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405\begin{document}
406\title{Using Convolutional Neural Networks to Distinguish Different Sign Language Alphanumerics}
407
408\author{Stephen L Green, Ivan Y. Tyukin, Alexander N. Gorban% <-this % stops a space
409\thanks{Stephen L. Green is with the University of Leicester, University Road, Leicester, Leicestershire (phone: 07760889686; e-mail: slg46@le.ac.uk).}
410\thanks{Ivan Y. Tyukin is with the University of Leicester, University Road, Leicester, Leicestershire (phone: 01162525106; e-mail: it37@le.ac.uk).}
411\thanks{Alexander N. Gorban is with the University of Leicester, University Road, Leicester, Leicestershire (phone: 01162231433; e-mail: ag153@leicester.ac.uk}}
412
413% The paper headers
414\markboth{Journal of \LaTeX\ Class Files,~Vol.~6, No.~1, January~2007}%
415{Shell \MakeLowercase{\textit{et al.}}: Bare Demo of IEEEtran.cls for Journals}
416
417\maketitle
418\thispagestyle{empty}
419
420\begin{abstract}
421%\boldmath
422Within the past decade, using Convolutional Neural Networks (CNN)’s to create Deep Learning systems capable of translating Sign Language into text has been a breakthrough in breaking the communication barrier for deaf-mute people. Conventional research on this subject has been concerned with training the network to recognize the fingerspelling gestures of a given language and produce their corresponding alphanumerics.\\
423One of the problems with the current developing technology is that images are scarce, with little variations in the gestures being presented to the recognition program, often skewed towards single skin tones and hand sizes that makes a percentage of the population’s fingerspelling harder to detect. Along with this, current gesture detection programs are only trained on one finger spelling language despite there being over two-hundred known variants so far. All of this presents a limitation for traditional exploitation for the state of current technologies such as CNN’s, due to their large number of required parameters.\\
424This work aims to present a technology that aims to resolve this issue by combining a pretrained legacy AI system for a generic object recognition task with a corrector method to uptrain the legacy network. This is a computationally efficient procedure that does not require large volumes of data even when covering a broad range of sign languages such as American Sign Language, British Sign Language and Chinese Sign Language (Pinyin). \\
425Implementing recent results on method concentration, namely the stochastic separation theorem, an AI system is supposed as an operate mapping an input present in the set of images $u \in U$ to an output that exists in set of predicted class labels $q \in Q$ of the alpha numeric that q represents and the language it comes from. These inputs and outputs, along with the interval variables $z \in Z$ represent the system's current state which implies a mapping that assigns an element $x \in \mathbb{R}^n$ to the triple ($u$, $z$, $q$). As all $x_i$ are i.i.d vectors drawn from a product mean distribution, over a period of time the AI generates a large set of measurements $x_i$ that are grouped into two categories: the correct predictions $M$ and the incorrect predictions $Y$.\\
426Once the network has made its predictions, a corrector can then be applied through centering S and Y by subtracting their means. The data is then regularized by applying the Kaiser rule to the resulting eigenmatrix and then whitened before being split into pairwise, positively correlated clusters. Each of these clusters produces a unique hyperplane and if any element x falls outside the region bounded by these lines then it is reported as an error.\\
427As a result of this methodology, a self-correcting recognition process is created that can identify finger spelling from a variety of sign language and successfully identify the corresponding alphanumeric and what language the gesture originates from which no other neural network has been able to replicate.
428\end{abstract}
429\begin{IEEEkeywords}
430Convolutional Neural Networks, Sign Language, Deep Learning, Shallow Correctors.
431\end{IEEEkeywords}
432\IEEEpeerreviewmaketitle
433\section{Introduction}
434\IEEEPARstart{S}{}ign language classification using neural networks has been a goal of data scientists since the start of the decade. Many papers exist on the subject and using Convolutional Neural Networks, each gesture can be assigned classes for the network to predict making them behave like most other iterations of CNN's. The direction that Sign Language recognition has focused on prioritises the correct identification of singular letters and numbers in an assigned language over whole words. This process called Fingerspelling is very appealing to classify as there are only the 26 letters of the alphabet and the ten numerical digits to categorise over the thousands of words that exist in any given sign language dictionary.\\
435The implications of a technology that could read sign language and convert the results into text would be a huge leap forward for communication of the deaf and hard of hearing. A study conducted by the World Health Organisation \cite{IEEEhowto:kopka} states that about 466 million people in the world suffer from hearing loss (with 34 million of these people being children) and 70 million of these people are adept in Sign Language. This number is split between over two hundred known variants of Sign Language practiced all over the world \cite{IEEEhowto:clarion}. Some of the difficulties of Sign Language detection is due to similarities over other types of gesture recognition is the similarities between poses. Changes that would otherwise be ignored in full body detection such as the placement of a thumb or the angle the hand makes with the wrist can change the meaning of the gesture being conveyed. This is why the majority of papers focus on specialising in the alphanumerics of one sign language.\\
436With this paper, the gesture sets for American Sign Language (practised by about half a million people in the United States)\cite{IEEEhowto:asl}, British Sign Language (practised by about one hundred and fifty thousand people in the United Kingdom)\cite{IEEEhowto:bsl} and Chinese (Pinyin) Sign Language are fed into the Inception neural network and an algorithm is created that can recognise all three languages. An error corrector is then appended to the results so any misclassification produced by Inception can be detected and amended before final output. This combination provides a neural network that is able to read multiple sign languages that is both fast and accurate.
437\section{Previous Literature}
438%\begin{figure}[h]
439%\centering
440%\begin{subfigure}{.25\textwidth}
441%  \centering
442%  \includegraphics[width=.8\linewidth]{Gloves.png}
443%  \caption{Motion Gloves \cite{IEEEhowto:gloveexample}}
444%  \label{fig:sub1}
445%\end{subfigure}%
446%\begin{subfigure}{.25\textwidth}
447%  \centering
448%  \includegraphics[width=.97\linewidth]{Kinect.png}
449%  \caption{Microsoft Kinect \cite{IEEEhowto:kinectexample}}
450%  \label{fig:sub2}
451%\end{subfigure}
452%\caption{The most common examples of gesture tracking in current literature, both glove based and vision based.}
453%\label{fig:test}
454%\end{figure}
455The two most popular categories of gesture recognition are with glove based systems and vision based systems. Glove based methods \cite{IEEEhowto:glove} have the advantage of being able to record every slight motion that the user makes that provides the specifics of the flex motion the hand is making along its tracjectory, overcoming the problem of movement based gestures that exist especially outside of sign language. They are also able to provide very accurate results, with a test of 5113 unique words in Chinese Sign Language giving an average accuracy of 91.9\% on this large vocabulary \cite{IEEEhowto:glove2}. The problem is that this method is cumbersome. Motion detection gloves are currently very expensive and are not recommended for everyday interactions with the hard of hearing. There is also a link that needs to be maintained between the gloves and the computer for the gestures to be captured effectively. There are examples of this being done wirelessly but this connection still needs to be maintained and therefore impractical for the required kind of of simultaneous translation this project needs.\\
456Vision based system often require devices such as the Microsoft Kinect which is able to track the positions of hand gestures relative to the human body with similar accuracy rates to gesture capture using gloves\cite{IEEEhowto:kinect}. Both of these methods however are impractical for this project so instead all gestures in the dataset were filmed with a Samsung Galaxy S8 camera. The video files were then split into images and this is what has made up the dataset.\\
457With one notable exception \cite{IEEEhowto:MultiSign}, The idea of a multi-language detection system has not been mentioned in the existing literature. The most likely reason is that current research dedicated to just one widely used language is already computationally expensive. Even the most basic alphabet fingerspelling recognition networks require large datasets to train on to receive good results and these sets only exist for a handful of known sign languages \cite{IEEEhowto:Multiplesets}.
458The appended error correction program is a continuation of our previous work \cite{IEEEhowto:OurPaper} where Inception is run on the American Sign Language signs for 0-9. The results of the initial experiments was a correct classification rate of 82.4\% on 10000 tested images. After the images were split into a training and testing set with a 4:1 ratio, the corrector was applied that was able to successfully remove misclassifications from the test set with very little change to the number of True Positive results that were falsely removed. The full algorithm is explained in Appendix A.
459\section{Implementation}
460\subsection{Pre-processing}
461For these experiments, Inception Version 3 was trained on 896000 RGB images covering 112 gestures filmed with multiple participants of varying age, gender and skin colour, with 8000 images for each respective gesture. Each image was taken with a Samsung Galaxy S8's front 8 megapixel camera with resolution 1920x1080, which are later resized to 299x299 when fed through Inception. Each image set represents the gesture taken at various angles and distances covering as many variations as possible where the camera is in front of the gesture at some angle. To mitigate the problem of background noise, each participant's gestures were taken in different locations so the only common element within each group was the gesture itself.\\ Conventional tracking software often requires the image to be within a certain distance from the camera for the sign to be detected while this method provide a plethora of images that can help detection regardless of which direction the camera is located when pointed at the sign. While the majority of static detection algorithms omit gestures that require movement (in this experiment, ASL J, ASL Z, BSL H and BSL J usually require motion), this work instead focuses on still images that are unique to the process of making the gesture and can be used to distinguish them from the rest of the set without the loss of an alphanumeric.
462\subsection{Architecture}
463The Inception model is a computationally efficient Convolutional Neural Network originally developed by Google in December 2015 to provide state of the art performance rates on the ImageNet Large Scale Visual Recognition Challenge \cite{IEEEhowto:InceptionExplain}. Unlike similar learning algorithms like VGGNet and AlexNet which use deep, wide networks to obtain high performance rates at the cost of long computation times which made these procedures much more impractical for computers with small processing power and lack of access to high-end GPU's, Inception utilises repeated modules to replicate these model's success at a quicker rate.\\
464%\begin{figure}[h!]
465%  \centering
466%  \includegraphics[width=\linewidth]{InceptionFramework.png}
467%  \caption{Inception framework}
468%\end{figure}
469\\
470The model starts with an 299x299x3 input corresponding to a 3 colour (RGB) channel square image with a size of 299 pixels that is processed through stacked Inception modules with five regular convolution layers along with a max pooling function and a softmax output that produces the predicted label for the input \cite{IEEEhowto:Inception}. Each module processes the correlation statistics of the layer before it and groups the clusters of units into filter banks \cite{IEEEhowto:InceptionFilter}. This results in a large percentage of units concentrated in single regions which can be covered with a 1x1 convolution preserving the original dimensions of the structure with minimal loss of information while other structures are fed through 3x3 or 5x5 filters depending on how spread out the clusters are (the operations through these larger filters will increase as Inception progresses once the spatial concentration decreases such that dimensionality needs to be reduced to compensate). A fourth pooling path is also included for outliers that have little to no relation to the rest of the data. Small 1x1 convolution filters are attached to the larger layers reducing the number of necessary calculations. These modules stacked in succession create a unique architecture that has 12 times less parameters and AlexNet and 36 times less parameters than VGGNet \cite{IEEEhowto:Inception}.
471\subsection{Training}
472The top layer of Inception is a softmax layer that takes a 2048-dimensional vector as an input called a bottleneck. With 112 labels, the sum of each of the weights and bias's necessary for Inception to be trained comes to 229,488 parameters that are learned in total \cite{IEEEhowto:Bottleneck}.\\
473Inception is then trained on the dataset of 896,000 images with a learning rate of 0.01 and 50000 training steps in total with a training batch size of 100 images. In total, 89600 images are used for testing, 89600 images are used for training and 716,800 images are used for training. Once these steps have been carried out, 448,000 images are given to the retrained Inception algorithm. For each image, the softmax layer takes the bottlenecks and produces a probability for each label that corresponds to the likelihood of that label correctly matching the given image according to what Inception has been trained on. The label with the highest respective probability is chosen as the final prediction made by Inception.
474\subsection{Post-processing}
475When each image has a predicted label attached toward it, a corrector can be appended to the current system that is able to detect incorrect labels and reassess them \cite{IEEEhowto:Corrector}. Each element is first sorted into with set $\mathcal{M}$ which contains each element with a correct label attached and $\mathcal{Y}$ which contains every element with an incorrect label attached along with their union $\mathcal{S} = \mathcal{M} \cup \mathcal{Y}$. The sets $\mathcal{M}^1=\mathcal{M}\text{, }\mathcal{Y}^1=\mathcal{Y}\text{ \& }\mathcal{S}^1=\mathcal{S}$ are then initialised, the number of clusters $p$ is chosen and the filtering threshold $\theta$ is set.
476\subsubsection{Centering}
477The data is first centered, where $\mathcal{S}^i_c\text{ \& }\mathcal{Y}^i_c$ are created by subtracting the mean $\overline{x}(\mathcal{S}^i)$ from the elements of each set respectively.
478\begin{center}
479$\mathcal{S}^i_c = \{\mathbf{x} \in \mathbb{R}^n | \mathbf{x} = \xi - \overline{\mathbf{x}}(\mathcal{S}^i)\text{, }\xi \in \mathcal{S}^i \}$
480$\mathcal{Y}^i_c = \{\mathbf{x} \in \mathbb{R}^n | \mathbf{x} = \xi - \overline{\mathbf{x}}(\mathcal{S}^i)\text{, }\xi \in \mathcal{Y}^i \}$
481\end{center}
482\subsubsection{Regularization}
483The covariance matrix of $\mathcal{S}^i$ is calculated along with the corresponding eigenvalues and eigenvectors. All eigenvectors $h_1\text{, }h_2\text{, }\ldots \text{, }h_m$ that's eigenvectors $\lambda_1\text{, }\lambda_2\text{, }\ldots \text{, }\lambda_m$ that pass the Kaiser-Guttman test are combined into a single matrix $H$ \cite{IEEEhowto:Kaiser} before being multiplied by each element in $\mathcal{S}^i_c\text{ \& }\mathcal{Y}^i_c$:
484\begin{center}
485$\mathcal{S}^i_r = \{\mathbf{x} \in \mathbb{R}^n | \mathbf{x} = H^T\xi\text{, }\xi \in \mathcal{S}^i_c\}$
486$\mathcal{Y}^i_r = \{\mathbf{x} \in \mathbb{R}^n | \mathbf{x} = H^T\xi\text{, }\xi \in \mathcal{Y}^i_c\}$
487\end{center}
488\subsubsection{Whitening}
489The two sets then undergo a whitening coordinate transformation ensuring that the covariance matrix of the transformed data is the identity matrix:
490\begin{center}
491$\mathcal{S}^i_w = \{\mathbf{x} \in \mathbb{R}^m | \mathbf{x} = Cov(\mathcal{S}^i_r)^{-\frac{1}{2}}\xi\text{, }\xi \in \mathcal{S}^i_r\}$
492$\mathcal{Y}^i_w = \{\mathbf{x} \in \mathbb{R}^m | \mathbf{x} = Cov(\mathcal{S}^i_r)^{-\frac{1}{2}}\xi\text{, }\xi \in \mathcal{Y}^i_r\}$
493\end{center}
494\subsubsection{Projection}
495Elements of $\mathcal{S}^i_w\text{, }\mathcal{Y}^i_w$ are then projected onto the unit sphere by scaling them to unit length $\mathbf{x}\mapsto\mathbf{x}/\|\mathbf{x}\|$
496\subsubsection{Clustering}
497The error set $\mathcal{Y}^i_w$ is partitioned into p clusters $\mathcal{Y}^i_{w\text{,}1}\text{, }\mathcal{Y}^i_{w\text{,}2}\text{, }\ldots \text{, }\mathcal{Y}^i_{w\text{,}p}$ with elements that are pairwise positively correlated.
498\subsubsection{Training}
499For each cluster $\mathcal{Y}_{w,i}$, $i=1,\dots,p$ and its complement $\mathcal{S}_w \setminus \mathcal{Y}_{w\text{, }i}$ we construct the following separating hyperplanes:
500\[
501\begin{split}
502h_i(\mathbf{x})=& \ell_i(\mathbf{x})-c_i, \\
503\ell_i(\mathbf{x}) =& \left\langle\frac{\mathbf{w}_i}{\|\mathbf{w}_i\|}\text{, }\mathbf{x}\right\rangle, \ c_i= \min_{\xi \in \mathcal{Y}_{w\text{, }i}}\left\langle\frac{\mathbf{w}_i}{\|\mathbf{w}_i\|}\text{, }\xi\right\rangle\\
504\mathbf{w}_i =& (Cov(\mathcal{S}^i_w \setminus \mathcal{Y}^i_{w\text{,}i}) + Cov(\mathcal{Y}^i_{w\text{,}i}))^{-1}\times\\
505&(\overline{\mathbf{x}}(\mathcal{Y}^i_{w\text{,}i}) - \overline{\mathbf{x}}(\mathcal{S}^i_w \setminus \mathcal{Y}^i_{w\text{ }i})).
506\end{split}
507\]
508The values of $c_j$ that are greater than $\theta$ have their respective hyperplanes kept and a corresponding element $f_j(x)$ is created.
509\begin{center}
510$f_j(\mathbf{x}) = f\left(\langle \frac{WH^T(\mathbf{x} - \overline{\mathbf{x}}(S^i)))}{|x|}\text{, }\frac{\mathbf{w}_j}{||\mathbf{w}_j||} \rangle - c_j\right)$
511\end{center}
512The set of elements $\mathbf{x} \in s^i_w \setminus y^i_w$ where $h_j(\mathbf{x}) \geq 0$ is called $\mathcal{C}$ and the elements of the set $\mathcal{C}_j \cup \mathcal{Y}^i_{w\text{,}j}$ are projected orthogonally onto the hyperplane $h_j(\mathbf{x}) = l_j(\mathbf{x}) - c_j$ as:
513\begin{center}
514$\mathbf{x}\mapsto\left(I - \frac{\mathbf{w}_j\mathbf{w}_j^T}{||\mathbf{w}_j||^2}\right)\mathbf{x} + \frac{c_j\mathbf{w}_j}{||\mathbf{w}_j||} = P(w_j)\mathbf{x} + b(\mathbf{w}_j\text{, }c_j)$
515\end{center}
516This determines a hyperplane $h_{j\text{,}2}(\mathbf{x}) = \langle \mathbf{w}_{j\text{, }2}\text{, }\mathbf{x} \rangle - c_{j\text{, }2}$ whose values is less than 0 for all projections of $\mathcal{C}_j$ and greater than or equal to 0 for all projections of $y^i_{\mathbf{w}\text{,}j}$. If no such planes exist,, Linear Fisher Discriminant is used.\\
517A second function is then created followed by an amalgamation that only produces a positive response when the output of the previous two functions is also positive.
518\begin{center}
519$f^\perp_j(\mathbf{x}) = f\left(\langle P(\mathbf{w}_j)\left(\frac{WH^T(\mathbf{x} - \overline{x}(S^i))}{||\mathbf{x}||}\right) + b(\mathbf{w}_j\text{, }c_j)\text{, }\mathbf{w}_{j\text{, }2}\rangle - c_{j\text{, }2}\right)$
520$f^c_j(\mathbf{x}) = f(\text{Step}(f_j(\mathbf{x})) + \text{Step}(f^\perp_j(\mathbf{x})) - 2)$
521\end{center}
522\subsubsection{Integration}
523For any $\mathbf{x}$ that produces a value of $f^c_j(\mathbf{x})$ that's greater than 0, the label can then be swapped accordingly to the next best matching label that Inception reported for that image.
524\subsubsection{Testing}
525The newly generated sets $\mathcal{M}^{i+1}\text{, }\mathcal{Y}^{i+1}\text{ \& }\mathcal{S}^{i+1}$, the cluster number $p$ and the filtering threshold $\theta$ can be carried over to another iteration of correcting if deemed necessary.
526\section{Results}
527???
528\section{Conclusion And Future Work}
529?????
530\appendices
531% appendices go here
532\ifCLASSOPTIONcaptionsoff
533  \newpage
534\fi
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575\end{document}