clean up

Numpy/Li.py

@@ -0,0 +1,36 @@
+def L_i(x, y, W):
+  """
+  unvectorized version. Compute the multiclass svm loss for a single example (x,y)
+  - x is a column vector representing an image (e.g. 3073 x 1 in CIFAR-10)
+    with an appended bias dimension in the 3073-rd position (i.e. bias trick)
+  - y is an integer giving index of correct class (e.g. between 0 and 9 in CIFAR-10)
+  - W is the weight matrix (e.g. 10 x 3073 in CIFAR-10)
+  """
+  delta = 1.0 # see notes about delta later in this section
+  scores = W.dot(x) # scores becomes of size 10 x 1, the scores for each class
+  correct_class_score = scores[y]
+  D = W.shape[0] # number of classes, e.g. 10
+  loss_i = 0.0
+  for j in xrange(D): # iterate over all wrong classes
+    if j == y:
+      # skip for the true class to only loop over incorrect classes
+      continue
+    # accumulate loss for the i-th example
+    loss_i += max(0, scores[j] - correct_class_score + delta)
+  return loss_i
+
+def L_i_vectorized(x, y, W):
+  """
+  A faster half-vectorized implementation. half-vectorized
+  refers to the fact that for a single example the implementation contains
+  no for loops, but there is still one loop over the examples (outside this function)
+  """
+  delta = 1.0
+  scores = W.dot(x)
+  # compute the margins for all classes in one vector operation
+  margins = np.maximum(0, scores - scores[y] + delta)
+  # on y-th position scores[y] - scores[y] canceled and gave delta. We want
+  # to ignore the y-th position and only consider margin on max wrong class
+  margins[y] = 0
+  loss_i = np.sum(margins)
+  return loss_i

Numpy/NeareastNeighbor.py

@@ -0,0 +1,23 @@
+import numpy as np
+
+class NearestNeighbor(object):
+  def __init__(self):
+    pass
+
+  def train(self, X, y):
+    self.Xtr = X
+    self.ytr = y
+
+  def predict(self, X):
+    num_test = X.shape[0]
+    Ypred = np.zeros(num_test, dtype = self.ytr.dtype)
+
+    # loop over all test rows
+    for i in xrange(num_test):
+      # find the nearest training image to the i'th test image
+      # using the L1 distance (sum of absolute value differences)
+      distances = np.sum(np.abs(self.Xtr - X[i,:]), axis = 1)
+      min_index = np.argmin(distances) # get the index with smallest distance
+      Ypred[i] = self.ytr[min_index] # predict the label of the nearest example
+
+    return Ypred

Numpy/gradient.py

@@ -0,0 +1,31 @@
+# compute the gradient numerically:
+# a generic function takes a function f, a vector x o evaluate 
+# the gradient on, and returns the gradient of f at x:
+
+def eval_numerical_gradient(f, x):
+  """ 
+  a naive implementation of numerical gradient of f at x 
+  - f should be a function that takes a single argument
+  - x is the point (numpy array) to evaluate the gradient at
+  """ 
+
+  fx = f(x) # evaluate function value at original point
+  grad = np.zeros(x.shape)
+  h = 0.00001
+
+  # iterate over all indexes in x
+  it = np.nditer(x, flags=['multi_index'], op_flags=['readwrite'])
+  while not it.finished:
+
+    # evaluate function at x+h
+    ix = it.multi_index
+    old_value = x[ix]
+    x[ix] = old_value + h # increment by h
+    fxh = f(x) # evalute f(x + h)
+    x[ix] = old_value # restore to previous value (very important!)
+
+    # compute the partial derivative
+    grad[ix] = (fxh - fx) / h # the slope
+    it.iternext() # step to next dimension
+
+  return grad

Numpy/neuron.py

@@ -0,0 +1,7 @@
+class Neuron(object):
+  # ... 
+  def forward(inputs):
+    """ assume inputs and weights are 1-D numpy arrays and bias is a number """
+    cell_body_sum = np.sum(inputs * self.weights) + self.bias
+    firing_rate = 1.0 / (1.0 + math.exp(-cell_body_sum)) # sigmoid activation function
+    return firing_rate