2.1 Arabic Vocabulary

Arabic is the language spoken by original Arabs. It counts more than 445 million speakers, ranked the 4^th in the number of speakers and the 8^th in the number of pages that circulate on the Internet [¹].

On the one hand, and with its morphological and syntactic properties, Arabic is considered difficult to non-native learners in the area of automatic language processing [²]. On the other hand, degradations contained in produced speeches increase this difficulty. Consequently, the introduction of other means to facilitate the comprehension of defective Arabic discourses presents a necessity. Then the automatic correction of pathological speeches will take place.

2.2 Domains of Application

Human-machine communication environments provide the accessibility to information through different modes (keyboard, gestures and voice commands) according to the preferred and/or adequate manner for each user. Voice communication between humans and machines can intervene in different practical areas. We can mention:

Despite diversity of practical applications involving voice human-machine communication, we mention that several factors prevent an effective dialogue. We distinguish:

An erroneous pronunciation can falsify information submitted to the machine which increases the difficulty of a good communication and even falsify the desired results. Therefore, the solution is to introduce a pathological speech corrector in the machine whose functionality is to adjust received data before their treatments.

2.3 People with Language Disabilities

The statistics of the World Health Organization show that 12% of the international population (700 million people) suffers from pathologies where the voice disability is on top of the list with 30% of this population [⁴]. Thus, the user can communicate with the machine only after adapting this latter to consider the speaker to produce a defective speech. Consequently, the introduction of a speech correction means can provide confidence and safety to the obtained results of communication. In Table 1, we mention the percentage of each disability.

As a recapitulation, the voice communication environments are characterized by:

Hence, the introduction of the means whose target is to detect and correct the mispronunciations contained in Arabic discourses (voice commands) can exceed these limits.

4.1 Voice Defect Detection

4.1.1 Probabilistic-Phonetic Model Generation

For this finality, an acoustic model and a large base of healthy Arabic speech are required. After that, this base is preprocessed; frames representing noise and non-Arabic words are suppressed. The next step consists in utilizing the Sphinx-align tool to calculate the vector summarizing the appearance probability of each Arabic bi-phoneme. The resulting vector forms the phonetic model referring to healthy Arabic speeches.

4.1.2 Scalar Product in ℜⁿ

The scalar product in ℜⁿ, noted by <x|y>, is the function which associates to the vectors x=(x₁, x₂, x_n)εℜⁿ and y=(y₁, y₂,…y_n) εℜⁿ the quantity:

This quantity can also be expressed as follows:

We note by:

- θ the angle which separates the two vectors x and y,

- ∥x∥ the norm of the vector x, ∥x∥=x12+x22+…+xi2+…+xn2

- ∥y∥ the norm of the vector y, ∥y∥=y12+y22+…+yi2+…+yn2

Consequently, we can deduce that:

If we can generate a vectorial representation in ℜⁿ for each produced speech signal, angle θ (equations (1) and (2)) can be used as a measure of similarity between the speech signals represented by these vectors. Indeed, the similarity between different acoustic signals is proportional to the angular distance (angle θ) which separates between the representative vectors.

4.1.3 Phonetic Distance

In this work, the notion of phonetic distance is invented for the first time. It describes the angular distance that separates two different phonetic models. In order to calculate the phonetic distance, n healthy speech bases are required. These bases are treated as follows:

4.1.4 Speech Classification

Each input speech undergoes two different decisions; it will be classified into healthy or pathological. The generated decision depends on the phonetic distance θ which separates between the probabilistic-phonetic model referring the healthy Arabic spoken vocabulary and the model characterizing the input speech recorded by a new speaker (native, non-native, healthy, with voice anomalies). Two cases are envisaged:

4.2 Correction Procedure

Correction procedure is based on two fundamental tasks. The first consists in identifying the problematic sounds (sounds begetting the voice anomalies and replacement ones). Based on identified phonemes in the first task, the second one will be dedicated for the matching between problematic sounds to generate the correct pronunciation corresponding to each faulty one.

4.2.1 Problematic Sound Identification

The current procedure will be applied only if the input acoustic signal contains voice anomalies and classified as defective. The proposed algorithm of identifying problematic sounds generates two main phoneme categories (substituted phonemes and substituent ones).

4.2.1.1 Substituted Sounds

This category of sounds prevents the correct pronunciation and presents the source of voice anomalies for the concerned talkers. The suggested algorithms whose aim is to identify these sounds are based on the hypothesis considering that one substituted phoneme does never figurate in the phonetic transcription summarizing the input speech. Accordingly, all coefficients of probabilistic-phonetic model corresponding to bi-phonemes containing a faulty produced sound will be equal to zero.

On the basis of the previously mentioned hypothesis, a simple comparison between the probabilistic-phonetic model referring to the Arabic healthy speech and the probabilistic-phonetic model proper to speaker can lead to the extraction of sounds posing degraded speeches. Figure 2 illustrates the obtained results for one practical case where the speaker suffers from the pronunciation of the Arabic sounds "خ/x” and "ؾ/q".

4.2.1.2 Substituent Sounds

This subsection treats the objective of identifying substituent sounds. These latter are phonemes that are pronounced instead of substituted ones. This finality is based on the hypothesis considering that the sum of occurrence probabilities of bi-phonemes containing substituted sounds will be distributed to bi-phonemes covering replacement sounds. Therefore, all coefficients of the probabilistic-phonetic model covering bi-phonemes containing a substituent sound will present a remarkable increase compared to the referenced probabilistic-phonetic model. Figure 3 shows the obtained results for the previous example (in Figure 2):

Fig. 2 An example of identification of substituted phonemes 

Fig. 3 An example of identification of substituent phonemes 

4.3 Defective Speech Correction

In this subsection, we give details of the proposed algorithms addressing the correction of pathological speeches. We distinguish two different correction procedures according to the type of pathological speech to be corrected: homogeneous or heterogeneous classes of defective speeches.

4.3.1 Correction of Homogeneous Classes

4.3.1.1 Procedure

Homogeneous classes cluster the pronunciations containing just one faulty pronounced phoneme in each one. The correction of one defective pronunciation contained in a homogeneous class necessitates just one possible substitution of the replacement phoneme, which appears in this pronunciation by one of the substituted phonemes. The correction of mispronunciations contained in this class follows Algorithm 1:

Algorithm 1 Correction of homogeneous class of defective pronunciations 

4.3.1.2 Practical Examples

First Example

Let us take the example of the correction of the pronunciation “”, where:

On the basis of the proposed solution in Algorithm 1, and applying possible matchings between problematic sounds, the pronunciation “” (planning) is calculated as a correct one which corresponds to the input elocution. The colored pronunciation in Figure 4 presents the accepted one (the other pronunciations are not accepted because they do not belong to the Arabic lexicon).

Fig. 4 Correction of the Arabic mispronunciation “فظط” 

Second Example

Let us take the correction of the badly pronunciation "", considering the following conditions:

Supporting Algorithm 1, we have obtained the tree as shown in Figure 5. The pronunciation “” (chair) (the colored pronunciation) is calculated as the correct one, which corresponds to the badly input elocution.

Fig. 5 Correction of the Arabic mispronunciation "ݢں ٸ" 

4.3.2 Correction of Heterogeneous Classes

Dissimilar classes assemble the mispronunciations covering more than one badly pronounced sound in each one. The correction of a pronunciation contained in a heterogeneous class requires (n+1)^m-1 substitutions between the substitute phonemes that appear in this pronunciation and the substituted phonemes. In order to facilitate the management of these matchings, we introduce for this treatment the decision trees. We note by:

In this class, the correction of badly pronunciations is based on Algorithms 2 and 3.

4.3.2.1 Tracing Algorithm

In order to be able to manage the very high number of substitutions between substituted phonemes and substituent ones, we propose a probabilistic-tree structure; the nodes are labeled by the phonemes and the arcs connecting these nodes are weighted by the probabilities of occurrence of the bi-phoneme [Phoneme Father-Phoneme Son].

We suggest the tracing procedure to ensure drawing the probabilistic-tree representing all possible pronunciations coming from the faulty input one:

Algorithm 2 Tracing algorithm 

4.3.2.1 Routing Algorithm

After drawing all possible pronunciations coming from the badly input one, the routing procedure will be used in browsing the probabilistic-tree and in calculating the list of Arabic words that correspond to the falsely pronounced ones. Details of this algorithm are as follows:

Algorithm 3 Routing algorithm 

4.3.2.1 Practical Examples

First Example

Let us take the correction of the badly pronunciation “”, considering the following conditions:

In the current case, the badly pronunciation "ۺ؍ڭ" contains the substituent sounds “ٽ” and “ك” Applying the possible substitutions, the tracing algorithm will generate the probabilistic-tree as depicted in Figure 6:

Fig. 6 Correction of the Arabic mispronunciation "ۺ؍ڭ" 

We apply thereafter the routing algorithm to find two correct pronunciations, accepted by the Arabic lexicon, “” (the orient) and “” (polytheist). The adequate correction from the obtained ones is the pronunciation following the same rhyme compared to the input badly pronounced one. The other pronunciations are not accepted by the reference lexicon, so they are not selected.

Second Example

Let us take the correction of the badly pronunciation “”, considering the following conditions:

In this case, phonemes "ح" and "ث" appear in the bad pronunciation “ﺨﺁﺰﺌﺔ”. Based on possible substitutions, the tracing algorithm will generate the probabilistic-tree detailed in Figure 7.

Fig. 7 Correction of the Arabic mispronunciation  

Applying the routing algorithm, we find two possible correct pronunciations “” (conclusion) and “” (smoothness). They are accepted by the Arabic lexicon. To select the adequate correction from the obtained ones, we can utilize semantic analysis. It may be possible also to choose the correction with the pronunciation rhyme similar to the input mispronunciation. The other pronunciations are not chosen because they are not accepted by the reference lexicon.

Third Example

Let us take the correction of the badly pronunciation “”, considering the following conditions are:

The falsely pronunciation "" contains the two phonemes "ح" and “ث” Applying the possible substitutions, the tracing algorithm will generate the probabilistic-tree illustrated by Figure 8.

Fig. 8 Correction of the Arabic mispronunciation  

Thus, we apply the routing algorithm to obtain the correct elocution "" (tortoise) (the colored pronunciation) corresponding to the input falsely pronounced one.

5.1 Data of Tests and Obtained Results

In order to test the proposed method, a large base of Arabic healthy and pathological speeches is required. For this finality, we collaborate with all members of our laboratory¹ to collect 14 hours of pathological speeches and 6 hours of healthy speeches. The collected base covers different areas like technology, education, economy, sports, sciences, migration and politics. The results of pathological speech correction are detailed in Table 2:

Table 4 Arabic to IPA mapping (vowels) 

Arabic vowels	IPA symbol	English approximation
	a	man
	i	him
	u	put
اَ, ى	a:	car
يَ	i:	sheep
وُ	u:	rule

Table 5 Transliteration of pronunciations used in this paper 

Pronunciations used in the example depicted in Figure 4

Pronunciations used in the example depicted in Figure 5

Pronunciations used in the example depicted in Figure 6

Pronunciations used in the example depicted in Figure 7

Pronunciations used in the example depicted in Figure 8

The obtained results, shown in Table 2, present the efficiency of our pathological speech corrector. Figure 9 depicts the speech classification and the defective speech correction rates for each gender and for each type of speeches (healthy and pathological).

Fig. 9 Speech classification and defective speech correction rates based on our methodology 

5.2 Discussion and Limits

Table 2 presents some misclassifications; i.e. a healthy speech classified as a pathological one and vice versa. These bad classifications can be due to the following reasons:

Sometimes the algorithm of defective speech correction generates several possible correct pronunciations for a single erroneous pronunciation. In such a case, semantic analysis is required to select the adequate correction. We also notice that the problematic phonemes for the same speaker are often clustered in the same category (hissing, emphatic, Occlusive, fricative, nasal, etc.)