def spearman_rho(worder, normalize=True):
"""
Calculates the Spearman's Rho correlation coefficient given the *worder*
list of word alignment from word_rank_alignment(), using the formula:
rho = 1 - sum(d**2) / choose(len(worder)+1, 3)
Given that d is the sum of difference between the *worder* list of indices
and the original word indices from the reference sentence.
Using the (H0,R0) and (H5, R5) example from the paper
>>> worder = [7, 8, 9, 10, 6, 0, 1, 2, 3, 4, 5]
>>> round(spearman_rho(worder, normalize=False), 3)
-0.591
>>> round(spearman_rho(worder), 3)
0.205
:param worder: The worder list output from word_rank_alignment
:param type: list(int)
"""
worder_len = len(worder)
sum_d_square = sum((wi - i)**2 for wi, i in zip(worder, range(worder_len)))
rho = 1 - sum_d_square / choose(worder_len + 1, 3)
if normalize: # If normalized, the rho output falls between 0.0 to 1.0
return (rho + 1) / 2
else: # Otherwise, the rho outputs falls between -1.0 to +1.0
return rho
def spearman_rho(worder, normalize=True):
"""
Calculates the Spearman's Rho correlation coefficient given the *worder*
list of word alignment from word_rank_alignment(), using the formula:
rho = 1 - sum(d**2) / choose(len(worder)+1, 3)
Given that d is the sum of difference between the *worder* list of indices
and the original word indices from the reference sentence.
Using the (H0,R0) and (H5, R5) example from the paper
>>> worder = [7, 8, 9, 10, 6, 0, 1, 2, 3, 4, 5]
>>> round(spearman_rho(worder, normalize=False), 3)
-0.591
>>> round(spearman_rho(worder), 3)
0.205
:param worder: The worder list output from word_rank_alignment
:param type: list(int)
"""
worder_len = len(worder)
sum_d_square = sum((wi - i)**2 for wi, i in zip(worder, range(worder_len)))
rho = 1 - sum_d_square / choose(worder_len+1, 3)
if normalize: # If normalized, the rho output falls between 0.0 to 1.0
return (rho + 1) /2
else: # Otherwise, the rho outputs falls between -1.0 to +1.0
return rho
def kendall_tau(worder, normalize=True):
"""
Calculates the Kendall's Tau correlation coefficient given the *worder*
list of word alignments from word_rank_alignment(), using the formula:
tau = 2 * num_increasing_pairs / num_possible_pairs -1
Note that the no. of increasing pairs can be discontinuous in the *worder*
list and each each increasing sequence can be tabulated as choose(len(seq), 2)
no. of increasing pairs, e.g.
>>> worder = [7, 8, 9, 10, 6, 0, 1, 2, 3, 4, 5]
>>> number_possible_pairs = choose(len(worder), 2)
>>> round(kendall_tau(worder, normalize=False),3)
-0.236
>>> round(kendall_tau(worder),3)
0.382
:param worder: The worder list output from word_rank_alignment
:type worder: list(int)
:param normalize: Flag to indicate normalization to between 0.0 and 1.0.
:type normalize: boolean
:return: The Kendall's Tau correlation coefficient.
:rtype: float
"""
worder_len = len(worder)
# With worder_len < 2, `choose(worder_len, 2)` will be 0.
# As we divide by this, it will give a ZeroDivisionError.
# To avoid this, we can just return the lowest possible score.
if worder_len < 2:
tau = -1
else:
# Extract the groups of increasing/monotonic sequences.
increasing_sequences = find_increasing_sequences(worder)
# Calculate no. of increasing_pairs in *worder* list.
num_increasing_pairs = sum(
choose(len(seq), 2) for seq in increasing_sequences)
# Calculate no. of possible pairs.
num_possible_pairs = choose(worder_len, 2)
# Kendall's Tau computation.
tau = 2 * num_increasing_pairs / num_possible_pairs - 1
if normalize: # If normalized, the tau output falls between 0.0 to 1.0
return (tau + 1) / 2
else: # Otherwise, the tau outputs falls between -1.0 to +1.0
return tau
def kendall_tau(worder, normalize=True):
"""
Calculates the Kendall's Tau correlation coefficient given the *worder*
list of word alignments from word_rank_alignment(), using the formula:
tau = 2 * num_increasing_pairs / num_possible pairs -1
Note that the no. of increasing pairs can be discontinuous in the *worder*
list and each each increasing sequence can be tabulated as choose(len(seq), 2)
no. of increasing pairs, e.g.
>>> worder = [7, 8, 9, 10, 6, 0, 1, 2, 3, 4, 5]
>>> number_possible_pairs = choose(len(worder), 2)
>>> round(kendall_tau(worder, normalize=False),3)
-0.236
>>> round(kendall_tau(worder),3)
0.382
:param worder: The worder list output from word_rank_alignment
:type worder: list(int)
:param normalize: Flag to indicate normalization
:type normalize: boolean
:return: The Kendall's Tau correlation coefficient.
:rtype: float
"""
worder_len = len(worder)
# Extract the groups of increasing/monotonic sequences.
increasing_sequences = find_increasing_sequences(worder)
# Calculate no. of increasing_pairs in *worder* list.
num_increasing_pairs = sum(choose(len(seq),2) for seq in increasing_sequences)
# Calculate no. of possible pairs.
num_possible_pairs = choose(worder_len, 2)
# Kendall's Tau computation.
tau = 2 * num_increasing_pairs / num_possible_pairs -1
if normalize: # If normalized, the tau output falls between 0.0 to 1.0
return (tau + 1) /2
else: # Otherwise, the tau outputs falls between -1.0 to +1.0
return tau