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model_comparison.py
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model_comparison.py
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import numpy as np
import pickle as pkl
import matplotlib.pyplot as plt
from model import *
from run_model import *
from skimage.measure import shannon_entropy
from skimage.feature import greycomatrix, greycoprops
_compare_dict = {'lbp': 0, 'cluster': 1, 'entropy': 2}
"""
This is an adjusted version of Arran's 'utils.py'
Since the classroom_seating module now provides a methods that directly gives the desired binary model state,
The 'reduction' method is not needed anymore.
We should merge them into one generally applicable version.
"""
"""
Returns a list of counts for each length of each cluster of seated students.
This method escentially returns a histogram of group "lengths". Note an aisle
is considered the end of a group. Only counts horizontal groupings and so
assumes rows are independent.
Args:
model_state: seating distribution as a binary matrix of seats
aisles: A list of vertical aisles.
Returns:
A numpy list of counts, where the ith element corresponds to the number of
i lengthed groups, up to the max possible length defined by the aisles
"""
def count_clusters(model_state, aisles=[6]):
# where the final counts will be stored
counts = np.zeros(model_state.shape[1] + 1)
for row in model_state:
# split the row into blocks and iterate over the seats
for block in np.split(row, aisles):
c = 0
for seat in block:
if seat == 1:
c += 1
else:
counts[c] += 1
c = 0
counts[c] += 1
# the value at i = 0 will be non-sensical, so set to 0
counts[0] = 0
return counts
"""
Returns a count of each value for a Local Binary Pattern (LBP) over all seats.
This method escentially returns a histogram that aims to capture
Advantages:
- Captures somewhat the spacial distribution of seating,
- The fine grain allows distinction between very similar but different models,
- Can be used to compare any sized lecture theater.
Args:
model_state: seating distribution as a binary matrix of seats
Returns:
A numpy list of length 256, with each element corresponding to the count of
each uniquley defined LBP
"""
def count_lbp(model_state):
# the relative coordinates in sequence in order to traverse around the
# seat so to build up the binary representation of the seat's 8 neighbors
i_deltas = [-1, -1, -1, 0, 1, 1, 1, 0]
j_deltas = [-1, 0, 1, 1, 1, 0, -1, -1]
# where the final counts will be stored
counts = np.zeros(256)
# iterate over all seats except the outer edges
for i in np.arange(1, model_state.shape[0] - 1):
for j in np.arange(1, model_state.shape[1] - 1):
# decimal representation of surrounding seats
dec = 0
for k, (i_d, j_d) in enumerate(zip(i_deltas, j_deltas)):
dec += model_state[i+i_d][j+j_d] * 2**k
# increase the count for this LBP
counts[int(dec)] += 1
return counts
"""
Calculates the entropy profile of a model state.
Advantages:
- Invariant to size, reflections, translations
- Captures large and small scale structure
Args:
model_state: seating distribution as a binary matrix of seats
Returns:
A list of entropies for neighborhood sizes k = 1 to minimium matrix side
length.
"""
def get_entropy(model_state):
entropies = []
height, width = model_state.shape
for k in range(1, min(height, width) + 1):
matrix_k = np.zeros([height - k + 1, width - k + 1])
# slide k by k window over model state and take the mean
for (row, col), val in np.ndenumerate(model_state):
if not ((row > (height - k)) or (col > (width - k))):
sub_matrix = np.zeros((k, k))
for i in range(k):
for j in range(k):
sub_matrix[i, j] = model_state[row+i, col+j]
matrix_k[row, col] = sub_matrix.mean()
# calculate entropy for this sub matrix by generating a discrete
# distribution of values and their frequencies
unique, counts = np.unique(matrix_k, return_counts=True)
total = sum(counts)
dist = np.array([x / total for x in counts])
entropy = -sum(dist * np.log2(dist))
entropies.append(entropy)
return entropies
"""
Insert aisles (represented by the given 'value') into the model_state.
"""
def insert_aisles(model_state, aisles, value):
for a in aisles:
if a < model_state.shape[1]:
model_state = np.insert(model_state, a, value, axis=1)
else:
model_state = np.concatenate((model_state, value*np.ones((model_state.shape[0],1))), axis=1)
return model_state
"""
############################################
Analysis Methods
############################################
"""
"""
Returns the Mean Square Error between two lists of numbers. If both lists are
different length, only compares up to the length of the shortest list.
Args:
list1: The first list.
list2: The second list.
Returns:
The MSE between the two lists.
"""
def calculate_mse(list1, list2):
mse = 0
for x, y in zip(list1, list2):
mse += (x - y)**2
return mse / min(len(list1), len(list2))
"""
Generates a profile of a set of models with selected method.
Args:
models: A list of models to analyse. Assumes all be the same shape.
method: {'lbp', 'cluster', 'entropy'} The method to use.
Returns:
A list of counts that is the average profile of the given models.
"""
def generate_profile(models, method='lbp'):
try:
val = _compare_dict[method]
except KeyError:
raise ValueError("Method must be 'lbp', 'cluster', or 'entropy'.")
# reduce all the models first
reduced_models = []
for m in models:
reduced_models.append(m.get_binary_model_state())
# setup profile depending on method type
if method == 'lbp':
profile = np.zeros(256)
f = count_lbp
args = []
elif method == 'cluster':
profile = np.zeros(reduced_models[0].shape[1]+1)
f = count_clusters
args = (models[0].classroom.aisles_x)
elif method == 'entropy':
profile = np.zeros(min(reduced_models[0].shape))
f = get_entropy
args = []
# build profile
for rm in reduced_models:
if method == 'cluster':
profile += f(rm, args)
else:
profile += f(rm)
return profile / len(models)
"""
Compute characteristic measures of a model state
Args:
model_state: seating distribution as a binary matrix of seats
method: {'homogeneity', 'correlation', 'rl_nonuniformity', 'rl_long_run_emphasis'} The method to use.
'homogeneity' and 'correlation' are features derived from the grey-level co-occurrence matrix (GLCM).
'rl_nonuniformity' and 'rl_long_run_emphasis' are features derived from the vector of run-lengths.
Returns:
The float value of the respective feature
"""
def get_characteristic_value(model_state, method='homogeneity', aisles=[0]):
if method == 'homogeneity':
# grey-level co-occurrence matrix for horizontal seat pairs with distance = 1
glcm = greycomatrix(model_state, [1], [0], symmetric=False, normed=True, levels=2)
return greycoprops(glcm, 'homogeneity')[0,0]
elif method == 'correlation':
# grey-level co-occurrence matrix for horizontal seat pairs with distance = 1
glcm = greycomatrix(model_state, [1], [0], symmetric=False, normed=True, levels=2)
return greycoprops(glcm, 'correlation')[0,0]
elif method == 'rl_nonuniformity':
run_lengths = count_clusters(model_state, aisles)
num_runs = sum(run_lengths)
return sum([rl**2 for rl in run_lengths])/num_runs
elif method == 'rl_long_run_emphasis':
run_lengths = count_clusters(model_state, aisles)
num_runs = sum(run_lengths)
return sum([rl * (j**2) for j, rl in enumerate(run_lengths)])/num_runs
else:
raise ValueError("No valid method name.")
"""
Compares two seating distributions by computing the Mean Square Error between their profiles.
Args:
model_state_1: Seating distribution as a binary matrix of seats
model_state_2: Seating distribution as a binary matrix of seats
method: {'lbp', 'cluster', 'entropy'} The method to be used to compute the profiles
aisles: If using the 'cluster' method, you can
specify where the aisles are as a list. Default [0].
Returns:
The MSE between the two profiles
"""
def compare(model_state_1, model_state_2, method='lbp', aisles=[0]):
try:
val = _compare_dict[method]
except KeyError:
raise ValueError("Method must be 'lbp', 'cluster', or 'entropy'.")
if model_state_1.ndim != 2 or model_state_2.ndim != 2:
raise ValueError("Models must be 2D.")
if method == 'lbp':
# Use the Local Binary Method
profile_1 = count_lbp(model_state_1)
profile_2 = count_lbp(model_state_2)
return calculate_mse(profile_1, profile_2)
elif method == 'cluster':
# Use the cluster size comparison
profile_1 = count_clusters(model_state_1, aisles)
profile_2 = count_clusters(model_state_2, aisles)
return calculate_mse(profile_1, profile_2)
elif method == 'entropy':
# Use the entropy comparison
profile_1 = get_entropy(model_state_1)
profile_2 = get_entropy(model_state_2)
return calculate_mse(profile_1, profile_2)
else:
return None
if __name__ == "__main__":
class_size = 100
models = [init_default_model([0,0,0,0], class_size), init_default_model([1,0,0,1], class_size), init_default_model([0,0,1,0], class_size)]
for i in range(100):
for m in models:
m.step()
model_states = [m.get_binary_model_state() for m in models]
aisles = models[0].classroom.aisles_x
for m in model_states:
plt.figure()
plt.imshow(m)
title = ""
for method in ['homogeneity', 'correlation', 'rl_nonuniformity', 'rl_long_run_emphasis']:
title += " {} = {:.2f} ".format(method, get_characteristic_value(m, method, aisles))
plt.title(title)
plt.show()