2.1 FEATURE EXTRACTION - FUZZY ENTROPY (FuzzyEn)

Let 𝑠_k(𝑖) be a N sample noisy speech sequence of kth frame, where i = 1, 2, 3, …, N, which is reconstructed by phase-space with an embedded dimension m, and the reconstructed phase-space speech vector SIm is given by in (2),

and is generalized by removing the baseline as in (3),

For given vector Sim, the similarity degree 𝐷_𝑖𝑗 of its neighboring vector Sjm through its similarity degree is defined by fuzzy function, given in (4),

and dijm is the maximum absolute difference of the scalar components of Sim and Sjm, given in (5),

Here μdijm,r is the fuzzy membership function, which is given by the exponential function, as in (6),

where n and r are the gradient and width of the fuzzy membership function.

For each Sim, averaging all similarity degree of the neighboring vectors Sjm, we get (7),

Now construct (8) and (9),

and

From this, FuzzyEn(𝑚,𝑟) of the speech, is defined by, given in (10),

In this work, the embedding dimension, m is 2 and the exponential function parameters n and r are set as 2 and 0.2 times standard deviation, respectively. Note, FuzzyEn in (10) will be denoted as nFE hereafter.

2.2 TOTAL VARIATION (TV) FILTER

The total variation (TV) of the fuzzy entropy feature (n^𝐹𝐸) is given by the sum of the absolute values of its first order difference, which is given by,

where LL is the length of n^ 𝐹𝐸. Note TV of the signal nFE can be written as,

Where

D=-11-11-11

is a matrix of size (LL - 1) x LL. The notation ||.||₁ denotes the l1 norm. Given noisy fuzzy entropy feature (nFE) from equation (10), the output of TV filter is defined as the solution 𝑛̂𝐹𝐸 to the minimization problem,

where 𝜆 is a parameter that controls the trade-off between denoising and signal distortion.

2.3 SAVITZKY - GOLAY (SG) FILTER

The FuzzyEn features (nFE) obtained using (10) are further smoothed using Savitzky-Golay (SG) filter. SG filter can be generalized as a least-squares smoothing filter, where the filter coefficients are obtained using least-squares fit using a polynomial. This filter depends on two main parameters, window size and degree of the polynomial, M. If M is too high, redundancies of data is obtained and when M is too low, the signal gets distorted. Similarly, when the size of the window is larger, valid information may be lost and when the window is smaller, poor denoised signal is obtained. Smoothing the obtained noisy features through SG filter is given by,

where 𝑛𝐹𝐸_𝑘 is the noisy FE features and 𝐹𝐸𝑆_𝑘 is the smoothed output of the SG filter, ci is the coefficient for the i-th smoothing, NN is the number of data points in the smoothing window and is equal to 2m + 1, where m is the half-width of the smoothing window. The essence of SG filtering is adopting a polynomial in a sliding window to fit the original signal piece-by-piece depending on the least-squares estimation algorithm. The polynomial can be modelled as:

2.4 CONVOLUTION OF ABSOLUTE FIRST ORDER DIFFERENCE OF TV FILTER (conFETV')

The output of the TV filter (FETV) is further optimized by computing the absolute first order difference of the TV filter which is given by,

where, 𝜇_{𝐹𝐸𝑇𝑉′}=∑i=1LLFETV'.

The absolute first order difference (𝐹𝐸𝑇𝑉′) obtained in equation (16) is further refined by replacing with zeros for values of 𝐹𝐸𝑇𝑉′ less than average of 𝐹𝐸𝑇𝑉′ (𝜇_{𝐹𝐸𝑇𝑉′}) and the resultant obtained is convoluted with the Fuzzy entropy, FE obtained in equation (10) which is given by,

where * is a convolution operator.

2.5 FORMATION OF FEATURE VECTOR

The nFE obtained using (10) is further processed as explained in section 2.2 to 2.4 to form the feature vector of dimension J x K, where J is the number of frames in the noisy speech signal and K to be 3. The first feature vector is obtained as the output of TV filter which flattens out the rapid changes in the signal due to “staircase-effect” while preserving the slow changes in the signal. The second feature vector obtained as a result of SG filtering preserves the peak information in the signal. The third feature vector which was obtained as a result of convolution shows better discrimination between HRs and HRns regions. The significance of the feature vectors considered is explained in Figure 2.

Fig. 2 Performance measures comparison for the feature vectors considered averaged over five SNRs for 5 noises. (a) CORRECT (b) HRs (c) HRns. 

2.6 FEATURE SCALING - minmax

This minmax scaling method, rescales the given feature vectors from one range of values to a new range of values. More often, the feature vectors are rescaled to lie within a range of [0, 1] or [-1, +1], depending on the output classes. This rescaling is accomplished by using a linear interpretation equation given in (20),

where smFE is the smoothed feature vectors obtained using TV filter, SG filter and 𝑐𝑜𝑛𝐹𝐸𝑇𝑉′ and 𝑠𝐹𝐸′ is the normalized feature vector which is rescaled to fit the range [0, 1].

2.7 CLASSIFIER - SUPPORT VECTOR MACHINE

In this work, SVM is used as a classifier, because of its effectiveness in classification accuracy and computational time than other conventional nonparametric classifiers such neural networks, kNN, etc. SVM constructs an optimal hyperplane [〈𝑤,〉+𝑏=0] that maximizes the margin using a known kernel function that accurately predicts the unknown data into two classes, where 𝑤 and 𝑏, shall be derived based on the classification accuracy of the linear problems. Let (𝑥𝑖,𝑦𝑖)𝑖=1𝑁 be the training set samples, where 𝑦𝑖 𝜖 𝑅𝑚 is the corresponding target classes for the input data 𝑥𝑖 𝜖 𝑅𝑚. This is achieved by minimizing the error function shown in (21),

Subject to yiwTφxi-b≥1-ξi ξi≥0,i=1,2,…,n

where 𝜑(𝑥_𝑖) is a mapping function to map 𝑥_𝑖 to its higher dimensional feature space, 𝜉_𝑖 is the misclassification error and 𝐶 controls the trade off between the cost of classification and the margin. The classification of the new data as +1 or −1 is obtained by minimizing the error function in (21) based on the decision function, Class i = 𝑠𝑖𝑔𝑛 (〈𝑤,〉+𝑏), yields 1 or 0 respectively. The mapping of the input training set into a higher dimensional space is done through a kernel function 𝐾 ( ,). In this work, the RBF kernel function is used for its excellent generalization and low computational cost (^{Hariharan, Fook, Sindhu, Adom, & Yaacob, 2013}). The RBF kernel function is given by (22),

where, the parameter 𝜎 is the width of the Gaussian function. For this given kernel function, the error function of the classifier is given by (23),

3.1 PERFORMANCE EVALUATION

Performance evaluation of VAD algorithm can be performed both subjectively and objectively. In subjective evaluation, a human listener evaluates for VAD errors, whereas, numerical computations are carried out for objective evaluation. However, subjective evaluation alone is insufficient to examine the VAD performance because listening tests like ABC fail to consider the effects of false alarm (^{Beritelli et al., 2002}; ^{Ghosh, Tsiartas, & Narayanan, 2011}). Hence numerical computations through objective evaluation help in reporting the performance of the proposed VAD algorithm.

VAD performance is calculated using (24) and (25)

And

where, HR_ns and HR_s, non-speech frames and speech frames correctly detected among non-speech and speech frames respectively. NS_ns and NS_s, refers to the number of non-speech and speech frames in the whole database, respectively, while NS_ns, ns and NS_s, _s, refers to the number of frames classified correctly as non-speech and speech frames. The overall accuracy rate is given by (26),

The best performance is achieved when three parameters referred in the equations (24), (25) and (26) become maximum.

Feature vector performance metrics:

The performance metrics (CORRECT, HRs, HRns) for the proposed TV - SG - 𝑐𝑜𝑛𝐹𝐸𝑇𝑉′ feature vector averaged for overall noises considered (Airport, Babble, Car, Subway and Train) for different SNR levels is shown in Table 1. The table clearly shows that the feature proposed 𝑐𝑜𝑛𝐹𝐸𝑇𝑉′ achieves better performance measures except for HRns. It also detects speech regions (HRs) in an effective way. But when combining all the three features namely TV, SG and 𝑐𝑜𝑛𝐹𝐸𝑇𝑉′, the performance increases for all three metrics giving better detection of HRs and HRns of about 90% and above when compared to that of features considered as a single one. Figure 2 (a) - (c) shows the performance evaluation metrics averaged over the five SNRs (-10 to 10) for the five nonstationary noises computed for the feature vectors TV, SG, 𝑐𝑜𝑛𝐹𝐸𝑇𝑉′, TV - SG, TV - 𝑐𝑜𝑛𝐹𝐸𝑇𝑉′, SG - 𝑐𝑜𝑛𝐹𝐸𝑇𝑉′, TV - SG - 𝑐𝑜𝑛𝐹𝐸𝑇𝑉′ (proposed feature vector) considered. From the Figure 2, it is clear that the proposed TV - SG - 𝑐𝑜𝑛𝐹𝐸𝑇𝑉′ feature vector is the best for all the performance metrics considered for CORRECT, HRs and HRns. The significance of the feature vector formed is misclassification rate of classifying HRs and HRns. The figure clearly shows that the error rate is minimal while forming the feature vector (TV - SG - 𝑐𝑜𝑛𝐹𝐸𝑇??′), because the proposed feature 𝑐𝑜𝑛𝐹𝐸𝑇𝑉′ detects speech regions (HRs) well when compared to that of -the non-speech regions (HRns) but when combining improves the overall efficiency of detecting HRs and HRns effectively.

Performance metrics comparison with other VADs (G.729B, VAD-SOHN, VAD-RAMIREZ)

The efficiency of the proposed smFESVM based VAD is examined by comparing the performance metrics with existing VAD algorithms which is explained below:

- G.729B VAD (^{ITU, 1995}) is a standard VAD method which utilizes several traditional features and is used in speech communication systems to improve the bandwidth.

-VAD-SOHN (^{Sohn, 1999}) is based on statistical modelling which estimates spectral SNR and Gaussian model distribution for speech and noise assuming that the Gaussian distribution for speech and noise in Fourier domain are independent.

- VAD-RAMIREZ (^{Ramı́rez, Segura, Benı́tez, De la Torre, & Rubio, 2004}) combines multiple-observation technique and statistical models VAD and the False Alarm Rate (FAR) is controlled by the use of contextual global hypothesis.

Figure 4 show the comparison of CORRECT rate performance metrics of the proposed smFESVM based VAD with G.729B, VAD-SOHN and VAD-RAMIREZ for different SNR levels (−10,-5, 0, 5 and 10 dB) for airport noise, babble noise, car noise, subway noise, and train noise. It is inferred from the figure that the smFESVM based VAD outperforms the rest of the VAD algorithms by obtaining best performance in CORRECT rate especially under low SNR levels (< 0 dB). There is a noticeable lag in car noise scenario, because a complex event has been encountered in the car noise scenario which is treated as valuable speech thereby increasing misclassification error.

Fig. 3 Misclasssification Error % for various feature vectors considered 

Fig. 4 CORRECT comparisons for G.729B (^{ITU, 1995}), VAD-SOHN (^{Sohn, 1999}), VAD-RAMIREZ (^{Ramı́rez et al., 2004}) and smFESVM based VAD for SNR values ranging between -10 and 10 dB (a) Airport (b) Babble (c) Car (d) Subway and (e) Train noises. 

Figure 5 and Figure 6 show hit rate performance evaluation metrics (HRs and HRns) with five SNRs for different kinds of noises computed for G.729B, VAD-SOHN, VAD-RAMIREZ, and the smFESVM based VAD. It is clear that the VAD methods used in comparison yields very high speech detection rates (HRs) for different SNR levels and for various noises, especially G.729B and VAD-RAMIREZ. But this performance behaviour degrades in non-speech detection (HRns) rates when the noise level increases which makes it less conservative in practical speech processing schemes. This is due to the effect of hangover scheme (^{Aneeja & Yegnanarayana, 2015}; ^{Davis et al., 2006}) used in these methods. As the energy towards the end of speech is relatively low, to control the risk of false alarm rates (FAR), hangover schemes are used. On the other hand, the proposed smFESVM based VAD yields better detection rates for speech (HRs) and non-speech (HRns) regions when compared to that of the other VAD algorithms. Its detection rate for non-speech regions is relatively higher and exhibits a very low marginal decay in performance while detection speech regions for certain noisy conditions. Table 2 shows the performance metrics averaged for all the noises with various SNR levels. The table clearly illustrates the consistency of the smFESVM based VAD in detecting HRs and HRns with different SNR levels. The challenge of VAD is to detect speech under low SNR levels (<0dB) and from the table it is clear that the smFESVM based VAD algorithm outperforms the rest of the VAD algorithms in detecting speech as well as non-speech regions under low SNR levels.

Fig. 5 HRs comparisons for G.729B (^{ITU, 1995}), VAD-SOHN (^{Sohn, 1999}), VAD-RAMIREZ (^{Ramı́rez et al., 2004}) and smFESVM based VAD for SNR values ranging between -10 and 10 dB (a) Airport (b) Babble (c) Car (d) Subway and (e) Train noises. 

Fig. 6 HRns comparisons for G.729 (^{ITU, 1995}), VAD-SOHN (^{Sohn, 1999}), VAD-RAMIREZ (^{Ramı́rez et al., 2004}) and smFESVM based VAD for SNR values ranging between -10 and 10 dB (a) Airport (b) Babble (c) Car (d) Subway and (e) Train noises. 

Table 3 shows the comparison of performance metrics under clean conditions, averaged for all noisy scenarios and averaged over both clean and noisy conditions with different SNR levels. It is clearly observed from the table that the smFESVM based VAD excels rest of VAD in every performance metrics especially for non-stationary noisy scenarios. There is a noticeable lag in speech detection rate when compared with other VADs, but the proportion of non-speech detection rate confirms that the proposed smFESVM based VAD is well suited in detecting both speech and non-speech regions effectively. Also, the detection of non-speech regions is very much higher for the smFESVM based VAD which is very useful in major speech applications like speech compression, VoIP, speech enhancement, etc. Therefore, based on these performance metrics, the smFESVM based VAD detects speech and non-speech regions effectively especially under low SNR conditions. noisy scenarios. There is a noticeable lag in speech detection rate when compared with other VADs, but the proportion of non-speech detection rate confirms that the proposed smFESVM based VAD is well suited in detecting both speech and non-speech regions effectively. Also, the detection of non-speech regions is very much higher for the smFESVM based VAD which is very useful in major speech applications like speech compression, VoIP, speech enhancement, etc. Therefore, based on these performance metrics, the smFESVM based VAD detects speech and non-speech regions effectively especially under low SNR conditions.