Calculating the IED (S1_u,v) , PCC (S2_u,v) , andCS (S3_u,v) measure as a Vague Set element of S-VSs. $h_{S - {VS}_{uv}} (a_{uv}) \leftarrow {S 1_{uv}, S 2_{uv}, S 3_{uv}}$ Step 6: Calculating the information energies of above VS $\begin{matrix} {RD}_{FF (cnt)} \leftarrow \frac{1}{3} (S 1 (u, v)^{2}) \\ + (S 2 (u, v)^{2}) + (S 3 (u, v)^{2}) \end{matrix}$

Step 7: cnt ← cnt + 1. Increment cnt

Step 8: end for

Step 9: Return D

Step 10: end

The redundancy between attributes are given by RDFF. Consider the FS = {1, 2} by the function 2, then the computation of S-VSs among 3^rd attribute and FS take place. The following classification is calculated by the function 2. The three S-VSs are generated by subsequent step. Therefore, A is considering by: A = {a₁₂, a₁₃, a₂₃ } and S-VSs are considered are: $S - {VS}_{uv} = {< a_{uv}, h_{S_{uv}} (a_{uv}) > | a_{uv} \in A}$ $h_{S - {VS}_{uv}} = {S 1_{uv}, S 2_{uv}, S 3_{uv}}$ where A indicates an synthetic creation of disclosure with the attribute a_uv is demarcated among the attributes u and v for signifying the relationship of redundancy. S - VS_uv specifies the VS that is produced based on SM among the u^th and u^th attributes, and h_{S-VS_uv} = {S1_uv, S2_uv, S3_uv } stands for the set of VSE. The h_{S-VS_uv} element S1_uv, S2_uv, and S3_uv gives the IED, PCC and CS among the u^th and v^th attributes, correspondingly. S - VS_uv, their IEs are weighed. The following equation is used for the computation of IE of S - VS_uv ${IE}_{VS} (S_{uv}) = \frac{1}{3} \sum_{k = 1}^{3} h_{S - {VS}_{uv σ (k)}}^{2} (a_{uv}^{j})$ $= \frac{1}{3} ((S 1_{uv}^{j})^{2} + (S 2_{uv}^{j})^{2} + (S 3_{uv}^{j})^{2})$ The value of IE_VS (S - VS_uv) substitutes the cnt^th element of the RDFF vector. ${RD}_{CF (cnt)} \leftarrow {IE}_{VS} (S - {VS}_{uv})$ The above function 2 is repetitive until the calculation of all pairs of P¯pairs. And in final, it gives a RDFF vector. After computing the RDFF, the function calculates its merit value of the candidate feature (j^thfeature) and FS by using merit equation.

4.1 Particle swarm optimization for searching optimal feature

Particle Swarm Optimization (PSO) has investigated on the basis of social behavior connected with bird’s accumulating for the optimization problem. A social behavior model of organisms that cooperate and live within big crowds is the impetus for PSO. The PSO is handier to put into accomplishment than Genetic Algorithm. It is for the motive that PSO doesn’t have an edge or mutation operators and flow of particles has effectively by using velocity function. In PSO, each particle transforms its flying memory and its partner’s flying inclusion following in mind the top goal of flying in the search space with velocity.

5 Results and discussion

5.1 Dataset description

The dataset is choosen from the famous dataset repository Kaggle.com. It is the dataset composed of churn and non-churn customers data of hte telecommunication industry. But the name of the company has not mentioned in this dataset. The subsequent Table 2 depicts the description about the dataset. This dataset is poised of 21 features [20]. It is the combination of churner and non-churners customer details. Their call rates, Message rates, International call rates etc are included in this dataset.

Table 2
Description of the Dataset

Feature Number Feature Name Description of the Feature

1 Account Length This holds the account number of the customer

2 VMail Message (Vmail msg) Number of messages to the Voice Mail number

3 Day Minutes (daymins) Holds the total day minutes of the customer

4 Evening Minutes (evemins) Holds the total evening minutes of the customer

5 Night Minutes (nightmins) Holds the total night minutes of the customer

6 International Minutes (intl mins) Holds the total international minutes of the customer

7 Customer Service Calls (cust serv) Total number of customer service calls

8 International Plan (intl plan) 1-Yes, 0-No

9 Vmail Plan (vmail plan) 1-Yes, 0-No

10 Day Calls Holds the total calls for that day by the customer

11 Day Charge Total Charge for that day

12 Evening Calls Total calls made in the evening

13 Evening Charge Total evening call charge in the evening

14 Night Calls Total calls made in the night

15 Night Charge Total night charge

16 International Calls Total international call

17 International Charge Charge made for the international calls

18 State Customer belonging to the state

19 Area code Area code of the customer

20 Phone Number Phone number of the customer

21 Churn 1-Yes, 0-No

Feature Number	Feature Name	Description of the Feature
1	Account Length	This holds the account number of the customer
2	VMail Message (Vmail msg)	Number of messages to the Voice Mail number
3	Day Minutes (daymins)	Holds the total day minutes of the customer
4	Evening Minutes (evemins)	Holds the total evening minutes of the customer
5	Night Minutes (nightmins)	Holds the total night minutes of the customer
6	International Minutes (intl mins)	Holds the total international minutes of the customer
7	Customer Service Calls (cust serv)	Total number of customer service calls
8	International Plan (intl plan)	1-Yes, 0-No
9	Vmail Plan (vmail plan)	1-Yes, 0-No
10	Day Calls	Holds the total calls for that day by the customer
11	Day Charge	Total Charge for that day
12	Evening Calls	Total calls made in the evening
13	Evening Charge	Total evening call charge in the evening
14	Night Calls	Total calls made in the night
15	Night Charge	Total night charge
16	International Calls	Total international call
17	International Charge	Charge made for the international calls
18	State	Customer belonging to the state
19	Area code	Area code of the customer
20	Phone Number	Phone number of the customer
21	Churn	1-Yes, 0-No

5.2 Performance Metrics

Our proposed HRLR-VS based feature selection was carried out using Python 3.0 and the Classification techniques are implemented on MATLAB R2018b. Following Table 3 depicts the performance metrics. These metrics has considered for evaluating the existing techniques with proposed technique.

Table 3
Performance Metrics for evaluation of proposed technique

Metrics Equation

Accuracy $\frac{TP + TN}{TP + FN + TN + FP}$

True Positive Rate (TPR) $\frac{TP}{TP + FN}$

False Positive Rate (FPR)

$\frac{FP}{FP + TN}$

Precision $\frac{TP}{TP + FP}$

Recall $\frac{TP}{TP + FN}$

F-Measure $2 . \frac{Precision . Recall}{Precision + Recall}$

Mean Absolute Error (MAE) $\frac{1}{N} \sum_{i = 1}^{N} | \hat{θ_{i}} - θ_{i} |$

Root Mean Squared Error (RMSE) $\sqrt{\frac{1}{N} \sum_{i = 1}^{N} (\hat{θ_{i}} - θ_{i})^{2}}$

Relative Absolute Error (RAE) $\frac{\sum_{i = 1}^{N} | \hat{θ_{i}} - θ_{i} |}{\sum_{i = 1}^{N} | \bar{θ_{i}} - θ_{i} |}$

Root Relative Squared Error (RRSE) $\sqrt{\frac{\sum_{i = 1}^{N} (\hat{θ_{i}} - θ_{i})^{2}}{\sum_{i = 1}^{N} (\bar{θ_{i}} - θ_{i})^{2}}}$

Metrics	Equation
Accuracy	$\frac{TP + TN}{TP + FN + TN + FP}$
True Positive Rate (TPR)	$\frac{TP}{TP + FN}$
False	Positive Rate (FPR)
$\frac{FP}{FP + TN}$
Precision	$\frac{TP}{TP + FP}$
Recall	$\frac{TP}{TP + FN}$
F-Measure	$2 . \frac{Precision . Recall}{Precision + Recall}$
Mean Absolute Error (MAE)	$\frac{1}{N} \sum_{i = 1}^{N} \| \hat{θ_{i}} - θ_{i} \|$
Root Mean Squared Error (RMSE)	$\sqrt{\frac{1}{N} \sum_{i = 1}^{N} (\hat{θ_{i}} - θ_{i})^{2}}$
Relative Absolute Error (RAE)	$\frac{\sum_{i = 1}^{N} \| \hat{θ_{i}} - θ_{i} \|}{\sum_{i = 1}^{N} \| \bar{θ_{i}} - θ_{i} \|}$
Root Relative Squared Error (RRSE)	$\sqrt{\frac{\sum_{i = 1}^{N} (\hat{θ_{i}} - θ_{i})^{2}}{\sum_{i = 1}^{N} (\bar{θ_{i}} - θ_{i})^{2}}}$

From the Table 3,

True Positive (TP) = the number of cases correctly identified as churners

True Negative (TN) = the number of cases correctly identified as Non-churners

False Positive (FS) = the number of cases incorrectly identified as churners

False Negative (FN) = the number of cases incorrectly identified as Non-churners

θ = True value of feature and $\hat{θ}$ = value estimated by the algorithm.

The correlation tells that how much θ and $\hat{θ}$ are related. It gives the value between 1 and -1, where 0 means no relation, 1 is very strong relation and -1 is an inverse linear relation. $\bar{θ}$ is the mean value of θ.

Table 4 depicts the number of features obtained by feature selection methods like Information Gain, Gain Ratio, Chi-Square and proposed HRLR-VS feature selection method. From Table 4, it is clear that the proposed method generates a smaller number of strongly relevant and low redundant features than the existing methods like IG, GR, and CS. IG gives 18 features, GR produces 13 features, CS generates 14 features whereas the proposed method gives only 11 features. The features from the proposed method are evaluated by using the metrics in Table 3. The evaluation has done in three classification methods by existing feature selection methods and the proposed method. The classification methods like Artificial Neural Network, Naïve Bayes and Support Vector Machine are utilized in this research work for evaluation of the proposed method and existing feature selection for the classification of churn customers.

Table 4

Number of features obtained by existing feature selection methods like Information Gain, Gain Ratio, Chi-Square and proposed method

Sl.No	Information Gain	Gain Ratio	Chi-Square	Proposed Method
1	Night mins	Night mins	Day charge	Night mins
2	Day charge	Day charge	Night mins	Day charge
3	Day mins	Eve mins	Day mins	Eve mins
4	Eve mins	Day mins	Eve mins	Day mins
5	Eve charge	Eve charge	Eve charge	Eve charge
6	Night Charge	Intl. Charge	Intl. charge	Intl. charge
7	Intl. charge	Intl. mins	Intl. mins	Intl. mins
8	Intl.mins	Account length	Night calls	Night calls
9	Custservcalls	Night calls	Eve calls	Eve calls
10	Account Length	Eve calls	Day calls	Day calls
11	Vmail message	Day calls	Custservcalls	Vmail plan
12	Intl plan	Vmail plan	State
13	Eve calls	Area code	Vmail plan
14	Night calls		areacode
15	Day calls
16	State
17	Vmail plan
18	Area code

Table 5 depicts the performance analysis on the accuracy of the existing and proposed feature selection method using ANN, NB, and SVM classification methods. From the Table 5, SVM gives maximum accuracy for original dataset, IG processed dataset and proposed feature selection processed dataset gives maximum accuracy when using Artificial Neural Network as the classifier, whereas GR and CS processed datasets attains maximum accuracy using SVM classification. Figure 2 depicts the graphical representation of the accuracy of the proposed feature selection method and existing methods by using classification methods like ANN, NB, and SVM.

Fig.2

Graphical representation of the accuracy of the proposed HRLR-VS method with existing feature selection methods using ANN, NB, and SVM.

Table 5

Performance analysis on Accuracy

Feature Selection	Classification Techniques
Method	ANN	NB	SVM
Original Dataset	51.667%	49.333%	73.667%
Information Gain	73.667%	50.333%	69.667%
Gain Ratio	85.333%	51.333%	86.667%
Chi-Square	73.333%	55.333%	87.333%
HRLR-VS	92.3667%	70.566%	88.233%

Table 6 depicts the performance analysis on the Kappa Statistic of the proposed HRLR-VS method and existing feature selection methods using ANN, NB, and SVM classification methods. From the Table 6, ANN gives the maximum value of Kappa Statistics for an original dataset and proposed HRLR-VS method processed a dataset, GR and CS processed datasets gives maximum Kappa statistic value using NB and SVM gives the maximum Kappa Statistic value for IG processed dataset. Figure 3 depicts the graphical representation of the Kappa Statistic of the proposed feature selection method and existing methods by using classification methods like ANN, NB, and SVM.

Fig.3

Graphical representation of the Kappa Statistic value of the proposed HRLR-VS method with existing feature selection methods using ANN, NB and SVM.

Table 6

Performance analysis on Kappa Statistic of the proposed HRLR-VS and existing feature selection methods using ANN, NB and SVM

Feature Selection	Classification Techniques
Method	ANN	NB	SVM
Original Dataset	0.1465	0.0397	0
Information Gain	0	0.0452	0.0471
Gain Ratio	0.0284	0.0315	0.0188
Chi-Square	0.0066	0.0339	0.0321
HRLR-VS	0.712	0.624	0.601

Table 7 depicts the performance analysis on True Positive Rate (TPR) of the proposed HRLR-VS method and existing feature selection methods using ANN, NB, and SVM classification methods. From the Table 7, ANN gives the maximum value of True Positive Rate (TPR) for IG processed dataset and proposed HRLR-VS method processed a dataset, Original dataset, GR and CS processed datasets gives maximum TPR value using SVM. Figure 4 depicts the graphical representation of the TPR value of the proposed feature selection method and existing methods by using classification methods like ANN, NB, and SVM.

Fig.4

Graphical representation of the True Positive Rate (TPR) value of the proposed HRLR-VS method with existing feature selection methods using ANN, NB and SVM.

Table 7

Performance analysis on True Positive Rate (Recall) of the proposed HRLR-VS and existing feature selection methods using ANN, NB and SVM

Feature Selection	Classification Techniques
Method	ANN	NB	SVM
Original Dataset	0.517	0.493	0.737
Information Gain	0.737	0.5	0.697
Gain Ratio	0.853	0.513	0.867
Chi-Square	0.733	0.553	0.873
HRLR-VS	0.892	0.712	0.881

Table 8 depicts the performance analysis on False Positive Rate (RPR) of the proposed HRLR-VSmethod and existing feature selection methods using ANN, NB, and SVM classification methods. From the Table 8, ANN gives minimum value of False Positive Rate (FPR) for IG, GR, CS processed datasets and proposed HRLR-VSmethod processed a dataset, original dataset gives least FPR value using NB. Figure 5 depicts the graphical representation of the FPR value of the proposed feature selection method and existing methods by using classification methods like ANN, NB, and SVM.

Fig.5

Graphical representation of the False Positive Rate (FPR) value of the proposed HRLR-VS method with existing feature selection methods using ANN, NB and SVM.

Table 8

Performance analysis on False Positive Rate (FPR) of the proposed HRLR-VS and existing feature selection methods using ANN, NB and SVM

Feature Selection	Classification Techniques
Method	ANN	NB	SVM
Original Dataset	0.741	0.696	0.737
Information Gain	0.439	0.539	0.702
Gain Ratio	0.433	0.54	0.855
Chi-Square	0.534	0.581	0.854
HRLR-VS	0.112	0.421	0.582

Table 10 depicts the performance analysis on F-Measure of the proposed HRLR-VS method and existing feature selection methods using ANN, NB, and SVM classification methods. From Table 10, ANN gives the maximum value of F-Measure only for the proposed HRLR-VS method, whereas other datasets give maximum value when using SVM as the classifier. Figure 7 depicts the graphical representation of the F-Measure value of the proposed feature selection method and existing methods by using classification methods like ANN, NB, and SVM.

Fig.7

Graphical representation of the F-Measure value of the proposed HRLR-VS method with existing feature selection methods using ANN, NB and SVM.

Table 10

Performance analysis on F-Measure of the proposed HRLR-VS and existing feature selection methods using ANN, NB and SVM

Feature Selection	Classification Techniques
Method	ANN	NB	SVM
Original Dataset	0.502	0.492	0.640
Information Gain	0.640	0.560	0.649
Gain Ratio	0.821	0.625	0.828
Chi-Square	0.623	0.653	0.841
HRLR-VS	0.893	0.762	0.826

Table 12 presents the performance analysis on Root Mean Squared Error (RMSE) of the proposed HRLR-VS method and existing feature selection methods using ANN, NB and SVM classification methods. From Table 12, ANN gives the least RMSE value for IG, GR and proposed HRLR-VS method processed a dataset, original dataset gives least RMSE value when using NB as the classifier. The other processed dataset gives the least RMSE value using SVM. Figure 9 depicts the graphical representation of the Root Mean Squared Error (RMSE) value of the proposed feature selection method and existing methods by using classification methods like ANN, NB, and SVM.

Fig.9

Graphical representation of the Root Mean Squared Error (RMSE) value of the proposed HRLR-VS method with existing feature selection methods using ANN, NB and SVM.

Table 12

Performance analysis on Root Mean Squared Error (RMSE) of the proposed HRLR-VS and existing feature selection methods using ANN, NB and SVM

Feature Selection	Classification Techniques
Method	ANN	NB	SVM
Original Dataset	0.6892	0.6301	0.6845
Information Gain	0.5132	0.6	0.6508
Gain Ratio	0.383	0.6032	0.5651
Chi-Square	0.5164	0.544	0.4559
HRLR-VS	0.1641	0.4245	0.3614

Table 9 depicts the performance analysis on Precision of the proposed HRLR-VS method and existing feature selection methods using ANN, NB, and SVM classification methods. From Table 9, ANN gives the maximum value of precision for original dataset, CS and Proposed HRLR-VS processed datasets and IG and GR processed datasets gives the least Precision value using NB. Figure 6 depicts the graphical representation of the Precision value of the proposed feature selection method and existing methods by using classification methods like ANN, NB, and SVM.

Fig.6

Graphical representation of the Precision value of the proposed HRLR-VS method with existing feature selection methods using ANN, NB and SVM.

Table 9

Performance analysis on Precision of the proposed HRLR-VS and existing feature selection methods using ANN, NB and SVM

Feature Selection	Classification Techniques
Method	ANN	NB	SVM
Original Dataset	0.543	0.493	0.488
Information Gain	0.608	0.637	0.543
Gain Ratio	0.794	0.8	0.793
Chi-Square	0.812	0.798	0.542
HRLR-VS	0.896	0.821	0.833

Table 11 presents the performance analysis on Mean Absolute Error (MAE) of the proposed HRLR-VS method and existing feature selection methods using ANN, NB, and SVM classification methods. From Table 11, ANN gives the least MAE value for the original dataset and proposed HRLR-VS method processed a dataset, whereas other feature selection processed datasets give maximum value when using SVM as the classifier. Figure 8 depicts the graphical representation of the Mean Absolute Error (MAE) value of the proposed feature selection method and existing methods by using classification methods like ANN, NB, and SVM.

Fig.8

Graphical representation of the Mean Absolute Error (MAE) value of the proposed HRLR-VS method with existing feature selection methods using ANN, NB and SVM.

Table 11

Performance analysis on Mean Absolute Error (MAE) of the proposed HRLR-VS and existing feature selection methods using ANN, NB and SVM

Feature Selection	Classification Techniques
Method	ANN	NB	SVM
Original Dataset	0.3358	0.5201	0.6692
Information Gain	0.2633	0.5044	0.2033
Gain Ratio	0.1467	0.4893	0.1333
Chi-Square	0.2667	0.4459	0.1267
HRLR-VS	0.0536	0.1357	0.0891

Table 13 presents the performance analysis on Relative Absolute Error (RAE) of the proposed HRLR-VS method and existing feature selection methods using ANN, NB, and SVM classification methods. From Table 13, ANN gives the least RAE value for original IG and proposed HRLR-VS method processed a dataset, whereas GR and CS processed dataset give the least RAE value when using SVM as the classifier. Figure 10 depicts the graphical representation of the Root Mean Squared Error (RMSE) value of the proposed feature selection method and existing methods by using classification methods like ANN, NB, and SVM.

Fig.10

Graphical representation of the Relative Absolute Error (RAE) value of the proposed HRLR-VS method with existing feature selection methods using ANN, NB and SVM.

Table 13

Performance analysis on Relative Absolute Error (RAE) of the proposed HRLR-VS and existing feature selection methods using ANN, NB and SVM

Feature Selection	Classification Techniques
Method	ANN	NB	SVM
Original Dataset	96.619	238.1586	186.7589
Information Gain	67.7257	129.8562	78.0131
Gain Ratio	67.1605	224.0694	61.055
Chi-Square	68.583	204.1779	58.0022
HRLR-VS	51.811	102.8178	57.2112

Table 14 presents the performance analysis on Root Relative Squared Error (RRSE) of the proposed HRLR-VS method and existing feature selection methods using ANN, NB, and SVM classification methods. From Table 14, ANN gives the least RRSE value for IG and proposed HRLR-VS method processed a dataset, whereas original, GR and CS processed dataset gives the least RAE value when using SVM as the classifier. Figure 11 depicts the graphical representation of the Root Mean Squared Error (RMSE) value of the proposed feature selection method and existing methods by using classification methods like ANN, NB, and SVM.

Fig.11

Graphical representation of the Root Relative Squared Error (RRSE) value of the proposed HRLR-VS method with existing feature selection methods using ANN, NB and SVM.

Table 14

Performance analysis on Root Relative Squared Error (RRSE) of the proposed HRLR-VS and existing feature selection methods using ANN, NB and SVM

Feature Selection	Classification Techniques
Method	ANN	NB	SVM
Original Dataset	145.1707	191.5635	141.5383
Information Gain	116.5024	136.2211	125.0381
Gain Ratio	116.4351	183.3864	111.0165
Chi-Square	112.2375	165.4063	87.2055
HRLR-VS	67.1468	80.7182	75.1866

5.3 Comparison of Proposed HRLR-VS with Existing Literature

The two commonly used feature selection approach like Minimum Redundancy Maximum Relevancy (mRMR) [12] and Fast Correlation-Based Filter (FCBF) [13] Method are considered for evaluating the proposed HRLR-VS feature selection method for telecommunication dataset. Table 15 depicts the number of features obtained by proposed HRLR-VS method and existing literature works. Table 16 represents the performance analysis of the proposed HRLR-VS method with mRMR and FCBF approach. For evaluating the proposed HRLR-VS with existing literature, Artificial Neural Network classification technique has used in the Table 16. From the Table 16, it is clear that the proposed HRLR-VS gives more accuracy, Kappa Statistic, TPR, Precision, Recall and F-Measure than mRMR and FCBF approaches. The error rates like MAE, RMSE, RRSE, RAE also reduced for proposed HRLR-VS method. Table 17 depicts the total execution time (in seconds) for the proposed HRLR-VS, IG, GR, CS, mRMR and FCBF methods. From the Table 17, proposed HRLR-VS method took less time for executing the algorithm than the existing methods

Table 15
Number of features obtained by proposed HRLR-VS method and existing literature (mRMR & FCBF)

Techniques Number of Features Obtained

Proposed HRLR-VS Method 11

mRMR 18

FCBF 19

Techniques	Number of Features Obtained
Proposed HRLR-VS Method	11
mRMR	18
FCBF	19

Table 16

Performance analysis of the Proposed HRLR-VS and existing Literature approaches (mRMR and FCBF) using ANN classification method

Performance	Proposed and Existing Literature
Metrics	HRLR-VS	mRMR	FCBF
Accuracy	92.37%	87.98%	87.98%
Kappa Statistic	0.712	0.452	0.562
TPR	0.892	0.741	0.785
FPR	0.112	0.351	0.342
Precision	0.896	0.751	0.792
Recall	0.892	0.741	0.785
F-Measure	0.893	0.739	0.786
MAE	0.0536	0.421	0.453
RMSE	0.1641	0.8652	0.8321
RAE	51.811	78.961	89.652
RRSE	67.1468	114.523	107.156

Table 17

Total Execution time in seconds for Existing and Proposed Feature selection methods

Feature Selection Methods	Total Execution Time in Seconds
Information Gain	125
Gain Ratio	119
Chi-Square	129
mRMR	108
FCBF	98
Proposed HRLR-VS	67

6 Conclusion

There are more number of problems currently exists with encountering many features. Customers and usage data generated in telecommunication industry come across such problems. A number of feature selection techniques have been assessed to determine their efficiency for decreasing the number of dimensions in a dataset and for enhancing the precision of classifier which uses these features.

In this paper, choosing the least feature subset having low redundancy and high relevancy by blending the similarity measures and filter feature selection method with the Particle Swarm search method are described. A new hybrid algorithm and methodology are proposed in this work and an exhaustive experiment is trialed for determining the effectiveness of the proposed techniques.

Threshold is the problem that is mainly suffered by the ranking of feature selection methods. The parameters and threshold are not essential for processing data using proposed HRLR-VS. Experimental results are explained on the performance of proposed algorithm for choosing the least feature subset with more Accuracy. The performance measures such as Kappa Statistic, Precision, True Positive Rate and F-Measure, and lower error rates like False Positive Rate, MAE, RMSE, RRSE and RAE values used for evaluating the proposed method. From the results, it is concluded that the proposed HRLR-VS method performs better than the existing methods like IG, GR, and CS when using Artificial Neural Network as the classifier.

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High relevancy low redundancy vague set based feature selection method for telecom dataset

Abstract

Keywords

1 Introduction

2 Preliminaries of vague set, feature selection and similarity measure

2.1 Vague set

4 High relevancy low redundancy vague set (HRLR-VS) based feature selection method

5 Results and discussion

5.1 Dataset description

Table 15 Number of features obtained by proposed HRLR-VS method and existing literature (mRMR & FCBF) Techniques Number of Features Obtained Proposed HRLR-VS Method 11 mRMR 18 FCBF 19

References

Table 15
Number of features obtained by proposed HRLR-VS method and existing literature (mRMR & FCBF)

Techniques Number of Features Obtained

Proposed HRLR-VS Method 11

mRMR 18

FCBF 19