1 Introduction
1.1 Problem Statement
The term CAPTCHA stands for “Completely Automated Public Turing" test to tell "Computers and Humans Apart” and was invented by von Ahn et al.[1]. The current CAPTCHAs can be categorized into three categories: Textbased CAPTCHAs [2,3], Imagebased CAPTCHAs [4,5] and Soundbased CAPTCHAs [6,7,8
]. Since CAPTCHAs can individuate between humans and computers with high probability, they are applicable for many various security applications such as preventing bots from voting in online polls, signing in for multiple of spam email accounts, buying tickets to buy an event by itself, etc. A web user has to properly put down the characters on the screen to be able to pass a common visual CAPTCHA. Although some of the CAPTCHAs have been broken by machine learning techniques [
9,10], there are still plenty of them actively secure against attacks. Due to improper visual entries of this type of CAPTCHA, audio CAPTCHAs were invented. A usual audio CAPTCHA consists of single or multiple talkers saying words or digits at some randomly selected time periods. A web client has to properly diagnose the digits or characters pronounced in the audio file to elapse the CAPTCHA.In this research, we used RASTAPLP features and SVM classifier to recognize audio CAPTCHAs. According to our tests, we reached
accuracy for individual digit recognition precision, and aroundaccuracy for the entire digit recognition. We provide a classification algorithm to recognize the digits in the data files and obtain the best accuracy via SVM classifiers using Principle Component Analysis (PCA). In regarding of this goal, we compare our results with non PCA Naive Bayes and default SVM classifier.
1.2 Metrics
We used two different measurements the first one is the digit success considering the digits are independent of each other, and the second one is the success of complete recognition of all these digits in the test file where they are usually varying between 4 and 6.
For example, assume that an audio file with a ground truth value of is successful on the second measurement if and only if the file recognized it as , that is,
(1) 
Otherwise it will be considered as a failure. However, the digit success measurement is more complicated than the other one. We used Dynamic Time Warping (DTW) algorithm to be able to measure the difference between the order of digit and the order of ground truth digit. In the following sections, we will mention some basic knowledge about DTW and will explain how it helped us to obtain better results.
DTW [11] is an algorithm that calculates an optimal warping path between two time series. The algorithm calculates the distance among two time series and the warping route values between them. The most common used technique for distance is the Euclidian distance between two data elements but we consider the Dirac delta function as our metric. Let’s consider the example at the begining of this section again as given by two audio file with a ground truth value of . That results in a matrix of distances having n lines and m columns of general term so our first performance metric is given by
for and the entire prediction accuracy is given by
(2) 
where is the total number of test elements.
On the other hand, the minimal distance matrix between sequences is determined using a dynamic programming algorithm and the following optimization process:
(3) 
where is the minimal distance between the subsequences and . A warping route is the route along minimal distance matrix from to including those elements that consist of the distance. The global warp cost of the two sequences can be formalize by
(4) 
where belongs to warping path, and is the number of them.
The difference function of Dirac delta is
Hence, the final calculated value of the cost function of
will give us how many digits are NOT equal each other. Therefore the second evaluation metric is the individual digit accuracy must be given by
(5) 
That is, is the total length of digit of the element, and is the sum of the incompatible digit length.
Roughly speaking, DTW shrinks between two number or string arrays to find the best match. For example, if the number array 123456 was predicted as 2456, then the prediction array would actually overlap with the first array as 2456 where stands for the incorrect predictions of the digits. It is easy to see that since 1 and 3 wasn’t predicted correctly, we will say the difference between these two number arrays is 2 and the accuracy of the prediction is or 66%.
2 Analysis and Algorithm Techniques
2.1 Data Exploration
We provide features from the audio CAPTCHA and use SVM classifier to perform automatic speech recognition on segments of the sample files to elapse the audio CAPTCHAs. There exist several wellknown methods for extracting specifications from audio files. The technique that we used here is relative spectral transformperceptual linear prediction (RASTAPLP). By using RASTAPLP, we could be able to train our classifiers to identify words and digits all by itself of who pronounce them.
In [12,13], authors used both PLP and RASTAPLP could identify particular digits during the existence of noise. However, the noise originating from telephone or microphone tapes in various scenes. In our sample files, we also add vocal or music noise that makes the problem more challenging. In [10] Chellapilla et al. struck over how many visual CAPTCHAs can be elapsed by successfully separating the challenge into two minor subchallenges as segmentation and recognition. Tam et al. [7] analyzed the security of audio CAPTCHAs from popular Web sites by using AdaBoost, SVM, and kNN, achieved correct solutions for test samples with accuracy up to . In addition, the same group at [14] analyzed the security of obtaining audio CAPTCHAs and provided a description and analysis of a new and improved audio CAPTCHA.
In this problem, we gathered 900 audio CAPTCHAs from various websites: google.com, digg.com, and recaptcha.net. Each of the CAPTCHAs annotated with the information regarding digit locations provided by the manual transcriptions. For each type of CAPTCHA, we randomly selected 800 samples for training and used the remaining 100 for testing set. The trained samples have been labeled manually one by one. First, we divide the audio file into segments of noise or words to be able to reveal the audio CAPTCHA. In the test files, the words include digits.
Next, we manage to identify where the locations of the digits in the CAPTCHA file starts and finishes. In 800 trained audio files, the digits 0,1,2,…,8,9 were mentioned loudly 627, 536, 555, 593, 552, 505, 662, 537, 637, 533 times, respectively. Furthermore, all the conversations, where a digit never been pronounced or random noise moments elapsed, have been determined as
class. We manually obtained 27718 segments of moments which belong to the class in the training set.We can see in Figure 1, a sample audio file is displayed in the time domain and in the frequency domain. In the time domain, the labels of the digits are also shown. In Figure 2, 04648 is pronounced in the sample file. As you can see, many nonnumeric regions resemble those in the time domain and the frequency domain. There may be periodic and random noisy background speeches that make automatic identification difficult in nondigitized places.
2.2 Algorithms and Techniques
The Matlab functions for extracting features were published and distributed worldwide at [15] and as part of the Voicebox package. We utilize SVM algorithms to carry out automatic digit recognition. We will explain our performance in detail.
The benefits of using SVM library on Python Scikitlearn is that they allow the immediate training of high amount of linear classifiers. Another advantage of SVMs is that they can be kernelled to solve nonlinear classification tasks conveniently. The main idea of kernel method to handle linearly inseparable data is to build nonlinear combinations of the basic features to project them on to a higher dimensional space via mapping a function that will be linearly separable. To solve SVM problems, we need to transform our training set on to a higher dimensional feature space using the function and train a linear SVM model to classify the data in our new feature space. Therefore, we may use that same to transform the unknown data to classify it by linear SVM model.
For our problem, we divide the files of the training set into 11 separate classes as 0, 1, 2, … , 9 and the noise class. We mentioned in Section 3 how many data points we have from each class. Then we extracted the features of these audio signals by using RASTAPLP. As a feature of RASTAPLP we obtained dimensional feature space. In this number of dimension, 13 is the number of RASTAPLP coefficients and 42 is the number of sliding windows that is, every digit have been scanned by 42 sliding windows, and then 13 coefficients have been calculated from each sliding window. Once we calculated the RASTAPLP coefficients of the digits where they belong to the generated 11 classes, we apply PCA to reduce dimensionality, and then we made a classification using multiclass SVMs.
Henceforth, an existing test audio file has been fragmentized into sliding windows as we did for the training files before. Then, it has been extracted 546 RASTAPLP features for each sliding window and we used PCA to reduce the dimensionality and SVM to classify these reduced number of features. If the output of the classification results a digit from 0 to 9, then we assigned it as an element of the digit class. Otherwise, if the output results a noise or an awkward silence, then we assigned it as an element of the socalled class.
SVMs are supervised machine learning algorithm that can be used for both classification and regression problems. For a determined multiple classes of labeled data, SVMs perform as a distinctive classifier via defining an optimal hyperplane(s) that seperate(s) all classes.
For a given training dataset of n points of the form, assume that the dataset can be linearly separable. Then,
(6) 
where indicates the class if the point belongs to it. The objective is finding the maximummargin hyperplane that divides the class of points where from the class of points where . The equation of any hyperplane can be written as
(7) 
where is the normal vector to the hyperplane.
Since we are dealing with a nonlinear classification, the clever way to obtain the classifier is using a kernel trick which applied by Aizerman et al. aizerman1964theoretical
originally. We will use the Gaussian radial basis function where
(8) 
for
The optimization problem for the hard margin, which is the distance from the hyperplane for the SVM’s decision boundary to the nearest training data point, SVM can be shown by
(9) 
subject to
(10) 
This problem essentially explains us to maximize the margin, while assuring to classify each sample safely and correctly. In practice, it is very hard to apply it, and since our data is not linearly separable, the optimization problem won’t give us a solution for parameters such as and . To deal with this problem, we introduce slack variables such that they allow us to classify each training sample safely and correctly.
Usually, slack variables are represented by and indicates how much we need to move our sample point in order to classify it safely and correctly. Then we penalize the objective function once we use slack variables, or else we assign the slack variables as high as we can and solve the optimization problem and obtain the following solution:
(11) 
subject to
(12) 
where
is the hyperparameter which tests how much we could penalize the usage of slack variables. The process is basically a tradeoff between penalizing slacks and attaining a large margin for the SVM. That is, if we set
(13) 
then we won’t penalize the slack variables, and conversely, once we increase the value of , we further penalize the slack variables. In our model, is the penalty parameter and we took default values for the rest of the SVM parameters.
We used Gaussian RBF in this problem that is very powerful method since we can transform the inner product with the kernel function . We may assuming that is from the training set and is from the testing set. The value of the kernel depends on the distance between vectors and measures the similarity between two data points. Since is an infinite dimensional space the kernel corresponds to a feature space transformation onto an infinite dimensional space. The hyper parameter
manages the tradeoff between the error because of bias and the variance in our model. The larger
value implies the smaller value, even though our input vectors have higher similarity. If the value is unnecessary large, then we have a big risk of overfitting and prone to high variance. Conversely, a smaller value leads that the vectors (support vectors) have stronger effect on the vectors (classification vectors).We used SVM with Radial Basis Function and separate the dataset into multiclass SVMs by one to one diagram. We did not take a constant penalty parameter where , we explored the optimum penalty parameter by applying cross validation. Moreover, we used Naive Bayes algorithm as a baseline model to compare the performances wit our proposed model.
The proposed model has two independent variables as the coefficient of penalty of SVM and the variance parameter of the PCA. These two values were tuned in the train set by crossvalidation. We obtained as optimum values of Penalty Parameter = 50, PCA Var = 0.9 and we decided to use tese particular coefficients when we implement our proposed model.
2.3 Benchmark Model
Without using PCA, we consider naive bayes method and SVM as benchmark models to compare our proposed model. Naive Bayes methods are a set of supervised learning algorithms based on applying Bayes’ theorem with the naive assumption of independence between every pair of features. These classifiers have worked well in many problems, such as text classification and spam filtering. They do not require a large amount of training data to estimate the involved parameters. Naive bayes method can be faster than SVMs when you compare them. On the other hand, although they are know as a smooth classifiers we can not say they are good estimator. Thus, we applied PCA to our SVM algorithm.
3 The Methodology of our Model
3.1 Data Preprocessing
In the proposed algorithm, preprocessing is used to determine the phonemes that are likely to be digitized. Therefore, there is no need for a preprocessing step in the train set, since the starting points for each digit set plus the nondigit set of are manually set. When extracting the features of the test set, it is necessary to automatically determine the regions that are likely to be digitized. Because now nobody has the possibility to run these zones manually. We implemented a preprocessing algorithm for this. During this preprocessing phase, the test audio signal is read, 0 is averaged, the signal’s energy is calculated, and then the 100point mean running average of the energy signal is calculated. The smoothed energy sequence is then run to determine the start of the potential digit regions with some hard thresholding operation. For this, the smoothed energy sequence is called cluster 1 for large parts from 0 to some degree (larger than 0.00001), and cluster 2 for parts smaller than 0.001. Then all the startend point pairs are calculated for the potential digit blanks that start with the element of cluster 1 and end with the element of cluster 2.
In Figure 4, we give the graph of the smoothed signal calculated for the sample audio file and showing the potential starting points.
3.2 Implementation & Refinement
We tested the accuracy of audio CAPTCHAs used by popular machine learning techniques algorithmically planned to break them.
Two different measurements were used for the accuracy of the classification. First, we considered the digits independently to obtain accurate digit prediction. Secondly, we measured the prediction accuracy of the digits where they are usually varying between 4 and 6 for the test files. We operated DTW algorithm to perform the difference between the ground truth and predicted digits.
For feature extraction we use RASTAPLP speech analysis [
17] by applying the following steps:
Calculate the crucialband spectrum (as in the PLP) and take its log.

Approximate the temporal derivative of log crucialband spectrum using 4 consecutive spectral values.

Apply SVM as nonlinear classifier for threshold filtering.

Integrate log crucialband temporal derivative.

According to ordinary PLP, add equal noise and multiply by 0.33 to create the power law of hearing

Operate exponential function of this log spectrum to produce audio spectrum.
To reduce the dimensionality, we used PCA since redundancy were growing as the dimension of the data increased. PCA is one of the most common method to utilize dimensions by transforming them to a new space. We applied kfold cross validation (in this case ) to decide the dimension for the usage of the classifier and found the optimum penalty parameter for the SVM algorithm. The variance parameter used by the PCA algorithm and the kfold cross validation of the train set were used to determine the best value of the penalty parameter that the SVM algorithm would need.
When subtracting the features of the train set, a signal of 0.4 seconds is taken from each digit, plus the manually set start point for the nondigits of the eleventh set. It is assumed here that each digit is read and finished in 0.4 seconds, which is quite sufficient. This signal is divided into 42 sliding subwindows that overlap 50% and 13 randomplp coefficients of each subwindow are calculated. Then these coefficients are combined for 42 sub windows to obtain feature vectors. Now an audio domain, labeled as one of 11 classes, is now expressed in 546 numbers, so its features have been extracted.
Before we extract the features of a test element, the data preprocessing determines the potential start point of the audio block. Then, from each starting point, another 0.4 second segment is taken and divided into 42 sliding windows overlapping 50% in the same way as train data. 13 randomplp coefficients of each subwindow are calculated. Then, these coefficients are combined for 42 subwindows to obtain feature vectors. We now have a 546length feature vector of this potential phoneme. This 546length vector is classed according to the method to be applied and is determined to be one of class according to the output of the method. Refinement executed by conducting cross validation so as to determine the most optimum values of PCA variance and Cvalue.
4 Numerical Results and Statistics
4.1 Model Evaluation & Validation
The 4fold cross validation was applied to the train set to determine the best value of the penalty parameter that the SVM algorithm would need with the variance variable used by the PCA algorithm. According to our algorithm, the entire train set is divided into 4 parts randomly, one part is tested and the remaining 3 parts are accepted as train. The system is trained with the given parameters, then the digit performance for the set determined. In this study, we used 11 different penalty parameters of 1, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, and 7 different penalty values of 0.25, 0.5, 0.6, 0.7, 0.8, 0.9, 0.99 where for each penalty value we used the value of the variance representation. As a result, 4fold validation was performed separately for 77 different parameters and the validation success was calculated for each case.
The Table 1 shows that the calculated validation accuracies for the varying penalty parameter and PCA variance. As you can see from there, the highest validation success was calculated for Penalty Parameter = 50, PCAVar = 0.9.
Penalty Parameter  

PCAVar  1  10  20  30  40  50  60  70  80  90  100 
0.25  0.4591  0.4641  0.4655  0.4656  0.4658  0.4669  0.4672  0.4672  0.4671  0.4674  0.4674 
0.5  0.7808  0.8281  0.8338  0.8331  0.8339  0.8350  0.8344  0.8347  0.8339  0.8337  0.8335 
0.6  0.8487  0.8924  0.8937  0.8919  0.8910  0.8882  0.8877  0.8889  0.8881  0.8881  0.8872 
0.7  0.8914  0.9240  0.9205  0.9189  0.9183  0.9166  0.9158  0.9156  0.9155  0.9150  0.9155 
0.8  0.9058  0.9372  0.9364  0.9352  0.9331  0.9323  0.9314  0.9312  0.9315  0.9313  0.9312 
0.9  0.8894  0.9418  0.9428  0.9421  0.9406  0.9478  0.9374  0.9371  0.9362  0.9362  0.9353 
0.99  0.8627  0.9360  0.9311  0.9316  0.9323  0.9318  0.9367  0.9366  0.9368  0.9373  0.9368 
Class  Naive Bayes  Default SVM  Proposed SVM 

0  0.8787  0.8867  1.0000 
1  0.8712  0.9738  1.0000 
2  0.8108  0.6108  0.9945 
3  0.8735  0.9005  1.0000 
4  0.9275  0.9565  1.0000 
5  0.9188  0.9524  1.0000 
6  0.5090  0.2143  0.9864 
7  0.8994  0.9143  1.0000 
8  0.6452  0.5635  0.9497 
9  0.9193  0.9418  1.0000 
Other  0.7234  0.9985  0.9993 
Type  Naive Bayes  Default SVM  Proposed SVM 

Digit Accuracy  0.4213  0.9220  0.9809 
Captcha Accuracy  0.0000  0.4400  0.8900 
5 Conclusion
5.1 Reflection
The Naïve Bayes method correctly identifies about 42% of the test digits. This method also failed because every class element in the train set is not balanced because the train set has a large number of noise class ( class) elements, while the elements from 0 to 9 are somewhat less. None of the 100 audio files in the test set were fully recognized by Naïve Bayes method. Since the number of elements is not balanced, even though the classes from 0 to 9 a are partially recognized even in the train set, the noise class has a relatively low success rate of 71%. This is why all test audio files are not recognized without error, yet even if a section is wrongly assigned to the noise class, it means that the test element is misclassified
On the other hand, when the default number of SVM elements is unstable, it has succeeded in achieving 92% independent digits, but only 44% of the test elements have been achieved. With the parameter we have optimized, the recognition of the complex chaptche sound file has reached 89%. Independent digit success has reached a very good value of 98%.
We applied 3 different algorithms naive bayes (no PCA), default SVM (no PCA) and SVM (with PCA) to optimize the parameters as promised. The naive bayes method failed because each class element in the train set was not balanced. Because there are a large number of noise classes in the train cluster, the elements from 0 to 9 are somewhat less. None of the 100 audio files in the test set were fully recognized by Naïve Bayes.
5.2 Improvement
We have accomplished in decoding a certain type of audio CAPTCHAs by machine learning techniques. It is obvious that our results can be improved by rearranging appropriate segments and algorithms. We have proved that our approach is is working out and might be used with various different audio CAPTCHAs that involve finite conversations and noise.
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