Handwritten Digit Classification And Sample Complexity Implementation Using Python

Supervised Learning

In this project to develop the handwritten digit classification and sample complexity. We are using the python code to develop the handwritten digit classification. The input sources such as paper document, photographs, touch screens and other devices. The text image converts to letter by using python code. The handwritten digit also called as kernel perceptron.Perceptron is an algorithm and it is one of the supervised learning. It has two type of classifier. One is linear classifier and another one is binary classifier. The binary classifier using to classify the binary in the set. It represent by vector of number. The second task to satisfy the sample complexity. It based on linear regression and winnow.

Supervised Learning

The supervised learning is the machine learning and it based on output and input. We import the training dataset and testing the dataset. In this algorithm analyze the data and produce the inferred function (CAI, 2010). The training dataset needs to be representative of real world use of the function. We import the data by using python code and it makes map or graph related to graph. In this project we implement the kernel perceptorn using python. We are using the supervised learning algorithm for implement the handwritten digit classification and sample complexity.

Kernel Perceptron 

The task is quasi realistic and working with the large dataset. The text image converts into latter using the python. First step to import the training dataset. The perceptron generalize in two ways. The first way to use the kernel function for generalize the perceptron.The second way generalize the perceptron into a majority network perceptron.It has two classes and it separate k classes.

Adding Kernel

We adding kernel one by one and it allows to map. It is linear function and it performs the ploynominal.The kernel mainly using the operating system. It is center part of operating system.It manages the operating system and hardware also. The micro kernel and monolithic kernel is kernel types.

Training and Testing the Kernel Perceptron 

We are using training dataset for implement the handwritten digit classification.The given input xt,yt and initialize value α0 = 0.The prediction value

We update the equation for single function and it added the value. It repeated the value and it called as cycle. The cycle known as epoch. The epoch classifies one by one and it generalizes the value. First we check the first epoch. If the first epoch table correct then we add the second epoch. For example we have the 40 element in the epoch the epoch separate three type of epoch. The element can be separate like {(x1,x1),(x2,x2)….(x40,x40)} and the dataset is {(x1,x1),(x2,x2)….(x40,x40)} first epoch and {(x41,x41)….(x80,x80)} second epoch. The epoch is equal to epoch of m.x1=x40=x80=xm.We training the dataset and it divided to test size. The predict value applied after divided the test size. Finally update the entire value.

Generalizing to K Classes

We use research method to generalizing the k classes. In this method return the vector value. We import the large dataset and it generalizes the two classifier function. The python code work on large dataset. We take the d value. In this task the given value 257 values and it separate 256 values for 16 x 16 matrixes. And remain value denoted -1 or 1.The result depending the d value. The value is 1 to 7.So the table value matrix 2 x 7.We split the dataset and it perform the cross validation.

Kernel Perceptron

Cross validation 

Cross validation is called as rotation estimation. It generalizes the independent dataset and analyzes the dataset. The given dataset is known dataset and validation dataset is unknown dataset. The validation dataset check the dataset and test the dataset. If any error occur in the dataset then it change the dataset value. If the dataset is correct then it generalizes the dataset. The cross validation involves the partioning.Partioining means dataset divided the small datasets. First analyze the dataset and it reduces the variability. The test error denoted as std and mean value denoted as d^t std.

Confusion 

To create matrix for given training dataset. It is classification model. It has positive and negative model. The positive values contains true positive and false positive. The negative value contains false negative and true negative. First classify the rate and accuracy. Consider total number of positive values and small number of FN.The recall defined as the total number of positive values divided by small number of FN. Precision has low precision and high precision. Consider total number of positive values and small number of FP.The precision defined as divided the total number of positive value and small number of FN. Finally we measure the F-measure. The F-measure value based on recall and precision. We take the sum of precision and recall value and multiply of precision and recall value. Both value divided by the two that is called as F measure.

Gaussian Kernel 

The Gaussian model measures the input value and its prototype vector. The input value and prototype is equal to 1.It has one dimensional input value and two dimensional input value. Consider the equation .C is width of the kernel and compute the cross validation for given equation. The Gaussian model based on Euclidean distance. The Euclidean distance calculates using input value and prototype vector. The Euclidean distance looks like v shape and the distance between x and 0 for one dimensional input. The two dimensional input has x value and y value. The two dimensional Euclidean distance between value(x,y) and (0,0). The Gaussian method based on variance. The variance curve looks like bell curve. The variance equation is  .Consider the sigma and beta. The sigma denoted as parameter and beta is input values.

Polynomial Kernel

Polynomial is non linear models and it support vector machines. The polynomial kernel takes only original values. The polynomial kernel is equal to polynomial regression.

Sparse Learning

It perform machine learning algorithm and it calculate accurate predictions. It is using for image processing and signal processing (CHENG, 2016). Sparse learning is unsupervised learning and it represents the data efficiency. The sparse learning data called as sparse data. Consider the x and y matrix values. The x is4 x 4 matrix and y is 1 x 1 matrixes. In this task we compute the sample complexity.

Sample Complexity

Sample complexity is one of the machine learning algorithms and it represents the number of training datasets. There are two different variants in sample complexity. The variants are worst case complexity and best case complexity (Feldman and Xiao, 2015). The sample complexity implement by python code. Take m and n values. The n denoted as x axis values and m denoted as y axis values. The n values are 20….100 and m values are 10……60.The graph based on n and m value using python.

Bias Variance Trade Off

It is one of the estimate theory and it set the predict values. Bias is used for error correction and it based on target output values. It analyzes the data in given dataset. It sum of bias, variance and quantity. Consider the m and n value from sample complexity. If the n value is infinite then the m value increase. If the n values zero then the m values decrease.

Linear Regression 

Linear Regression is a linear approach and relation between independent variable and dependent variable. Dependent variable called as scalar response and independent variable called as explanatory variables (Christie, 2011). One or more variable present in the dataset that is called as multiple linear regressions. The linear regression model is called as linear model. It used to observe the dataset and it predict the value

Nearest Neighbour Algorithm

It allows the sample complexity model and it generalizes the data. In this algorithm related to nearest neighbour regression model. It calculates the minimum value in the dataset. The k nearest algorithm is one of the nearest neighbour algorithms. K nearest neighbour algorithm is supervised algorithm. Compare with k nearest neighbour algorithm it is very simple and easily calculate the minimum value.

Conclusion 

In this project to develop the handwritten digit classification and sample complexity. The text image converts into letter. In using python code for convert text image to letter. The input sources are photo, document or any devices. In this task the input source convert to letter. It is called as kernel perceptron. First adding the kernel for create map. The kernel divides to two type. The types are one dimensional kernel and two dimensional kernels. The k classes are using to implement the map. The perceptron to use the kernel function.

It takes positive integer and negative integer. The positive integer and negative integer. The positive integer controlling the dimensional of polynomial. Test the kernel perceptron after adding kernel. It based on input and initialize values. Third step generalize the k classes. This step returns the vector value. The next step crate confusion matrix computes the cross validation using python. The second task to solve the sample complexity problem using python code. It take x and y matrix value and plot the graph based on m and n value. Finally compute the nearest neighbour algorithm and find the minimum value successfully.

References

CAI, Q. (2010). Face recognition algorithm based on supervised neighborhood preserving embedding. Journal of Computer Applications, 29(12), pp.3349-3351.

CHENG, H. (2016). Sparse representation, modeling and learning in visual recognition. [Place of publication not identified]: SPRINGER LONDON LTD.

Christie, M. (2011). Simplicity, complexity, and modelling. Chichester, West Sussex, U.K.: Wiley.

Feldman, V. and Xiao, D. (2015). Sample Complexity Bounds on Differentially Private Learning via Communication Complexity. SIAM Journal on Computing, 44(6), pp.1740-1764.