This is a neural network which is trained to recognize hand written digits. MNIST dataset was used to train the network. Using Python we obtained our training parameters. JS, HTML and CSS were used to create user interface. Accuracy obtained was close to 93%.
MNIST datapoints is made of 2 parts: image and corresponding label. Image in the dataset is present as a 2D array of size 28 * 28. The numbers in the array define pixel intensity at that point. These arrays are flattened into a 784- dimensional vector. The label associated with each image is also processed and converted into a vector of desired form. The labels store the integer which describe the corresponding image. We shall store the vector as ”one-hot” vector, which means that it’s value is 1 in one dimension and is 0 in every other dimension. For example, 2 would be represented as [0,0,1,0,0,0,0,0,0,0].
This step involves creating ”evidence”, which is used to decide to which group our image belongs. To calculate evidence we perform weighted sum of the pixel intensities. To this a ”bias” is added as well. What bias does is that some output are more likely than others. Mathematically we can express evidence as follows:
Evidence[i] = Summation(Weights * Input + Biases)
We convert the previously calculated evidence is used to get probabilities. The evidence is fed to ”activation” function which generates a probability distribution over 10 digits. The softmax function is defined as follows:
In this step our motive is minimize our cost function. First, we cost function as a ”cross entropy”, which is defined as follows:
Here y is our predicted probability distribution, and y’ is the true distribution. Backpropagation and gradient descent algorithm is applied in order to minimize the cost.
In this step we compare our group with highest predicted probability against the label.
The neural network processes the image entered by the user and assigns percentage against ten numbers ranging from 0-9. The percentage indicates which number is most likely drawn by the user. We output the number with the highest percentage among all the 10 numbers.
The accuracy obtained after training and testing neural network is as follows:
| Digit | (Correctly Deduced Samples)/(Total Samples) | Accuracy |
|---|---|---|
| 0 | 954/980 | 0.973469387755 |
| 1 | 1114/1135 | 0.981497797357 |
| 2 | 936/1032 | 0.906976744186 |
| 3 | 913/1010 | 0.90396039604 |
| 4 | 936/982 | 0.953156822811 |
| 5 | 816/892 | 0.914798206278 |
| 6 | 895/958 | 0.934237995825 |
| 7 | 962/1028 | 0.93579766537 |
| 8 | 877/974 | 0.900410677618 |
| 9 | 917/1009 | 0.90882061447 |
The average accuracy comes out to be 0.931312 or 93%.