!pip install mxnet==1.6.0 import numpy as np import mxnet as mx from mxnet import nd def transform(data, label): # define a function to transfer data return (nd.floor(data/128)).astype(np.float32), label.astype(np.float32) # floor of 255/128 = 1 pixel value = 1 when it is on. # Devide dataset to 2 sets: one for training and one for testing mnist_train = mx.gluon.data.vision.MNIST(train=True, transform=transform) mnist_test = mx.gluon.data.vision.MNIST(train=False, transform=transform) import matplotlib.pyplot as plt %matplotlib inline image_index=8888 # Pick one to take a look. Any integer <60,000 # 8888 is digit with label 3, as printed below print(mnist_train[image_index][1]) #image stored in 0; label in 1 plt.imshow(mnist_train[image_index][0].reshape((28, 28)).\ asnumpy(), cmap='Greys') #image pixel: 28 by 28 # Initialize arrays for counts for computing p(y), p(xi|y) # We initialize all numbers with a count of 1 to avoid # division by zero, known as Laplace smoothing. ycount = nd.ones(shape=(10)) #10 possible digits xcount = nd.ones(shape=(784, 10)) #784 (= 28*28) variables # Aggregate the count of the labels in training dataset # and number of its cooresponding pixels being on (value=1) for data, label in mnist_train: # loop over the dataset x = data.reshape((784,)) y = int(label) # get the digit-number ycount[y] += 1 # add 1 to (digit)th entry xcount[:, y] += x # add the image data to # the (digit)th column # compute the probabilities p(xi|y) (divide per pixel counts # by total count of the label in the training dataset) for i in range(10): xcount[:, i] = xcount[:, i]/ycount[i] # Compute the probability p(y) py = ycount / nd.sum(ycount)

from PIL import Image, ImageOps from numpy import asarray from matplotlib import pyplot as plt logxcount = nd.log(xcount) # pre-computations logxcountneg = nd.log(1-xcount) logpy = nd.log(py) fig, figarr = plt.subplots(2, 2, figsize=(15, 3)) # test and show 10 images ctr = 0 # initialize the control iterator y = [] pxm = np.array([]) xi = () # A = mx.img.imread("4_image.jpg",flag = 0) # AA = mx.ndarray.image.resize(A,size =(28,28)) # CC = AA.reshape((28,28)) # k = [1,2] #importing image im1 = nd.array(ImageOps.invert(Image.open('image6.jpg').resize((28,28)).convert('L'))) im2 = nd.array(ImageOps.invert(Image.open('image4.jpg').resize((28,28)).convert('L'))) im1 = (nd.floor(im1/160)).astype(np.float32) im2 = (nd.floor(im2/160)).astype(np.float32) truelable = [6,4] imgdatas = (im1, im2) for j in range(2): data = imgdatas[j] label = float(truelable[j]) x = data.reshape((784,)) y.append(int(label)) # Incorporate the prior probability p(y) since p(y|x) is # proportional to p(x|y) p(y) logpx = logpy.copy() #nd.zeros_like(logpy) for i in range(10): # compute the log probability for a digit logpx[i]+=nd.dot(logxcount[:,i],x)+nd.dot(logxcountneg[:,i],1-x) # normalize to prevent overflow or underflow by subtracting # the largest value logpx -= nd.max(logpx) # and compute the softmax using logpx px = nd.exp(logpx).asnumpy() px = px*py.asnumpy() # this proportional to P(y|x) px /= np.sum(px) pxm = np.append(pxm,max(px)) # use the one with max Pr. xi = np.append(xi,np.where(px == np.amax(px))) # bar chart and image of digit figarr[1, ctr].bar(range(10), px) figarr[1, ctr].axes.get_yaxis().set_visible(False) figarr[0, ctr].imshow(x.reshape((28,28)).asnumpy(),cmap='gray') figarr[0, ctr].axes.get_xaxis().set_visible(False) figarr[0, ctr].axes.get_yaxis().set_visible(False) ctr += 1 np.set_printoptions(formatter={'float': '{: 0.0f}'.format}) plt.show() print('True label: ',y) xi = np.array(xi) print('Predicted digits:',xi) print('Correct?',np.equal(y,xi)) np.set_printoptions(formatter={'float': '{: 0.1f}'.format}) print('Maximum probability:',pxm)

from PIL import Image, ImageOps from numpy import asarray from matplotlib import pyplot as plt logxcount = nd.log(xcount) # pre-computations logxcountneg = nd.log(1-xcount) logpy = nd.log(py) fig, figarr = plt.subplots(2, 2, figsize=(15, 3)) # test and show 10 images ctr = 0 # initialize the control iterator y = [] pxm = np.array([]) xi = () # A = mx.img.imread("4_image.jpg",flag = 0) # AA = mx.ndarray.image.resize(A,size =(28,28)) # CC = AA.reshape((28,28)) # k = [1,2] #importing image im1 = nd.array(ImageOps.invert(Image.open('image6.jpg').resize((28,28)).convert('L'))) im2 = nd.array(ImageOps.invert(Image.open('image4.jpg').resize((28,28)).convert('L'))) im1 = (nd.floor(im1/160)).astype(np.float32) im2 = (nd.floor(im2/160)).astype(np.float32) truelable = [6,4] imgdatas = (im1, im2) for j in range(2): data = imgdatas[j] label = float(truelable[j]) x = data.reshape((784,)) y.append(int(label)) # Incorporate the prior probability p(y) since p(y|x) is # proportional to p(x|y) p(y) logpx = logpy.copy() #nd.zeros_like(logpy) for i in range(10): # compute the log probability for a digit logpx[i]+=nd.dot(logxcount[:,i],x) # normalize to prevent overflow or underflow by subtracting # the largest value logpx -= nd.max(logpx) # and compute the softmax using logpx px = nd.exp(logpx).asnumpy() px = px*py.asnumpy() # this proportional to P(y|x) px /= np.sum(px) pxm = np.append(pxm,max(px)) # use the one with max Pr. xi = np.append(xi,np.where(px == np.amax(px))) # bar chart and image of digit figarr[1, ctr].bar(range(10), px) figarr[1, ctr].axes.get_yaxis().set_visible(False) figarr[0, ctr].imshow(x.reshape((28,28)).asnumpy(),cmap='gray') figarr[0, ctr].axes.get_xaxis().set_visible(False) figarr[0, ctr].axes.get_yaxis().set_visible(False) ctr += 1 np.set_printoptions(formatter={'float': '{: 0.0f}'.format}) plt.show() print('True label: ',y) xi = np.array(xi) print('Predicted digits:',xi) print('Correct?',np.equal(y,xi)) np.set_printoptions(formatter={'float': '{: 0.1f}'.format}) print('Maximum probability:',pxm)