X-Git-Url: https://piware.de/gitweb/?p=handwriting-recognition.git;a=blobdiff_plain;f=train.py;fp=train.py;h=8a6dc96f2c1d40281d452fc3c894fffb79a73436;hp=0000000000000000000000000000000000000000;hb=0ea12b213873b4bef12e1f2b65eed64704ee040f;hpb=8af4223121b60d5d67b7121d87c5c6fed01b58e7

diff --git a/train.py b/train.py
new file mode 100755
index 0000000..8a6dc96
--- /dev/null
+++ b/train.py
@@ -0,0 +1,82 @@
+#!/usr/bin/python3
+
+import numpy as np
+
+import mnist
+
+# use a constant seed to keep things reproducible
+rg = np.random.default_rng(1)
+
+# transfer functions
+
+# https://en.wikipedia.org/wiki/Sigmoid_function
+# classic, differentiable, apparently worse for training
+def sigmoid(x):
+    return 1 / (1 + np.exp(-x))
+
+
+def sigmoid_prime(x):
+    return sigmoid(x) * (1 - sigmoid(x))
+
+
+# https://en.wikipedia.org/wiki/Rectifier_(neural_networks)
+# mostly preferred these days, not differentiable at 0, but slope can be defined arbitrarily as 0 or 1 at 0
+def reLU(x):
+    return np.maximum(x, 0)
+
+
+def reLU_prime(x):
+    return np.heaviside(x, 1)
+
+
+train_images, train_labels, rows, cols = mnist.load('train-images-idx3-ubyte', 'train-labels-idx1-ubyte')
+test_images, test_labels, rows2, cols2 = mnist.load('t10k-images-idx3-ubyte', 't10k-labels-idx1-ubyte')
+assert rows == rows2
+assert cols == cols2
+
+# neural network structure: two hidden layers, one output layer
+SIZES = (rows * cols, 20, 16, 10)
+NUM_LAYERS = len(SIZES)
+
+# initialize weight matrices and bias vectors with random numbers
+weights = []
+biases = []
+for i in range(1, NUM_LAYERS):
+    weights.append(rg.normal(size=(SIZES[i], SIZES[i-1])))
+    biases.append(rg.normal(scale=10, size=SIZES[i]))
+
+
+def feed_forward(x, transfer=reLU):
+    '''Compute all z and output vectors for given input vector'''
+
+    a_s = [x]
+    z_s = []
+    for w, b in zip(weights, biases):
+        x = w @ x + b
+        z_s.append(x)
+        a_s.append(transfer(x))
+    return (z_s, a_s)
+
+
+def classify(y):
+    # the recognized digit is the index of the highest-valued output neuron
+    return np.argmax(y), np.max(y)
+
+
+def test():
+    """Count percentage of test inputs which are being recognized correctly"""
+
+    good = 0
+    num_images = test_images.shape[1]
+    for i in range(num_images):
+        # the recognized digit is the index of the highest-valued output neuron
+        y = classify(feed_forward(test_images[:, i])[1][-1])[0]
+        good += int(y == test_labels[i])
+    return 100 * (good / num_images)
+
+
+res = feed_forward(test_images[:, 0])
+print(f'output vector of first image: {res[1][-1]}')
+digit, conf = classify(res[1][-1])
+print(f'classification of first image: {digit} with confidence {conf}; real label {test_labels[0]}')
+print(f'correctly recognized images after initialization: {test()}%')