Automatic classification of Indian Music using EMD

doi:10.21203/rs.3.rs-2870303/v1

Indian music is very rich in emotional content and technicalities. It is also contrasting having multiple genres which may be broadly classified as Classical (Hindustani or Carnatic) music, Semi-classical music (including Ghazals) and Light (including folk) music. The so called “rasa” or emotional content in Indian music is of much significance, e.g. selection of the right kind of music for therapeutic intervention by the music therapist who might be an expert in western art music (WAM) but could be new to Indian music. This paper presents a novel classification technique based on empirical mode decomposition (EMD), applied for the first time in Indian music. In this work, two genres of Indian music, Classical and Semi-classical, are considered. Highest classification accuracy of 98.68% is reported in the paper using SVM binary classifier after extraction of relevant features such as time domain features, frequency domain features, MFCC and Chroma vector.

Indian music

audio features

empirical mode decomposition

SVM

t-test

Andrew’s plot

Automatic genre classification of music has been an interesting topic of research in the past two decades. When we consider Indian Music, which is having multiple genres, exploring relevant features and classifiers turns out to be very crucial. Although Raga, a melodic structure with fixed notes and a set of rules that characterize a particular mood conveyed by performance, is the nucleus of Indian music, there could be other music genres such as bhajan (a devotional song and a sub-genre of light music) may or may not be based on raga.

Although significant works have been carried out in Indian Music in general, yet genre classification requires more attention. Music therapy on the other hand is a topic of research in the past decade, identification/ selection of music for some specific purpose/task is an unexplored area. This study presents the classification task of discriminating two classes namely: Hindustani raga under classical music and Raga based devotional song (Shyama Sangeet) under semi-classical music. The nucleus of both these forms is raga.

In our dataset, the first category is Hindustani music; where raga rules (grammar) must be maintained strictly. On the other hand, the second dataset comprises of Semi-classical music (Shyama Sangeet-a devotional Song dedicated to Goddess Shyama or Kali) and is a sub-genre of Bengali music based on raga. Our dataset comprises of recordings of trained musicians who are professional and expert.

Three feature sets for representing timbral texture, rhythmic content and pitch content of music signals using statistical pattern recognition classifiers are evaluated for ten musical genres, classification of 61% (non-real time) and 44% (real time) was achieved[1]. Improved cepstrum feature extraction for optimal music and speech discrimination is done in [2], in which dynamic time warping based classification resulted in approximately 85% accuracy. Comparison between models of auditory perception based features and generic audio features in done using four audio feature sets to distinguish between five audio classes[3].

EMD has been employed in [4] to extract significant musical structures from audio where, it is demonstrated that a rhythmic and harmonic analysis of the signal may be carried out utilizing EMD. The suitability of ensemble EMD for musical tempo estimation for over 450 songs is shown in [5]. In [6] and [7], six types of audio are included in the database: and linear predictive coefficients based features gave classification accuracies of 92.1% and 93.7% with Support Vector Machine and Radial Basis Function Neural Network respectively. On the other hand, Auto Associative Neural Network model and Gaussian Mixture Model yielded classification accuracies of 93.1% and 92.9% respectively. In [8], characteristics from voice and music data in the time-domain and frequency-domain are taken and the performance was evaluated using SVM audio classifier, yielding an accuracy of roughly 90%. Tempo and modulation spectra of timbral features are extracted from the dataset comprising of Hindustani music, which yielded classification accuracy of 92.86% in order to discriminate between bhajan and qawwali genres using SVM and GMM model [9]. Five genres of Indian music are considered in order to classify them using GMM and k-NN models giving accuracy of 91.25% only[10]. Highest classification accuracy of 96.96 was achieved for classification of Tamil Classical & Tamil Folk music using SVM & k-NN models [11]. Using Classical, Folk, Ghazal and Sufi songs of Indian music as the dataset, spectral features are extracted and a classification accuracy of 90.8% was obtained with SVM model; Naïve-based model and k-NN based models showed even lesser accuracy [12]. Most recent works such as [13] used deep neural network model 1-layer RNN- LSTM in order to classify Hindustani & Carnatic music with highest classification accuracy of 96.08% using MFCC features only. Five different genres of Bangla music are classified using spectral features alone, thereby giving accuracy of 90.8% with a deep neural network model named BMNet-5[14].

After an extensive literature survey of the works carried out in both WAM and Indian music, we observed the trade-off between dataset used, audio features and classification models. Thus, we propose to use EMD based feature extraction and evaluate the performance using a k-NN classifier and SVM classifier. Also, very less works have been done so far in Indian music classification.

The first stage involves pre-processing of the song in which silence removal, down-sampling and normalization is done. The next stage involves decomposition of the pre-processed signal using EMD. Features are then extracted from the IMFs and after we get the normalized feature vectors, they are fed to the classifier. Hundred iterations were performed using ten-fold cross validation mechanism in order to evaluate the performance of the classifier. 80% of the dataset are used for training the model, whereas 10% each were assigned for validation and testing purpose.

EMD can be used for the analysis of nonlinear non-stationary signals, such as music signals. In this work, we have incorporated this technique where intrinsic mode functions (IMFs) of those many extracted features are taken. After normalization of the feature vectors, these normalized feature vectors are fed to the binary classifier. The block diagram of the proposed methodology is shown in Fig. 1 below:

2.1 Database:

Recording was done at CD quality i.e 44,100 Hz sampling rate, 16 kHz mono channel with 16 bits/sample format in a standard recording room. Only the voice of the singer was taken for recording and the sound of the accompanying instrument, here drone (or tanpura) was provided to the vocalist through an earphone. The approximate duration of each type of audio was kept of 4–5 minutes duration. For classical recording, a total of 15 vocalists comprising of 10 male vocalists and 5 female vocalists who were asked to render ten different ragas according to their choice. The raga recordings comprised of bandish, a song like composition in a raga maintaining the raga rules strictly. The same procedure was followed in the recordings for semi-classical, where the raga rules need not be maintained strictly rendered by not only the previous set of vocalists but few more. Hence, our database comprises of 150 files each for two different classes of audio samples.

2.2 Pre-Processing: It is the initial step required for further signal processing. Here, tasks namely silence removal, down sampling, framing & windowing and normalization were done prior to empirical mode decomposition of the signal into intrinsic mode functions.

2.3 Empirical Mode Decomposition (EMD): There are certain class of mathematical functions that are based on their local properties, popularly known as intrinsic mode functions (IMFs) for which the instantaneous frequency can be defined everywhere. EMD is data dependent and of dyadic filter bank nature [15]. Given a real signal $x\left(t\right)$, EMD is applied to obtain a set of IMFs which can be summarized in the form of a flow-chart as shown in Fig. 2.

There are a number of considerations to be taken into account when implementing EMD relating to the number of siftings, stopping criteria and envelope interpolation; details of which can be found in [16, 17].

2.4 Feature Extraction:

An essential step in audio analysis is feature extraction. In pattern recognition and machine learning applications, extracting useful features—in this case, audio features—from a given dataset is the overall goal of feature extraction, which is a crucial processing step. These features are presented in Table 1. It comprises of time domain features, frequency domain features, MFCC and Chroma vector [18].

Table 1

Audio Features, formula for computing and their brief description.
S. N.	Feature	Formula	Remarks
1.	Energy	$E=\sum _{i=1}^{n}{\left\|{x}_{i}\left(n\right)\right\|}^{2}$ x_i(n), n = 1, .. . ,W_L be the sequence of audio samples of the i^th frame, where W_L is the length of the frame.	Short-term energy, usually normalised in order to remove dependency of frame length, gives signal power when divided by frame length.
2.	Entropy of energy	$H\left(i\right)=-\sum _{j=1}^{K}ej .\text{l}\text{o}\text{g}\left({e}_{j }\right)$ e_j = 1, 2,....K, are sub-frame energy values,	Measure of abrupt change in energy level
3.	Zero-Crossing Rate	$Z\left(i\right)=\frac{1}{2WL}\sum _{n=1}^{WL}$	Signal's sign change across an audio frame, a metric used to determine how noisy a signal is
4.	Spectral Centroid	${C}_{i}=\frac{}{}$	gravitational centre of the spectrum
5.	Spectral Spread	${S}_{i}=\sqrt{\frac{}{}}$	Second central moment of the spectrum
6.	Spectral Entropy	$H=-\sum _{f=0}^{L-1}{n}_{f}.{log}_{2}\left({n}_{f}\right)$ where, ${n}_{f}$ is the normalised energy	Entropy in frequency domain
7.	Spectral Rolloff	$\sum _{k=1}^{m}{X}_{i}\left(k\right)=C\sum _{k=1}^{{W}_{f}}{X}_{i}\left(k\right)$	The frequency below which a specific amount of the magnitude distribution of the spectrum is concentrated
8.	Mel frequency cepstral coefficients (MFCCs)	Steps for computing MFCCs is shown below figure (Fig. 3))	Short time power spectral representation of a Signal
9.	Chroma Vector	${v}_{k}=\sum _{nϵ{S}_{k}}\frac{{X}_{i\left(n\right)}}{{N}_{k}}$. k$ϵ\text{0,1},2\dots .11$	A 12-dimensional vector that resembles a histogram, with each dimension standing for a different pitch class

2.5 Steps for computing MFCCs:

2.6 Classification:

2.6.1 Support Vector Machines(SVMs):

All of the data points are divided into two classes by a hyperplane (also known as a linear decision boundary). The hyperplane with the biggest margin between the two classes is the optimum hyperplane for an SVM where the data can be linearly divided. The input to the classifier is a set of feature vector extracted from the audio signals.

In our work, we have used SVM as a two binary classifier, to classify the two classes of Indian music. For a given training data sets $({x}_{m},{y}_{m})$, where $i = 1, 2, ...M , {x}_{m} \in RN$ and ${y}_{m}\in (1,-1),$ first step is to map the data vectors into feature space using mapping function $\varPhi : xm \to \varPhi \left(xm\right)$. The separation distance between two classes is $\frac{2}{‖x‖}$ in feature space. This is done in order to maximize the margin between two classes, and thereby minimizing the training errors $\xi m$[19].

2.6.2 k Nearest Neighbour (k-NN):

k-NN categorizes objects based on the classes of their nearest neighbours in the dataset. K-NN predictions assume that objects near each other are similar. Distance metrics, such as Euclidean, city block, Chebychev etc. are used to find the nearest neighbour. Here, we have used distance measures such as Euclidean, Minkowski, Cityblock,, Chebychev and Mahalanobis. These distance measures are summarized in the form of table (Table 2) shown below:

Table 2

Different distance measures used in k-NN classifier
Sl. No.	Distance Metric	Brief description	Formula for computation
1.	Minkowski	distance between two real-valued vectors	$D\left(x,y\right)={\left(\sum _{i=1}^{n}{\left(\left\|{x}_{i}{-y}_{i}\right\|\right)}^{p}\right)}^{1/p}$
2.	Euclidean	distance between two points in Euclidean space	$D\left(x,y\right)\text{=}\sqrt{\sum _{i=1}^{n}{\left({x}_{i}{-y}_{i}\right)}^{2}}$
3.	City Block	A special case of Minkowski distance	$D\left(x,y\right)=\sum _{i=1}^{n}\left\|{x}_{i}{-y}_{i}\right\|$
4.	Chebychev	distance between two points as the maximum difference over any of their axis values	$D\left(x,y\right)={max}_{i}\left\|{x}_{i}{-y}_{i}\right\|$
5.	Mahalanobis	distance between a point and a distribution	${D}^{2}={\left(x-m\right)}^{T}.{C}^{-1}.(x-m)$ Where, D² is the square of the distance $x$is the vector of observation $m$is the vector of mean values & $C$is the inverse covariance matrix

First, we have extracted the audio features using baseline features and then the feature vectors were fed to both k-NN classifier and SVM classifier where it was found that the classification accuracy was low. Secondly, we used EMD based features for classification and it was found that the classification accuracy is higher as compared to the baseline features with SVM, as shown in Fig. 4. Finally, we have compared our result with previous works ([9],[10],[11] &[12] and also with most recent works([13] &[14])who have used deep learning techniques to classify other genres of Indian music. We found significant improvement (increase) in classification accuracies as 5.82%, 7.43%, 1.72% & 7.88% respectively (machine learning models) and 2.6% & 8.36%respectively(deep learning models), which are quite effective for our methodology proposed. The comparison table is shown in Table 3 below:

Table 3

Comparison of results between performance of previous works.
Study	Database and Model	Features	Performance (% Accuracy)
Sujeet Kini et. al (2011)[9]	Database: North Indian- Bhajan & Qawwali Model: GMM, SVM	Tempo and modulation spectra of timbral features	92.86
S. Jothilakshmi et.al (2012)[10]	Database: Hindustani, Carnatic, Ghazal, Folk and Indian Western, Model: GMM, k-NN	Spectral shape features and perceptual features	91.25
B. Rajesh et.al (2016)[11]	Database: Tamil Classical & Tamil Folk Music Model: SVM, k-NN	FrFT based MFCC features	96.96
Deepti Chaudhari et. al(2019)[12]	Database: Classical, Folk, Ghazal and Sufi Model: SVM	Spectral features	90.8
A K Sharma et. al (2021)[13]	Database: Hindustani music & Carnatic music RNN-LSTM and 1 layer CNN	MFCC	96.08
K. M. Hasib et al (2022)[14]	Database: Five genres of Bangla Music Model: BMNet 5	Spectral features	90.32
Proposed work	Database: Classical Music and Semi-classical music Model: SVM, k-NN	EMD Based Features	98.68(SVM) 95.72(k-NN)

Energy feature showed accuracy of 90% irrespective of distance measures. The audio feature ZCR showed maximum accuracy of 95.83% with ‘Cityblock’ distance measure. 91.67% accuracy was reported for spectral energy feature with ‘Chebychev’ distance measure. Spectral centroid gave 93% accuracy with ‘Euclidean’, ‘Cityblock’ and ‘Minkowski’ distance measures. Thus, SVM performance is better than k-NN as seen from the data and hence the comparison is shown for SVM.

5.1 T-test:

Evaluation of p-value using t-test is necessary to measure the importance of each feature in the classification. The p-value of EMD based features is tabulated in Table 4. Lower p-value reveals that the feature is more significant to classify the classes and are more statistically different. From this study it is concluded that, spectral centroid and spectral spread shows more significance for classification as compared with other EMD based features. Previously, we have performed t-test in order to investigate the audio features for scientific study of time theory in ragas [20].

Table 4

p-values of EMD based features using t-test.
Feature	p-value
Energy	0.0012
ZCR	0.0010
Entropy	0.0015
Spectral Entropy	0.0030
Spectral Centroid	0.0005
Spectral Spread	0.0009
Spectral Rolloff	0.0096
MFCC	0.0064
Chroma Vector	0.0034

5.2 Andrews Plot:

Andrews curves were developed as a method for visualizing multi-dimensional data by mapping each observation onto a function. This is similar to star plots in that each observation or sample point is represented by a glyph, except that in this case the glyph is a curve. This function is defined as:

$${f}_{X}\left(t\right)=\frac{{x}_{1}}{\sqrt{2}}+{x}_{2}sint+{x}_{2}sint{+x}_{3}cost+ {x}_{4}sin2t+{x}_{5}cos2t+\dots$$

1

Where, the range of $t$ is given from $-\pi \le t\le \pi .$Each observation is projected onto a set of orthogonal basis functions represented by sines and cosines and then plotted. Thus, each sample point is now represented by a curve given by Eq. 1. Various types of problems arise when statistical analysis involves multidimensional data. Conventionally, we prefer to reduce the dimensionality to one, two, or three for better visualization of the multidimensional dataset. we get structural details of the dataset by reducing the dimension. The technique we use here to reduce dimensionality is Andrews Plot. Each point $x=\{{x}_{1},{x}_{2},{x}_{3},{x}_{4},{x}_{5}\}$ in the dataset denotes a finite Fourier series. The function is then plotted for $-\pi \le t\le \pi .$. Each point is now a line between $-\pi$ and $\pi$. Any structure in a dataset is now visible as curves on a two-dimensional plot. If any two n dimensional points are close then the corresponding curves in two dimensions are also close. Two ragas associated with the same performance time are likely to be very close. An Andrews plot is a graphical data analysis technique for plotting multivariate data.

For further literature, the reader is suggested to go through the paper by D. F. Andrews [21].

Remark:The techniques for reducing an n-dimensional problem into a two-dimensional one without losing information on the original variables is collectively called ‘projection pursuit’. Andrews plot, parallel coordinates and PCA (principle component analysis) fall under this category.

As an implementation of the above technique, we got the following graphical representation of Andrews plot illustrated in Fig. 5 and Fig. 6 for a classical song and a semi-classical song respectively.

It can be clearly observed from Fig. 5 and Fig. 6 that the pattern exhibited by classical songs is quite different from that exhibited by semi-classical songs. Also, there is commonality in the patterns of both these genres of Indian music. Hence, the features which represented the variables in Andrews plot are able to achieve the desired classification.

Although, the performance based on generic feature extraction techniques involving time domain and frequency domain features for audio classification are satisfactory, one can use EMD based features for better classification accuracy as seen from the present work. Statistical test validates our present work since EMD based features shows better significance for classification as confirmed further by Andrews plot of projection pursuit.

Thus, the present work could be of great help for selecting the right kind of music for therapeutic intervention by the music therapist who might be an expert in western art music (WAM) but could be new to Indian music. Further, as an application, consider a note sequence of a raga being simulated by the computer using the concept of semi-natural composition as described in Chap. 9 of the recently published book by Chakraborty et. al 2014 [22]. We can use the EMD technique to decide whether the generated note sequence qualifies to be a raga bandish or whether it is good enough to be an opening line of a raga based song. For a young music learner or a composer, this can prove to be useful. On the other hand, if the musician is an expert, he or she can compare the subjective assessment of one of the two classes into which the note sequence falls with its objective counterpart as provided by the EMD technique. Considering the tremendous power a modern computer has in simulation, such applications in artificial or semi-natural composition will always be appreciated by music composers, musicologists and music researchers.

The authors have no relevant financial or non-financial interests to disclose.
The authors have no competing interests to declare that are relevant to the content of this article.
All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.
The authors have no financial or proprietary interests in any material discussed in this article.

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Automatic classification of Indian Music using EMD

Status:

Version 1

Abstract

Figures

Introduction

Related Works

Methodology

2.1 Database:

2.4 Feature Extraction:

2.5 Steps for computing MFCCs:

2.6 Classification:

2.6.1 Support Vector Machines(SVMs):

2.6.2 k Nearest Neighbour (k-NN):

Experimental Results

Statistical Analysis

5.1 T-test:

5.2 Andrews Plot:

Conclusion

Declarations

References

Status:

Version 1

S. N.	Feature	Formula	Remarks
1.	Energy	\(E=\sum _{i=1}^{n}{\left\|{x}_{i}\left(n\right)\right\|}^{2}\) x_i(n), n = 1, .. . ,W_L be the sequence of audio samples of the i^th frame, where W_L is the length of the frame.	Short-term energy, usually normalised in order to remove dependency of frame length, gives signal power when divided by frame length.
2.	Entropy of energy	\(H\left(i\right)=-\sum _{j=1}^{K}ej .\text{l}\text{o}\text{g}\left({e}_{j }\right)\) e_j = 1, 2,....K, are sub-frame energy values,	Measure of abrupt change in energy level
3.	Zero-Crossing Rate	\(Z\left(i\right)=\frac{1}{2WL}\sum _{n=1}^{WL}\)	Signal's sign change across an audio frame, a metric used to determine how noisy a signal is
4.	Spectral Centroid	\({C}_{i}=\frac{}{}\)	gravitational centre of the spectrum
5.	Spectral Spread	\({S}_{i}=\sqrt{\frac{}{}}\)	Second central moment of the spectrum
6.	Spectral Entropy	\(H=-\sum _{f=0}^{L-1}{n}_{f}.{log}_{2}\left({n}_{f}\right)\) where, \({n}_{f}\) is the normalised energy	Entropy in frequency domain
7.	Spectral Rolloff	\(\sum _{k=1}^{m}{X}_{i}\left(k\right)=C\sum _{k=1}^{{W}_{f}}{X}_{i}\left(k\right)\)	The frequency below which a specific amount of the magnitude distribution of the spectrum is concentrated
8.	Mel frequency cepstral coefficients (MFCCs)	Steps for computing MFCCs is shown below figure (Fig. 3))	Short time power spectral representation of a Signal
9.	Chroma Vector	\({v}_{k}=\sum _{nϵ{S}_{k}}\frac{{X}_{i\left(n\right)}}{{N}_{k}}\). k\(ϵ\text{0,1},2\dots .11\)	A 12-dimensional vector that resembles a histogram, with each dimension standing for a different pitch class

Sl. No.	Distance Metric	Brief description	Formula for computation
1.	Minkowski	distance between two real-valued vectors	\(D\left(x,y\right)={\left(\sum _{i=1}^{n}{\left(\left\|{x}_{i}{-y}_{i}\right\|\right)}^{p}\right)}^{1/p}\)
2.	Euclidean	distance between two points in Euclidean space	\(D\left(x,y\right)\text{=}\sqrt{\sum _{i=1}^{n}{\left({x}_{i}{-y}_{i}\right)}^{2}}\)
3.	City Block	A special case of Minkowski distance	\(D\left(x,y\right)=\sum _{i=1}^{n}\left\|{x}_{i}{-y}_{i}\right\|\)
4.	Chebychev	distance between two points as the maximum difference over any of their axis values	\(D\left(x,y\right)={max}_{i}\left\|{x}_{i}{-y}_{i}\right\|\)
5.	Mahalanobis	distance between a point and a distribution	\({D}^{2}={\left(x-m\right)}^{T}.{C}^{-1}.(x-m)\) Where, D² is the square of the distance \(x\)is the vector of observation \(m\)is the vector of mean values & \(C\)is the inverse covariance matrix