## 4 Proposed Work  
In this paper, we have proposed a FS technique based on HSA, which we have named as supervised filter harmony search algorithm (SFHSA). SFHSA uses cosine similarity and mRMR combined with PCC. HSA has proved to be an efficient technique [52; 53; 54; 55] for providing an optimal solution to real life problems, in terms of feasible computation time and usage of memory, as proposed by [PERSON] and [PERSON] in [53]. It simulates the procedure opted by the musicians to find out the finest tune by selecting  
Figure 4: Calculation of horizontal–vertical neighborhood local binary pattern (hvnLBP) feature descriptor where clockwise direction gives \((00100111)_{2}=(39)_{10}\) as the center pixel after evaluation. a particular combination of frequencies produced by sundry musical instruments. It optimizes an objective function by selecting an appropriate combination of solutions from existing set of solutions by employing random search. In [56], an improved version of HSA has been formulated which uses fine-tuning parameters of mathematical techniques to enhance the performance of HSA. Due to the efficient nature of HSA in finding the global optimum solution, it has been exploited in various works related to FS. The traditional approach of HSA involves adjustment of the pitch considering a parameter named Bandwidth (BW). In this phase of the algorithm, we have made a modification in adjustment of the pitch. In our case it was the adjustment of the features by replacing their values with the values of their cosine similar features subject to satisfaction of certain conditions rather than selecting adjacent features as in conventional way. The goodness of a subset was determined using mRMR. The proposed algorithm is a supervised filter method. As mentioned before, the proposed algorithm is used to optimize the features extracted for FER; the objective of SFHSA is to reduce the feature dimensions while maintaining or increasing the accuracy score. Prior to execution of the algorithm, each feature vector was divided into training and testing sets in the ratio of 2:1. The training set was then used to find the optimal feature subset. The algorithm used is provided in Algorithm 1. ```
1:Input: Original-feature set
2:Output: Reduced-feature subset
3:User defined parameters: HMS = 15, HMCR = 0.8 and PAR = 0.5
4:Determine the worst feature subset from HM
5:



The HMS determines the size of the harmony memory (HM), i.e., the number of feature subsets present in the HM. Throughout the process, HMCR was applied in order to decide whether the feature to be selected from a feature subset in the HM or not. Its value is in the range of \([0,1]\) and based on experiments we have initialized it to 0.8. The parameter PAR was used (upon satisfaction of condition) to select a feature randomly whose cosine similarity measure with the pre-selected feature is within the range \((-\varepsilon,\varepsilon)\), where \(\varepsilon\) is a randomly generated value of range \([-1,\ 1]\). Its value lies in the range \([0,\ 1]\) and we have fixed it to 0.5 on an experimental basis, in order to set the probability of PAR being satisfied equal to the probability of PAR not being satisfied. At the commencement of SFHSA, all the parameter values were initialized. The value of HMS was set to 15 in order to keep 15 feature subsets in HM and to have more diverse feature subsets for obtaining better results and the maximum number of iterations was set to 20. The initialization phase was followed by the random selection of feature subsets from the training set. In this phase, we have randomly created \(m\) feature subsets, where \(m=HMS\). The feature subsets were considered to have a dimension ranging from 80% to 90% of the dimension \(n\) of the actual feature set, which is to be reduced in the subsequent phases. These \(m\) feature subsets were used to populate the HM initially. To find the cosine similarity of the features, the each of the feature sets was normalized.