def de_mean(A):
""" returns result of subtracting from every value of A the mean value
of its column """
num_rows, num_cols = Ch4.shape(A)
col_means, _ = scale(A)
return Ch4.make_matrix(num_rows, num_cols,
lambda i, j: A[i][j] - col_means[j])
def de_mean(A):
""" returns result of subtracting from every value of A the mean value
of its column """
num_rows, num_cols = Ch4.shape(A)
col_means, _ = scale(A)
return Ch4.make_matrix(num_rows,num_cols,
lambda i,j: A[i][j]-col_means[j])
def new_point_distance(labeled_point):
""" helper function to calculate distance between a (point, label)
tuple and new_point """
# get the location from the labeled_point
point = labeled_point[0]
# return distance
return Ch4.distance(point, new_point)
def new_point_distance(labeled_point):
""" helper function to calculate distance between a (point, label)
tuple and new_point """
# get the location from the labeled_point
point = labeled_point[0]
# return distance
return Ch4.distance(point, new_point)
def directional_variance_i(r_i, w):
"""" computes for row r_i the projection of r_i onto w """
# we square this because we later sum to get a resultant vector
return Ch4.dot_product(r_i, direction(w))**2
def direction(w):
""" returns a normalized vector in direction w """
mag = Ch4.magnitude(w)
return [w_i / float(mag) for w_i in w]
def remove_projection_from_vector(v, w):
""" projects v onto w and then subtracts the projection from v """
return Ch4.vector_subtract(v, project(v, w))
def project(v, w):
""" projects vector v onto w """
projection_length = Ch4.dot_product(v, w)
return Ch4.scalar_multiply(projection_length, w)
# Remove the mean of the data #
###############################
def de_mean(A):
""" returns result of subtracting from every value of A the mean value
of its column """
num_rows, num_cols = Ch4.shape(A)
col_means, _ = scale(A)
return Ch4.make_matrix(num_rows, num_cols,
lambda i, j: A[i][j] - col_means[j])
de_meaned_data = de_mean(data)
de_xs = Ch4.get_col(de_meaned_data, 0)
de_ys = Ch4.get_col(de_meaned_data, 1)
# Compute Directional Variance Gradient #
#########################################
# given a directional vector 'd' (magnitude=1) each row in 'r' data extends
# in 'd' direction by dot(r,d). Lets first define a directional vector
def direction(w):
""" returns a normalized vector in direction w """
mag = Ch4.magnitude(w)
return [w_i / float(mag) for w_i in w]
def directional_variance_i(r_i, w):
def directional_variance_gradient_i(r_i, w):
""" computes the gradient of the directioanl variance for row_i in
data """
return [2 * Ch4.dot_product(r_i, direction(w)) * r_ij for r_ij in r_i]
def directional_variance_i(r_i, w):
"""" computes for row r_i the projection of r_i onto w """
# we square this because we later sum to get a resultant vector
return Ch4.dot_product(r_i, direction(w))**2
def direction(w):
""" returns a normalized vector in direction w """
mag = Ch4.magnitude(w)
return [w_i/float(mag) for w_i in w]
def remove_projection_from_vector(v,w):
""" projects v onto w and then subtracts the projection from v """
return Ch4.vector_subtract(v, project(v,w))
def project(v,w):
""" projects vector v onto w """
projection_length = Ch4.dot_product(v,w)
return Ch4.scalar_multiply(projection_length,w)
# make a matrix of the data
data = [list(tup) for tup in zip(xs,ys)]
# Remove the mean of the data #
###############################
def de_mean(A):
""" returns result of subtracting from every value of A the mean value
of its column """
num_rows, num_cols = Ch4.shape(A)
col_means, _ = scale(A)
return Ch4.make_matrix(num_rows,num_cols,
lambda i,j: A[i][j]-col_means[j])
de_meaned_data = de_mean(data)
de_xs = Ch4.get_col(de_meaned_data,0)
de_ys = Ch4.get_col(de_meaned_data,1)
# Compute Directional Variance Gradient #
#########################################
# given a directional vector 'd' (magnitude=1) each row in 'r' data extends
# in 'd' direction by dot(r,d). Lets first define a directional vector
def direction(w):
""" returns a normalized vector in direction w """
mag = Ch4.magnitude(w)
return [w_i/float(mag) for w_i in w]
def directional_variance_i(r_i, w):
"""" computes for row r_i the projection of r_i onto w """
# we square this because we later sum to get a resultant vector
def directional_variance_gradient_i(r_i, w):
""" computes the gradient of the directioanl variance for row_i in
data """
return [2 * Ch4.dot_product(r_i, direction(w)) * r_ij for r_ij in r_i]
def directional_variance_gradient(data, w):
""" computes the variance gradient for all rows in data """
return Ch4.vector_sum(
[directional_variance_gradient_i(r_i, w) for r_i in data])
def directional_variance_gradient(data, w):
""" computes the variance gradient for all rows in data """
return Ch4.vector_sum([directional_variance_gradient_i(r_i,
w) for r_i in data])