def scale(data_matrix):
# data matrix e.g. [[63,67,70], [160,170.2,177.8], [150,160,171]]
"""returns the means and standard deviations of each column"""
num_rows, num_cols = shape(data_matrix)
means = [mean(get_column(data_matrix, j))
for j in range(num_cols)]
stdevs = [standard_deviation(get_column(data_matrix, j))
for j in range(num_cols)]
return means, stdevs
One way to see this is by randomly generating pairs of points in the d-dimensional
"unit cube" in a variety of dimensions, and calculating the distances between
them.
"""
import sys
sys.path.insert(0, "../statistics")
from central_tendencies import mean
def random_point(dim):
return [random.random() for _ in range(dim)]
def random_distances(dim, num_pairs):
return [distance(random_point(dim), random_point(dim))
for _ in range(num_pairs)]
dimensions = range(1, 101)
avg_distances = []
min_distances = []
random.seed(0)
for dim in dimensions:
distances = random_distances(dim, 10000) # 10,000 random pairs
avg_distances.append(mean(distances)) # track the average
min_distances.append(min(distances)) # track the minimum
# ratio between the closest distance and the average distance
min_avg_ratio = [min_dist / avg_dist
for min_dist, avg_dist in zip(min_distances, avg_distances)]
def mean_deviations(nums):
nums_mean = mean(nums)
return [num - nums_mean for num in nums]
def de_mean(x):
"""translate x by subtracting its mean (so the result has mean 0)"""
x_bar = mean(x)
return [x_i - x_bar for x_i in x]
def de_mean(x):
"""translate x by subtracting its mean (so the result has mean 0)"""
x_bar = mean(x)
return [x_i - x_bar for x_i in x]
from central_tendencies import mean
def random_point(dim):
return [random.random() for _ in range(dim)]
def random_distances(dim, num_pairs):
return [
distance(random_point(dim), random_point(dim))
for _ in range(num_pairs)
]
dimensions = range(1, 101)
avg_distances = []
min_distances = []
random.seed(0)
for dim in dimensions:
distances = random_distances(dim, 10000) # 10,000 random pairs
avg_distances.append(mean(distances)) # track the average
min_distances.append(min(distances)) # track the minimum
# ratio between the closest distance and the average distance
min_avg_ratio = [
min_dist / avg_dist
for min_dist, avg_dist in zip(min_distances, avg_distances)
]
def squared_mean_deviations(a_vector):
list_mean = mean(a_vector)
return map(lambda num: (num - list_mean)**2, a_vector)
def least_squares_fit(xs, ys):
beta = correlation(xs,
ys) * standard_deviation(ys) / standard_deviation(xs)
alpha = mean(ys) - beta * mean(xs)
return alpha, beta
