Study of Supply Vector Machine (SVM) for Emotion Recognition

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1 Study of Supply Vector Machine (SVM) for Emotion Recognition 1 Soma Bera, Shanthi Therese 2,Madhuri Gedam 3 1 Department of Computer Engineering, Shree L.R. Tiwari College of Engineering, Mira Road, Thane, India 2 Department of Information Technology, Thadomal Shahani Engineering College, Bandra, Mumbai, India 3 Department of Computer Engineering, Shree L.R. Tiwari College of Engineering, Mira Road, Thane, India Abstract This paper is mainly concerned with Speech Emotion Recognition. The main work is concerned with Supply Vector Machine (SVM) that allows training the desired data set from the databases. The Support Vector Machine (SVM) performs classification by finding the decision boundary also known as hyperplane that maximizes the margin between two different classes. The vectors that define the hyperplane are the support vectors. Keywords: Speech, Emotion Recognition, Linear SVM, Nonlinear SVM, hyperplane 1. INTRODUCTION Speech Emotional Recognition is identifying the emotional state of human being from his or her voice [12]. Speech is a complex signal consisting of information about the message, speaker, language and emotions. Emotions on the contrary are an individual mental state that arises spontaneously rather than through conscious effort. Speech may contain various kinds of emotions such as Happy, Sarcastic, Sad, Compassion, Anger, Surprise, Disgust, Fear, Neutral, etc. 2. SUPPLY VECTOR MACHINE CLASSIFICATION Supply Vector Machine (SVM) is a promising new method for the classification of both linear and nonlinear data [18]. SVM is a binary classifier. A binary classifier is the one that classifies exactly two different classes. It can be also used for classifying multiple classes. Multiclass SVM is the SVM that classifies more than two classes. Each feature is associated with its class label e.g. happy, sad, fear, angry, neutral, disgust, etc. The following figure 1 shows the process of SVM classification. The SVM classifier may separate the data elements linearly or nonlinearly depending upon the placements of the data elements within the dimensional space area as illustrated in figure 2. Figure 1 Block Diagram of Speech Emotion Recognition System using SVM Classification Figure 2 Examples illustrating linear and nonlinear classifications Algorithm 1. Generate an optimal hyperplane: generally, maximizing margin. 2. Apply the same for linearly inseparable problems. 3. Map data elements to higher dimensional space where it is easier to classify with linearly separable hyperplane. Volume 4, Issue 3, May June 2015 Page 91

2 2.1Linear Separability Suppose we have two features X1 and X2 and we want to classify all these elements (X1=green dots, X2= red dots). Figure 3 Graph showing support vectors with margin width So the objective of the SVM is to generate a hyperplane that distinguishes or classifies all training vectors in two different classes. The line or the boundary dividing both the classes is the hyperplane that classifies into two classes. To define an optimal decision boundary we need to maximize the width of the margin (w). The margin is defined to be the distance between the hyperplane and the closest elements from these hyperplanes. Figure 5 Maximizing margin An easy way to separate two groups of data element is with a linear straight line (1 dimension), flat plane (2 dimensions) or an N-dimensional hyperplane. However, there are possibilities where a nonlinear region can classify the groups more proficiently. SVM achieves this by using a kernel function (nonlinear) to map the data into a different space where a hyperplane (linear) cannot be used to do the separation. It means a linearly inseparable function is learned by a linear learning machine in a high dimensional feature space while the capacity of the system is controlled by a parameter that is independent of the dimensionality of the space. This is termed as kernel trick [17] which means the kernel function transform the data into a higher dimensional feature space so as to perform the task of linear separation. The main notion of SVM classification is to a convert the original input set to a high dimensional feature space by making use of kernel function [4]. Figure 6 Illustrating difference between nonlinear and linear hyperplane respectively Figure 4 Process of calculating margin width The beauty of SVM is that if the data is linearly separable, then in that case a unique global minimum value is generated. An ideal SVM analysis should generate a hyperplane that entirely classifies the support vectors into two non-overlapping classes [16]. However, exact separation may not be possible, thereby resulting in classifying the data incorrectly. In this situation, SVM encounters the hyperplane that maximizes the margin and minimizes the misclassifications. Consider the following simple example to understand the concept of SVM. Suppose we have 2 features namely X1 and X2 located on the X axis and Y axis respectively. We have, say for example, 2 set of elements. 1. Blue Dots 2. Red square We consider the Blue Dots to be the negative class and the Red square to be the positive class. The objective of the SVM classifier is to define an optimum boundary to differentiate both the classes. Volume 4, Issue 3, May June 2015 Page 92

3 Figure 11 Augmented Vector with 1 as a bias input Now, we need to find 3 parameters α 1, α 2 and α 3 based on the following 3 equation: Figure 7 Graph showing Blue (negative) and Red (positive) class The following figures demonstrates the possible hyper planes that could be plotted to classify these elements separately. α 1 S 1.S 1 + α 2 S 2.S 1 + α 3 S 3.S 1 = -1 (-ve class) α 1 S 1.S 2 + α 2 S 2.S 2 + α 3 S 3.S 2 = -1 (-ve class) α 1 S 1.S 3 + α 2 S 2.S 3 + α 3 S 3.S 3 = +1 (+ve class) Lets substitute the values in the above equation Figure 8 Illustrating one and two possible hyper planes resp Figure 9 Illustrating multiple possible hyperplanes resp Here, we select 3 support vectors to start with. They are s 1, s 2 and s 3. After simplification, we get: Figure 12 6α 1 + 4α 2 + 9α 3 = -1 4α 1 + 6α 2 + 9α 3 = -1 9α 1 + 9α α 3 = +1 Figure 10 Graph illustrating the selected Support Vectors for classification Here, we will use vector augmented with 1 as a bias input, and for clarity we will differentiate these with an overtilde. Simplifying all the above equations, we get: α 1 = α 2 = and α 3 = 3.5 The hyper plane that differentiates the positive class from the negative class is given by: Volume 4, Issue 3, May June 2015 Page 93

4 w isi Substituting the values we get: i number of support vectors. The following figure illustrates data items that are non linearly separable. Figure 15 Example of nonlinear separability Our vectors are augmented with a bias. Hence we can equate the entry in as the hyper plane with an offset b. Therefore, the separating hyper plane equation is given by: Y = wx + b with w= 1 and offset b = -3 0 The nonlinear SVM may classify the multiple classes by using any of the suitable techniques such as One V/s All, One v/s One, All v/s All, Polynomial kernel (homogenous and inhomogeneous), Lagranges multiplier, Kernel function, Gaussian Radial Basis Function, Hyperbolic tangent. Consider the following scenario to understand the concept of nonlinear separability: This is the expected decision surface area of the Linear SVM. Figure 13 Plotted hyperplane Figure 16 Illustrating nonlinear separability In the above figure, it is clearly seen that both the classes that is, the blue class and the red class, are not linearly separable. Blue class vectors are: , 1, -1, -1 Red class vectors are: Figure 14 Offset location for plotting hyperplane 2.2 Nonlinear Separability Nonlinear separability stems from the fact that the training data can be rarely separated using a hyperplane thereby resulting in misclassification of some of the data samples. In the case when linear method fails, project the data non linearly into a higher dimensional space.nonlinearly separated data is handled by the nonlinear SVM but is not that efficient as the linear classifier. Its complexity is multiplied with the , 2, 0, -2 Next, the aim is to find a nonlinear function which can transform this into new feature space where a separating hyperplane can be found. Considering the following mapping function: Figure 17 Mapping (plotting) function Volume 4, Issue 3, May June 2015 Page 94

5 From the above equation, it is very clear that the blue class falls into the second condition and the red class lies into the first condition. Now let us transform the blue class and the red class vectors using the nonlinear mapping function. Blue class vectors are: , 1, -1, -1 But for the red class vectors are: , 2, 0, -2 So, the transformation features formed are as follows: Figure 20 Nonlinearly separable elements transformed to higher dimensional feature space So now, our problem has been transformed into linear SVM. Now our task is to find suitable linear support vectors to classify these two classes using linear separability which is very similar to the one that we illustrated above in the linear separability method. Hence the new support vectors turn out to be: Figure 18 Transformation features into higher dimensions Figure 21 New Support Vectors at higher dimensional feature space So, the new coordinates are: Figure 22 The entire problem will be solved very similar to that of a linear separability. After calculating all the simultaneous equation, the values that we get are: Figure 23 Figure 19 And an offset b= /0.1243= So, the new hyperplane that is plotted is: Volume 4, Issue 3, May June 2015 Page 95

6 Figure 24 Expected Decision surface of Nonlinear SVM This is the expected decision surface of non Linear SVM. 3. OPTIMIZATION OF SVM MODEL In order to optimize the problem, the distance between the hyperplane and the support vectors should be maximized [13] [14]. h (x) = 1/1+e - Tx Example: -(y log h (x) + (1-y) log(1- h (x))) = -y log 1/1+e - Tx - (1-y) log(1-1/1+e - Tx ) If y=1, then h (x) 1, T x>>0 Figure 25 Optimized SVM: When y=1 If y=0, then h (x) 0, T x<<0 4. COMPARATIVE STUDY AND ANALYSIS This section describes the various related work done in the field of emotion recognition. It briefly surveys about different techniques used for feature extraction of the audio speech signal and the various different classifiers used for classification of emotions. The above Table I illustrates the application of various classifier for Speech Emotion Recognition. Annexure I illustrate the table showing the year and the author of the particular papers, the different databases that have been used for testing and training. It also states the number of emotions (happy, sad, anger, disgust, boredom, fear, neutral) that have been classified. The table illustrates the accuracy level that have been reached in the research work so far over years including their corresponding drawbacks in their designed systems. 5. ANNEXURE I The different feature extraction method techniques used are Mel Frequency Cepstrum Coefficient (MFCC), Mel Energy Spectrum Dynamic Coefficients (MEDC), Linear Predictive Cepstral Coefficients (LPCC), Spectral features, Modulation Spectral features (MSF), Linear Predictive Coding (LPC), etc. The various classifiers used are Supply Vector Machine (SVM), Gaussian Mixture Model (GMM), Granular SVM (GSVM), SVM Radial Basis Function (RBF), Hidden Markov Model (HMM), Back Propogation Neural Network (BPNN), k-nn, etc. 6. CONCLUSION In this paper, a survey of current research work in Speech Emotion Recognition system and detail description about the various concepts included in SVM has been discussed. This paper describes briefly about what linear and nonlinear classification is and how they are classified with the help of an example. It also describes the method for optimizing SVM. In addition, it also presents a brief survey about different applications of Speech Emotion Recognition. This study aimed to provide a simple guide to the researcher for those carried out their research study in the Speech Emotion Recognition system Figure 26 Optimized SVM: When y=0 Volume 4, Issue 3, May June 2015 Page 96

7 Table 1: Survey on different Classifiers for Emotion Recognition Volume 4, Issue 3, May June 2015 Page 97

8 Volume 4, Issue 3, May June 2015 Page 98

9 References [1] Akshay S. Utane, Dr. S.L.Nalbalwar, Emotion Recognition Through Speech Using Gaussian Mixture Model And Hidden Markov Model, International Journal of Advanced Research in Computer Science and Software Engineering, Volume 3, Issue 4, April 2013, ISSN: X [2] Siqing Wu, Tiago H. Falk, Wai-Yip Chan, Automatic speech emotion recognition using modulation spectral features, Elsevier, Speech Communication 53 (2011) [3] Yixiong Pan, Peipei Shen, Liping Shen, Speech Emotion Recognition Using Support Vector Machine, International Journal of Smart Home, Vol. 6, No. 2, April, [4] Aastha Joshi, Speech Emotion Recognition Using Combined Features of HMM & SVM Algorithm, International Journal of Advanced Research in Computer Science and Software Engineering, Volume 3, Issue 8, August 2013 ISSN: X. [5] Bhoomika Panda, Debananda Padhi, Kshamamayee Dash, Prof. Sanghamitra Mohanty, Use of SVM Classifier & MFCC in Speech Emotion Recognition System, International Journal of Advanced Research in Computer Science and Software Engineering, Volume 2, Issue 3, March 2012 ISSN: X. [6] K Suri Babu, Srinivas Yarramalle, Suresh Varma Penumatsa, Text-Independent Speaker Recognition using Emotional Features and Generalized Gamma Distribution, International Journal of Computer Applications ( ) Volume 46 No.2, May [7] Nitin Thapliyal, Gargi Amoli, Speech based Emotion Recognition with Gaussian Mixture Model, International Journal of Advanced Research in Computer Engineering & Technology, Volume 1, Issue 5, July 2012, ISSN: [8] S. Demircan, H. Kahramanl, Feature Extraction from Speech Data for Emotion Recognition, Journal of Advances in Computer Networks, Vol. 2, No. 1, March [9] Jagvir Kaur, Abhilash Sharma, Speech Emotion- Speaker Recognition Using Mfcc and Neural Network, Global Journal of Advanced Engineering Technologies, Vol3, Issue ISSN: [10] Eun Ho Kim, Kyung Hak Hyun, Soo Hyun Ki, Yoon Keun Kwak, Improved Emotion Recognition With a Novel Speaker-Independent Feature, Ieee/Asme Transactions On Mechatronics, Vol. 14, No. 3, June [11] S. Ramakrishnan, Ibrahiem M.M. El Emary, Speech emotion recognition approaches in human computer Interaction, Published online: 2 September 2011 Springer Science+Business Media, LLC 2011, Telecommun Syst (2013) 52: , DOI /s z. [12] Showkat Ahmad Dar, Zahid Khaki, Emotion Recognition Based On Audio Speech, IOSR Journal of Computer Engineering (IOSR-JCE) e-issn: , p- ISSN: Volume 11, Issue 6 (May. - Jun. 2013), PP [13] Bo Yu, Haifeng Li and Chunying Fang, Speech Emotion Recognition based on Optimized Support Vector Machine, Journal Of Software, Vol. 7, No. 12, December Volume 4, Issue 3, May June 2015 Page 99

10 [14] Optimization Objective, Artificial Intelligence CoursesVideo from Coursera - Standford University - Course: Machine Learning: [15] Non Linear Support Vector Machines (Non Linear SVM), Scholastic Tutor, June 2014, [16] Dr. Saed Sayad, Support Vector Machine- Classification (SVM), 2015, vector machine.htm. [17] J. Christopher Bare, Support Vector Machines, Digithead s Lab Notebook, November 30,2011. [18] Jiawei Han and Micheline Kamber, Data Mining:Concepts and Techniques,Elsevier, Second Edition, Morgan Kaufmann Publishers, 2006,ISBN: AUTHOR Soma Bera received the B.E degree in Information Technology from Atharva College of Engineering in Presently I am pursuing Masters in Engineering (M.E) in Computer Engineering from Shree L.R. Tiwari College of Engineering. I am with Atharva Institute of Information Technology training young and dynamic IT undergraduates. Volume 4, Issue 3, May June 2015 Page 100