Quality Measurement of Speech Recognition Features in Context of Nearest Neighbour Classifier

The selection of the quality feature system is the key of successful speech recognition system. Therefore, the inquiry can be stated how to choose the quality feature system? The concept of quality can be defined by comparing a set of inherent characteristics with a set of requirements. If these subjects are met, then high quality is achieved [16]. Also, more quality descriptions are represented in [6, 7, 18, 26]. The choice of quality features is the essential as low classification error can be achieved if quality features are used. On the contrary high classification error is achieved for not quality feature system. A variety of speech feature systems exists. Accordingly, currently quality of features is used to estimate by calculating the classification error. However, this method is limited as it causes running classification experiments with each explored feature system. The major issue of current research is to propose the method for quality estimation of speech recognition feature system with the approach that doesn‘t require performing classification experiments. Moreover, the method is based on metrics: feature volume of class boundary, nearest neighbour distances ratio of classes, overstep of class boundary. The paper is structured as follows. Firstly, the proposed method for quality estimation of speech recognition feature system is presented. Then, metrics for quality estimation of speech recognition features are displayed. Next, the results of experimental researches are represented. Finally, conclusions are made.


Introduction
The selection of the quality feature system is the key of successful speech recognition system.Therefore, the inquiry can be stated -how to choose the quality feature system?The concept of quality can be defined by comparing a set of inherent characteristics with a set of requirements.If these subjects are met, then high quality is achieved [16].Also, more quality descriptions are represented in [6,7,18,26].The choice of quality features is the essential as low classification error can be achieved if quality features are used.On the contrary high classification error is achieved for not quality feature system.A variety of speech feature systems exists.Accordingly, currently quality of features is used to estimate by calculating the classification error.However, this method is limited as it causes running classification experiments with each explored feature system.
The major issue of current research is to propose the method for quality estimation of speech recognition feature system with the approach that doesn't require performing classification experiments.Moreover, the method is based on metrics: feature volume of class boundary, nearest neighbour distances ratio of classes, overstep of class boundary.
The paper is structured as follows.Firstly, the proposed method for quality estimation of speech recognition feature system is presented.Then, metrics for quality estimation of speech recognition features are displayed.Next, the results of experimental researches are represented.Finally, conclusions are made.

Method of quality measurement for speech recognition features
The quality of features has been estimated using classification error.Therefore, this method requires classification experiments running with each feature system.Let's suppose that we have five feature systems 1 S , 2 S , 3 S , 4 S , 5 S under exploration.In order to choose the quality feature system, the classification process must be run five times.Consequently, we propose a new method of quality estimation for speech recognition features.Quality feature system is defined using metrics instead of making classification (Fig. 1).Let's suppose that quality feature system was established 4 S .The detailed scheme of the method is presented in Fig. 2 and steps of the method are displayed below.
Selection of feature system.The metrics are calculated for investigated feature systems.
Calculation of metrics for classes.The metrics are calculated for instances combinations that belong to certain classes combination ) , ( ) , ( where ) , ( instance of i-th class and j m h is m-th instance of j-th class, k=1,...,K, n=1,...,NH, m=1,...,MH, i, j=1,...C, j i  , Knumber of metrics, NH , MH -instances numbers of i-th and j-th classes, C -number of classes.Low value of metrics identifies high quality feature system.The average of metrics is calculated for each combination where PBsk is the number of classes combinations.Calculation of quality for the feature systems.After the averages of metrics are calculated for each class combination, the index of feature system is calculated for each classes combination by "voting" )) , ( min (arg S is the p-th feature system that was established to have the lowest value of k-th metric for i-th and j-th class combination, Pnumber of feature systems, the equality is satisfied, otherwise it gives 0. Then "the quality indexes of feature systems" are calculated where ) (  function gives 1 if p-th feature system is identified as the best one in case of i-th and j-th class combination.Otherwise, 0 is given, KBsk -the number of class combinations.It defines the quality of feature system in percentages, where 0% identifies low quality and 100% high quality Decision taking about the quality feature system.The quality feature system is established with the highest quality index Validation of the adequateness of the proposed method.To validate the adequateness of the proposed method classification error has to be calculated for the explored feature systems.

Length of class boundary (G1).
The metric counts the number of samples connected to the opposite class by the edges in Minimum Spanning Tree (MST) [1,14,20] is the vertex set of MST [2,3,9].These vertexes (samples) belong to the edges (Euclidean distance between samples), that connect vertexes of different classes, K -the number of the vertexes.The metric is defined as the ratio of such vertexes number to the all vertexes number Ratio of intra/inter class nearest neighbour distances (G2).The metric is calculated as the ratio of nearest neighbours distances sum from the same class over the sum from opposite class [13,14,24,25] ) , ( min where ) , ( min

Overstep boundary (G3).
Let us suppose that every class is represented by the sphere.The radius of the sphere is defined as the distance from centre to the farthest sample of the class, where the centre is the mean of the class [19].The metric is calculated: ) , ( max where ) , ( is the number of samples satisfying the overstep condition (10).

Experimental results and discussion
The experimental researches were made with 14 sets of different phonemes.Each set consisting of 100 instances of single phoneme.Most frequent Lithuanian phonemes were selected as the target for this experimental study [22]
The experimental results of the proposed method are presented by providing quality indexes of feature systems.The results of the experiments with estimated quality indexes of feature systems are showed in Fig. 3. Also, in order to validate the adequateness of the proposed method, NN classification errors were calculated and are provided in Table 1.The experimental results of Data set1.The results of quality indexes showed that PLP feature system gained the highest quality index.It identifies PLP system to be the highest quality.As well as this, the results of NN classification error showed that the lowest classification error was achieved for PLP.
The experimental results of Data set2.The results of quality indexes identified that PLP gained the highest quality index.Additionally, the results of NN classification error showed that the lowest classification error was achieved in case of PLP feature system.
The experimental results of Data set3.The results of quality indexes also showed that PLP gained the highest quality index.As well as this, the results of NN classification error identified that the lowest classification error was achieved for PLP.
As a result, the experimental results of feature quality estimation using the proposed method coincided with the results of quality estimation using the classification error.In both cases, with all three data sets it was established that PLP is the quality feature system.The results of the experimental researches approbated the correctness of the proposed method.

Conclusions
The paper attributes to the issue of quality estimation method of speech recognition features.The new method for quality estimation of speech recognition features is proposed that doesn't require executing classification experiments.The method is based on the usage of metrics: feature volume of class boundary, nearest neighbour distances ratio of classes and as well as this -overstep of class boundary.
The experiments were performed with feature systems of PLP and LFCC, composing three data sets.The experimental results of feature quality estimation using the proposed method showed that PLP is the quality feature system, as it gained the highest quality index.As well as this, Nearest neighbour classification error was calculated to validate the adequateness of the method.The lowest error was achieved for PLP feature system.Therefore, the highest quality index identifies the feature system with the lowest classification error In conclusion, the experimental results of feature quality estimation using the proposed method coincided with the results of quality estimation using the classification error.Therefore, the results of the experimental researches approbated the adequateness of the proposed method of quality estimation of speech recognition features.

Fig. 1 .
Fig. 1.Features quality estimation using the proposed method

Fig. 2 .
Fig. 2. Scheme of the method for establishing the quality feature system Euclidean distance between i  -centre of the i-th class and i n x -n-th sample of i-th class, i rradius of the sphere of i-th class,

Table 1 .
Nearest neighbour classification error