It comes to something where I have a day off work and do nothing other than clean the house…. that’s how bad this lockdown is getting.
That’s a slight exaggeration – my new found domesticatedness started just before lockdown but it has certainly been cemented as a habit. I tend to now sort things when I spot they need doing instead of leaving them to another time. It has helped massively on the domestic front and has helped keep all those petty housework arguments to a minimum.
So today has been a day of tiding the kitchen and giving it a good deep clean. In between that my parents dropped some shopping off from Cristyn and we arranged to go for a socially responsible, regulation distance, walk over Beechwood park later in the week. I’m hoping that on Friday the Welsh government start relaxing the rules slightly – certainly I’m hoping to be able to drive somewhere else for a walk.
There are many things keeping us going over the long lock down – not just debating the actions of politicians and their special advisers. Films and box-sets have been great….some new finds, some old classics.
So for today’s post here are the top ones for the past 10 weeks.
import matplotlib.pyplot as plt
from matplotlib import style
import numpy as np
style.use('ggplot')
# build SVM class
class Support_Vector_Machine:
# The __init__ method of a class is one that runs whenever an object is created with the class
# calling self in the class allows sharing of variables across the class, so is included in all function defs
def __init__(self, visualisation=True):
# sets visualisations to what ever the user specifies (defaults to True)
self.visualisation = visualisation
# defines colours for the two states 1 & -1
self.colors = {1:'r', -1:'b'}
# sets some standards for the graphs
if self.visualisation:
self.fig = plt.figure()
self.ax = self.fig.add_subplot(1,1,1)
# train
def fit(self, data):
# set up access to the data that's passed when the function is called
self.data = data
# { ||w||: [w,b] }
opt_dict = {}
#
transforms = [[1,1],
[-1,1],
[-1,-1],
[1,-1]]
# finding values to work with for our ranges.
all_data = [] # set up a placeholder for the values
# for loop to step through data and append it to all_data (list of values)
for yi in self.data:
for featureset in self.data[yi]:
for feature in featureset:
all_data.append(feature)
# next define the max and min value in list
self.max_feature_value = max(all_data)
self.min_feature_value = min(all_data)
# free up memory once we've got the values
all_data=None
# define step size for optimisation Big through to small
step_sizes = [self.max_feature_value * 0.1,
self.max_feature_value * 0.01,
# starts getting very high cost after this.
self.max_feature_value * 0.001]
# extremely expensive
b_range_multiple = 5
b_multiple = 5
# first element in vector w
latest_optimum = self.max_feature_value*10
## Begin the stepping process
for step in step_sizes:
w = np.array([latest_optimum,latest_optimum])
# we can do this because convex
optimized = False
while not optimized:
# we're not optimising b as much as w (not needed)
for b in np.arange(-1*(self.max_feature_value*b_range_multiple),
self.max_feature_value*b_range_multiple,
step*b_multiple):
for transformation in transforms:
w_t = w*transformation
found_option = True
# weakest link in the SVM fundamentally
# SMO attempts to fix this a bit
# yi(xi.w+b) >= 1
#
# #### add a break here later..
for i in self.data:
for xi in self.data[i]:
yi=i
if not yi*(np.dot(w_t,xi)+b) >= 1:
found_option = False
if found_option:
opt_dict[np.linalg.norm(w_t)] = [w_t,b]
if w[0]<0:
optimized = True
print('optimised a step')
else:
w = w - step
# break out of while loop
# take a list of the magnitudes and sort them
norms = sorted([n for n in opt_dict]) # sorting lowest to highest
#||w|| : [w,b]
opt_choice = opt_dict[norms[0]] # smallest magnitude
self.w = opt_choice[0] # sets w to first element in the smallest mag
self.b = opt_choice[1] # sets b to second element in the smallest mag
latest_optimum = opt_choice[0][0]+step*2 # resetting the opt to the latest
def predict(self,features):
# sign( x.w+b )
classification = np.sign(np.dot(np.array(features),self.w)+self.b)
if classification !=0 and self.visualisation:
self.ax.scatter(features[0], features[1], s=100, marker='*', c=self.colors[classification])
return classification
def visualise(self):
#scattering known featuresets using a one line for loop
[[self.ax.scatter(x[0],x[1],s=100,color=self.colors[i]) for x in data_dict[i]] for i in data_dict]
# hyperplane = x.w+b
def hyperplane(x,w,b,v):
# v = (w.x+b)
return (-w[0]*x-b+v) / w[1]
datarange = (self.min_feature_value*0.9,self.max_feature_value*1.1) # gives space on the graph
hyp_x_min = datarange[0]
hyp_x_max = datarange[1]
# w.x + b = 1
# pos sv hyperplane
psv1 = hyperplane(hyp_x_min, self.w, self.b, 1) # define the ys
psv2 = hyperplane(hyp_x_max, self.w, self.b, 1) # define the ys
self.ax.plot([hyp_x_min,hyp_x_max], [psv1,psv2], "k") # plot xs, ys then colour k=black g-- = green
# w.x + b = -1
# negative sv hyperplane
nsv1 = hyperplane(hyp_x_min, self.w, self.b, -1)
nsv2 = hyperplane(hyp_x_max, self.w, self.b, -1)
self.ax.plot([hyp_x_min,hyp_x_max], [nsv1,nsv2], "k")
# w.x + b = 0
# decision
db1 = hyperplane(hyp_x_min, self.w, self.b, 0)
db2 = hyperplane(hyp_x_max, self.w, self.b, 0)
self.ax.plot([hyp_x_min,hyp_x_max], [db1,db2], "g--")
plt.show()
# define data dictionary
data_dict = {-1:np.array([[1,7],
[2,8],
[3,8],]),
1:np.array([[5,1],
[6,-1],
[7,3],])}
svm = Support_Vector_Machine()
svm.fit(data=data_dict)
predict_us = [[0,10],
[1,3],
[3,4],
[3,5],
[5,5],
[5,6],
[6,-5],
[5,8]]
for p in predict_us:
svm.predict(p)
svm.visualise()
import matplotlib.pyplot as plt
from matplotlib import style
import numpy as np
style.use('ggplot')
# build SVM class
class Support_Vector_Machine:
# The __init__ method of a class is one that runs whenever an object is created with the class
# calling self in the class allows sharing of variables across the class, so is included in all function defs
def __init__(self, visualisation=True):
# sets visualisations to what ever the user specifies (defaults to True)
self.visualisation = visualisation
# defines colours for the two states 1 & -1
self.colors = {1:'r', -1:'b'}
# sets some standards for the graphs
if self.visualisation:
self.fig = plt.figure()
self.ax = self.fig.add_subplot(1,1,1)
# train
def fit(self, data):
# set up access to the data that's passed when the function is called
self.data = data
# { ||w||: [w,b] }
opt_dict = {}
#
transforms = [[1,1],
[-1,1],
[-1,-1],
[1,-1]]
# finding values to work with for our ranges.
all_data = [] # set up a placeholder for the values
# for loop to step through data and append it to all_data (list of values)
for yi in self.data:
for featureset in self.data[yi]:
for feature in featureset:
all_data.append(feature)
# next define the max and min value in list
self.max_feature_value = max(all_data)
self.min_feature_value = min(all_data)
# free up memory once we've got the values
all_data=None
# define step size for optimisation Big through to small
step_sizes = [self.max_feature_value * 0.1,
self.max_feature_value * 0.01,
# starts getting very high cost after this.
self.max_feature_value * 0.001]
# extremely expensive
b_range_multiple = 5
b_multiple = 5
# first element in vector w
latest_optimum = self.max_feature_value*10
## Begin the stepping process
for step in step_sizes:
w = np.array([latest_optimum,latest_optimum])
# we can do this because convex
optimized = False
while not optimized:
# we're not optimising b as much as w (not needed)
for b in np.arange(-1*(self.max_feature_value*b_range_multiple),
self.max_feature_value*b_range_multiple,
step*b_multiple):
for transformation in transforms:
w_t = w*transformation
found_option = True
# weakest link in the SVM fundamentally
# SMO attempts to fix this a bit
# yi(xi.w+b) >= 1
#
# #### add a break here later..
for i in self.data:
for xi in self.data[i]:
yi=i
if not yi*(np.dot(w_t,xi)+b) >= 1:
found_option = False
if found_option:
opt_dict[np.linalg.norm(w_t)] = [w_t,b]
if w[0]<0:
optimized = True
print('optimised a step')
else:
w = w - step
# break out of while loop
# take a list of the magnitudes and sort them
norms = sorted([n for n in opt_dict]) # sorting lowest to highest
#||w|| : [w,b]
opt_choice = opt_dict[norms[0]] # smallest magnitude
self.w = opt_choice[0] # sets w to first element in the smallest mag
self.b = opt_choice[1] # sets b to second element in the smallest mag
latest_optimum = opt_choice[0][0]+step*2 # resetting the opt to the latest
def predict(self,features):
# sign( x.w+b )
classification = np.sign(np.dot(np.array(features),self.w)+self.b)
return classification
# define data dictionary
data_dict = {-1:np.array([[1,7],
[2,8],
[3,8],]),
1:np.array([[5,1],
[6,-1],
[7,3],])}
import matplotlib.pyplot as plt
from matplotlib import style
import numpy as np
style.use('ggplot')
# build SVM class
class Support_Vector_Machine:
# The __init__ method of a class is one that runs whenever an object is created with the class
# calling self in the class allows sharing of variables across the class, so is included in all function defs
def __init__(self, visualisation=True):
# sets visualisations to what ever the user specifies (defaults to True)
self.visualisation = visualisation
# defines colours for the two states 1 & -1
self.colors = {1:'r', -1:'b'}
# sets some standards for the graphs
if self.visualisation:
self.fig = plt.figure()
self.ax = self.fig.add_subplot(1,1,1)
# train
def fit(self, data):
# set up access to the data that's passed when the function is called
self.data = data
# { ||w||: [w,b] }
opt_dict = {}
#
transforms = [[1,1],
[-1,1],
[-1,-1],
[1,-1]]
# finding values to work with for our ranges.
all_data = [] # set up a placeholder for the values
# for loop to step through data and append it to all_data (list of values)
for yi in self.data:
for featureset in self.data[yi]:
for feature in featureset:
all_data.append(feature)
# next define the max and min value in list
self.max_feature_value = max(all_data)
self.min_feature_value = min(all_data)
# free up memory once we've got the values
all_data=None
# define step size for optimisation Big through to small
step_sizes = [self.max_feature_value * 0.1,
self.max_feature_value * 0.01,
# starts getting very high cost after this.
self.max_feature_value * 0.001]
# extremely expensive
b_range_multiple = 5
b_multiple = 5
# first element in vector w
latest_optimum = self.max_feature_value*10
## Begin the stepping process
for step in step_sizes:
w = np.array([latest_optimum,latest_optimum])
# we can do this because convex
optimized = False
while not optimized:
pass
def predict(self,features):
# sign( x.w+b )
classification = np.sign(np.dot(np.array(features),self.w)+self.b)
return classification
# define data dictionary
data_dict = {-1:np.array([[1,7],
[2,8],
[3,8],]),
1:np.array([[5,1],
[6,-1],
[7,3],])}
import matplotlib.pyplot as plt
from matplotlib import style
import numpy as np
style.use('ggplot')
# build SVM class
class Support_Vector_Machine:
# The __init__ method of a class is one that runs whenever an object is created with the class
# calling self in the class allows sharing of variables across the class, so is included in all function defs
def __init__(self, visualisation=True):
# sets visualisations to what ever the user specifies (defaults to True)
self.visualisation = visualisation
# defines colours for the two states 1 & -1
self.colors = {1:'r', -1:'b'}
# sets some standards for the graphs
if self.visualisation:
self.fig = plt.figure()
self.ax = self.fig.add_subplot(1,1,1)
# train
def fit(self, data):
pass
def predict(self,features):
# sign( x.w+b )
classification = np.sign(np.dot(np.array(features),self.w)+self.b)
return classification
# define data dictionary
data_dict = {-1:np.array([[1,7],
[2,8],
[3,8],]),
1:np.array([[5,1],
[6,-1],
[7,3],])}
galiquis
