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linear_classifier.py
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linear_classifier.py
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from forward_mode import *
from random import uniform
def vplus(u, v): return [u[i]+v[i] for i in range(len(u))]
def ktimesv(k, u): return [k*u[i] for i in range(len(u))]
def dot(u, v):
sum = 0
for i in range(len(u)): sum += u[i]*v[i]
return sum
def vminus(u, v): return vplus(u, ktimesv(-1, v))
def distance(u, v): return dot(vminus(u, v), vminus(u, v))
def naive_gradient_descent(f, x0, learning_rate, n):
x = x0
for i in range(n): x = vminus(x, ktimesv(learning_rate, gradient(f)(x)))
return x
def linear_model(point, weights, bias):
return dot(weights, point)+bias
def cost(points, labels, weights, bias):
cost = 0
for i in range(len(points)):
cost += distance([linear_model(points[i], weights, bias)], [labels[i]])
return cost
def pack(weights, bias):
parameters = [bias]
for weight in weights: parameters.append(weight)
return parameters
def unpack(parameters):
bias = parameters[0]
weights = parameters[1:]
return weights, bias
def initialize(points, labels):
weights = [uniform(-1, 1) for i in range(len(points[0]))]
bias = uniform(-1, 1)
return weights, bias
def step(points, labels, weights, bias):
def loss(parameters):
weights, bias = unpack(parameters)
return cost(points, labels, weights, bias)
parameters = pack(weights, bias)
parameters = vminus(parameters, ktimesv(0.01, gradient(loss)(parameters)))
weights, bias = unpack(parameters)
return weights, bias
def train(points, labels):
def loss(parameters):
weights, bias = unpack(parameters)
return cost(points, labels, weights, bias)
weights = [uniform(-1, 1) for i in range(len(points[0]))]
bias = uniform(-1, 1)
parameters = pack(weights, bias)
parameters = naive_gradient_descent(loss, parameters, 0.01, 100)
weights, bias = unpack(parameters)
return weights, bias
def classify(point, weights, bias):
if linear_model(point, weights, bias)<0: return -1
else: return +1
def all_labels(labels):
red = False
blue = False
for label in labels:
if label<0: red = True
else: blue = True
return red and blue