Binary-Classification

################################DATASETS############################ Each dataset corresponds to a JSON file named as $dataset$.json. JSON is a lightweight data-interchange format, similar to a dictionary. After loading a dataset, you can access its training, validation, and test splits using the keys ‘train’, ‘valid’, and ‘test’, respectively. For example, suppose we load mnist subset.json to the variable x. Then, x['train0'] refers to the training set of mnist subset. This set is a list with two elements: x['train'][0] containing the features of size N (samples) ×D (dimension of features), and x['train'][1] containing the corresponding labels of size N. Next we will describe each one of the three datasets in more detail. • toydata1 includes 240 data instances with binary labels that are linearly separable. The data is split into a training set and a test set. You can look up training and test sets in toydata1.json with ['train'] and ['test'], respectively. • toydata2 includes 240 data instances with binary labels that are not linearly separable. The data is split into a training set and a test set. You can look up training and test sets in toydata2.json with ['train'] and ['test'], respectively. • mnist subset: MNIST is one of the most well-known datasets in computer vision, consisting of images of handwritten digits from 0 to 9. We will be working with a subset of the official version of MNIST. In particular, we randomly sample 700 images from each category and split them into training, validation, and test sets, which can be reached in mnist subset.json via keys ['train'], ['valid'] and ['test'], respectively. ################################ALGORITHM############################ • K-Nearest Neighbors The standard agorithm is implemented using euclidean distance and the K among [1,3,5,7,9] that gives the best classification accuracy is found. • Logistic Regression The optimal parameters for logistic regression is found using gradient descent. The objective is the cross-entropy function. At each iteration, the average gradients from all training samples is computed and the parameters are updated using the chosen step size (or learning rate).