import numpy as np
import pandas as pd
import pandas.tools.rplot as rplot
import pylab as pl
import matplotlib as mpl
import matplotlib.pyplot as plt
%matplotlib inline
pd.set_option('display.notebook_repr_html', False)
pd.set_option('display.max_columns', 20)
pd.set_option('display.max_rows', 25)
#Load data
getData = np.asmatrix(np.loadtxt('/Users/mayank/Dropbox/Columbia University/Machine Learning/Lecture Notes/hw_2/girls_2_20_train.csv',
dtype='float',
delimiter=',',
usecols=(0,1),
unpack=True,
ndmin=0))
x = getData[0, :] #this is the age and also the featre vector in this case
y = getData[1, :] #this is the height
m = y.size # this is the number of examples
y = y.T #creating a vector matrix
x = x.T #creating a vector matrix
#creating design metrix to enable
#intercept
x0 = np.power(x,0)
#of order 1
x1 = x
z1 = np.concatenate((x0,x1),1)
beta1 = ((z1.T*z1).I)*(z1.T*y)
predictedValue1 = np.dot(z1, beta1)
#of order 2
x2 = np.power(x,2)
z2 = np.concatenate((x0,x1,x2),1)
beta2 = ((z2.T*z2).I)*(z2.T*y)
predictedValue2 = np.dot(z2, beta2)
#of order 3
x3 = np.power(x,3)
z3 = np.concatenate((x0,x1,x2,x3),1)
beta3 = ((z3.T*z3).I)*(z3.T*y)
predictedValue3 = np.dot(z3, beta3)
#of order 4
x4 = np.power(x,4)
z4 = np.concatenate((x0,x1,x2,x3,x4),1)
beta4 = ((z4.T*z4).I)*(z4.T*y)
predictedValue4 = np.dot(z4, beta4)
#of order 5
x5 = np.power(x,5)
z5 = np.concatenate((x0,x1,x2,x3,x4,x5),1)
beta5 = ((z5.T*z5).I)*(z5.T*y)
predictedValue5 = np.dot(z5, beta5)
#Plot the regression
age = np.array(x)
height = np.array(y)
Y0 = np.array(x0)
Y1 = np.array(predictedValue1)
Y2 = np.array(predictedValue2)
Y3 = np.array(predictedValue3)
Y4 = np.array(predictedValue4)
Y5 = np.array(predictedValue5)
plt.figure(1, figsize=(16, 9))
plt.clf()
plt.plot(age, height, 'ro')
#plt.plot(age, Y0, '-', label="d0")
plt.plot(age, Y1, 'b--', label="d1")
plt.plot(age, Y2, 'g--', label="d2")
plt.plot(age, Y3, 'r-', label="Best Fit - d3")
plt.plot(age, Y4, 'y--', label="d4")
plt.plot(age, Y5, 'k--', label="d5")
plt.legend(loc='best')
plt.title('Age and Stature')
plt.xlabel('Age in Years')
plt.ylabel('Height')
plt.show()
def getCost(z, y, beta):
#calculate the cost of a particular choice of beta
predictedValue = np.dot(z, beta)
#calculate squared error
sqErrors = np.power((predictedValue - y),2)
#calculate cost
J = (1.0 / (2 * m)) * sqErrors.sum()
return J
J1train = getCost(z1, y, beta1)
J2train = getCost(z2, y, beta2)
J3train = getCost(z3, y, beta3)
J4train = getCost(z4, y, beta4)
J5train = getCost(z5, y, beta5)
print J1train
print J2train
print J3train
print J4train
print J5train
51.0500560088
49.6515074062
20.0464096622
16.061916226
4.37596745653
####The best fit is for d=3
# validate model against girls_2_20_validation
#Load data
getData = np.asmatrix(np.loadtxt('/Users/mayank/Dropbox/Columbia University/Machine Learning/Lecture Notes/hw_2/girls_2_20_validation.csv',
dtype='float',
delimiter=',',
usecols=(0,1),
unpack=True,
ndmin=0))
x = getData[0, :] #this is the age and also the featre vector in this case
y = getData[1, :] #this is the height
m = y.size # this is the number of examples
y = y.T #creating a vector matrix
x = x.T #creating a vector matrix
#creating design metrix to enable
#intercept
x0 = np.power(x,0)
#of order 1
x1 = x
z1 = np.concatenate((x0,x1),1)
beta1 = ((z1.T*z1).I)*(z1.T*y)
predictedValue1 = np.dot(z1, beta1)
#of order 2
x2 = np.power(x,2)
z2 = np.concatenate((x0,x1,x2),1)
beta2 = ((z2.T*z2).I)*(z2.T*y)
predictedValue2 = np.dot(z2, beta2)
#of order 3
x3 = np.power(x,3)
z3 = np.concatenate((x0,x1,x2,x3),1)
beta3 = ((z3.T*z3).I)*(z3.T*y)
predictedValue3 = np.dot(z3, beta3)
#of order 4
x4 = np.power(x,4)
z4 = np.concatenate((x0,x1,x2,x3,x4),1)
beta4 = ((z4.T*z4).I)*(z4.T*y)
predictedValue4 = np.dot(z4, beta4)
#of order 5
x5 = np.power(x,5)
z5 = np.concatenate((x0,x1,x2,x3,x4,x5),1)
beta5 = ((z5.T*z5).I)*(z5.T*y)
predictedValue5 = np.dot(z5, beta5)
#Plot the regression
age = np.array(x)
height = np.array(y)
Y0 = np.array(x0)
Y1 = np.array(predictedValue1)
Y2 = np.array(predictedValue2)
Y3 = np.array(predictedValue3)
Y4 = np.array(predictedValue4)
Y5 = np.array(predictedValue5)
plt.figure(1, figsize=(16, 9))
plt.clf()
plt.plot(age, height, 'ro')
#plt.plot(age, Y0, '-', label="d0")
plt.plot(age, Y1, 'b--', label="d1")
plt.plot(age, Y2, 'g--', label="d2")
plt.plot(age, Y3, 'r-', label="Best Fit - d3")
plt.plot(age, Y4, 'y--', label="d4")
plt.plot(age, Y5, 'k--', label="d5")
plt.legend(loc='best')
plt.title('Age and Stature')
plt.xlabel('Age in Years')
plt.ylabel('Height')
plt.show()
def getCost(z, y, beta):
#calculate the cost of a particular choice of beta
predictedValue = np.dot(z, beta)
#print predictedValue
#print y
#print y.shape
#print predictedValue.shape
#calculate squared error
sqErrors = np.power((predictedValue - y),2)
#calculate cost
J = (1.0 / (2 * m)) * sqErrors.sum()
#print J
return J
J1valid = getCost(z1, y, beta1)
J2valid = getCost(z2, y, beta2)
J3valid = getCost(z3, y, beta3)
J4valid = getCost(z4, y, beta4)
J5valid = getCost(z5, y, beta5)
#Plot training and validation errors against dimensions
TrainingError = [J1train, J2train, J3train, J4train, J5train]
ValidationError = [J1valid, J2valid, J3valid, J4valid, J5valid]
Dimension = [1,2,3,4,5]
plt.figure(1, figsize=(16, 9))
plt.clf()
plt.plot(Dimension, TrainingError, 'r-', label="Training Error")
plt.plot(Dimension, ValidationError, 'b-', label="Validation Error")
plt.legend(loc='best')
plt.title('Estimation error by degree of Polynomial')
plt.xlabel('degree')
plt.ylabel('Error')
plt.show()
####As the validation error curve is below the test error curve for d3 and d4, either of them can be used as a model. However, d3 is the better of the two as it reduces over fitting.
Problem 2: Logistic Regression on the iris dataset Download the iris dataset from the repository. Read the description of the data.
The Iris dataset contains 50 examples each for 3 class of the Iris plant. The features are:
- sepal length in cm
- sepal width in cm
- petal length in cm
- petal width in cm
The label/class are:
- Iris Setosa
- Iris Versicolour
- Iris Virginica
#set data source path
path = '/Users/mayank/Dropbox/Columbia University/Machine Learning/Lecture Notes/hw_2/iris_data.csv'
#set column names as the data doesn't have headers
headers = ['sLength', 'sWidth', 'pLength', 'pWidth', 'cLabel']
#get the data, specify that there are no headers as the default will read first row as headers
getData = pd.read_csv(path, header=None, names=headers)
#confirm data extration
getData.head()
sLength sWidth pLength pWidth cLabel
0 5.1 3.5 1.4 0.2 Iris-setosa
1 4.9 3.0 1.4 0.2 Iris-setosa
2 4.7 3.2 1.3 0.2 Iris-setosa
3 4.6 3.1 1.5 0.2 Iris-setosa
4 5.0 3.6 1.4 0.2 Iris-setosa
[5 rows x 5 columns]
getData.groupby("cLabel").describe()
sLength sWidth pLength pWidth
cLabel
Iris-setosa count 50.000000 50.000000 50.000000 50.000000
mean 5.006000 3.418000 1.464000 0.244000
std 0.352490 0.381024 0.173511 0.107210
min 4.300000 2.300000 1.000000 0.100000
25% 4.800000 3.125000 1.400000 0.200000
50% 5.000000 3.400000 1.500000 0.200000
75% 5.200000 3.675000 1.575000 0.300000
max 5.800000 4.400000 1.900000 0.600000
Iris-versicolor count 50.000000 50.000000 50.000000 50.000000
mean 5.936000 2.770000 4.260000 1.326000
std 0.516171 0.313798 0.469911 0.197753
min 4.900000 2.000000 3.000000 1.000000
25% 5.600000 2.525000 4.000000 1.200000
50% 5.900000 2.800000 4.350000 1.300000
75% 6.300000 3.000000 4.600000 1.500000
max 7.000000 3.400000 5.100000 1.800000
Iris-virginica count 50.000000 50.000000 50.000000 50.000000
mean 6.588000 2.974000 5.552000 2.026000
std 0.635880 0.322497 0.551895 0.274650
min 4.900000 2.200000 4.500000 1.400000
25% 6.225000 2.800000 5.100000 1.800000
50% 6.500000 3.000000 5.550000 2.000000
75% 6.900000 3.175000 5.875000 2.300000
max 7.900000 3.800000 6.900000 2.500000
[24 rows x 4 columns]
#visually explore the datafrom pandas.tools.plotting import scatter_matrix
pd.scatter_matrix(getData, alpha=0.2, figsize=(8, 8), diagonal='kde')
array([[<matplotlib.axes.AxesSubplot object at 0x1118c0a50>,
<matplotlib.axes.AxesSubplot object at 0x111e58dd0>,
<matplotlib.axes.AxesSubplot object at 0x111e55e10>,
<matplotlib.axes.AxesSubplot object at 0x111df84d0>],
[<matplotlib.axes.AxesSubplot object at 0x111e06590>,
<matplotlib.axes.AxesSubplot object at 0x111e3b1d0>,
<matplotlib.axes.AxesSubplot object at 0x111e87210>,
<matplotlib.axes.AxesSubplot object at 0x103541690>],
[<matplotlib.axes.AxesSubplot object at 0x111e3e050>,
<matplotlib.axes.AxesSubplot object at 0x1035837d0>,
<matplotlib.axes.AxesSubplot object at 0x1035a6d10>,
<matplotlib.axes.AxesSubplot object at 0x10578b790>],
[<matplotlib.axes.AxesSubplot object at 0x1057b5210>,
<matplotlib.axes.AxesSubplot object at 0x105799850>,
<matplotlib.axes.AxesSubplot object at 0x1057f5710>,
<matplotlib.axes.AxesSubplot object at 0x1129149d0>]], dtype=object)
#Insert a column 'newLabel' to traslate string values in 'cLabel' to numberical vlaues
#Initialize the column with numberical value 0
#getData.insert(5, 'newLabel', 0)
#Insert values in newLabel based ont he value in cLabel
getData['newLabel'] = getData.apply(lambda row: (1
if row['cLabel']=='Iris-setosa'
else 2
if row['cLabel']=='Iris-versicolor'
else 3), axis=1)
getData.head()
sLength sWidth pLength pWidth cLabel newLabel
0 5.1 3.5 1.4 0.2 Iris-setosa 1
1 4.9 3.0 1.4 0.2 Iris-setosa 1
2 4.7 3.2 1.3 0.2 Iris-setosa 1
3 4.6 3.1 1.5 0.2 Iris-setosa 1
4 5.0 3.6 1.4 0.2 Iris-setosa 1
[5 rows x 6 columns]
2.2 Plot the distribution of the data. For each pair of features, create a scatter plot of the 3 species of Iris
#For Sepal Length and Sepal Width
setosaSeries = getData[getData.newLabel == 1]
versicolorSeries = getData[getData.newLabel == 2]
verginicaSeries = getData[getData.newLabel == 3]
plt.figure(1, figsize=(16, 9))
plt.scatter(setosaSeries.sLength , setosaSeries.sWidth, s=35, marker='o', color='green', label='Iris-setosa')
plt.scatter(versicolorSeries.sLength , versicolorSeries.sWidth, s=35, marker='o', color ='red', label= 'Iris-versicolor')
plt.scatter(verginicaSeries.sLength , verginicaSeries.sWidth, s=35, marker='o', color='blue', label='Iris-virginica')
plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
plt.title('Distribution for Sepal Length and Width')
plt.xlabel('Sepal Length')
plt.ylabel('Sepal Width')
<matplotlib.text.Text at 0x111e0d050>
#For Petal Length and Petal Width
setosaSeries = getData[getData.newLabel == 1]
versicolorSeries = getData[getData.newLabel == 2]
verginicaSeries = getData[getData.newLabel == 3]
plt.figure(1, figsize=(16, 9))
plt.scatter(setosaSeries.pLength , setosaSeries.pWidth, s=35, marker='o', color='green', label='Iris-setosa')
plt.scatter(versicolorSeries.pLength , versicolorSeries.pWidth, s=35, marker='o', color ='red', label= 'Iris-versicolor')
plt.scatter(verginicaSeries.pLength , verginicaSeries.pWidth, s=35, marker='o', color='blue', label='Iris-virginica')
plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
plt.title('Distribution for Petal Length and Width')
plt.xlabel('Petal Length')
plt.ylabel('Petal Width')
<matplotlib.text.Text at 0x1129f1750>
#For Sepal Length and Petal Width
setosaSeries = getData[getData.newLabel == 1]
versicolorSeries = getData[getData.newLabel == 2]
verginicaSeries = getData[getData.newLabel == 3]
plt.figure(1, figsize=(16, 9))
plt.scatter(setosaSeries.sLength , setosaSeries.pWidth, s=35, marker='o', color='green', label='Iris-setosa')
plt.scatter(versicolorSeries.sLength , versicolorSeries.pWidth, s=35, marker='o', color ='red', label= 'Iris-versicolor')
plt.scatter(verginicaSeries.sLength , verginicaSeries.pWidth, s=35, marker='o', color='blue', label='Iris-virginica')
plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
plt.title('Distribution for Sepal Length and Petal Width')
plt.xlabel('Sepal Length')
plt.ylabel('Petal Width')
<matplotlib.text.Text at 0x11381f210>
#For Sepal Length and Petal Length
setosaSeries = getData[getData.newLabel == 1]
versicolorSeries = getData[getData.newLabel == 2]
verginicaSeries = getData[getData.newLabel == 3]
plt.figure(1, figsize=(16, 9))
plt.scatter(setosaSeries.sLength , setosaSeries.pLength, s=35, marker='o', color='green', label='Iris-setosa')
plt.scatter(versicolorSeries.sLength , versicolorSeries.pLength, s=35, marker='o', color ='red', label= 'Iris-versicolor')
plt.scatter(verginicaSeries.sLength , verginicaSeries.pLength, s=35, marker='o', color='blue', label='Iris-virginica')
plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
plt.title('Distribution for Sepal Length and Petal Length')
plt.xlabel('Sepal Length')
plt.ylabel('Petal Length')
<matplotlib.text.Text at 0x11382f8d0>
#For Sepal Width and Petal Width
setosaSeries = getData[getData.newLabel == 1]
versicolorSeries = getData[getData.newLabel == 2]
verginicaSeries = getData[getData.newLabel == 3]
plt.figure(1, figsize=(16, 9))
plt.scatter(setosaSeries.sWidth , setosaSeries.pWidth, s=35, marker='o', color='green', label='Iris-setosa')
plt.scatter(versicolorSeries.sWidth , versicolorSeries.pWidth, s=35, marker='o', color ='red', label= 'Iris-versicolor')
plt.scatter(verginicaSeries.sWidth , verginicaSeries.pWidth, s=35, marker='o', color='blue', label='Iris-virginica')
plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
plt.title('Distribution for Sepal Width and Petal Width')
plt.xlabel('Sepal Width')
plt.ylabel('Petal Width')
<matplotlib.text.Text at 0x113831bd0>
#For Sepal Width and Petal Legth
setosaSeries = getData[getData.newLabel == 1]
versicolorSeries = getData[getData.newLabel == 2]
verginicaSeries = getData[getData.newLabel == 3]
plt.figure(1, figsize=(16, 9))
plt.scatter(setosaSeries.sWidth , setosaSeries.pLength, s=35, marker='o', color='green', label='Iris-setosa')
plt.scatter(versicolorSeries.sWidth , versicolorSeries.pLength, s=35, marker='o', color ='red', label= 'Iris-versicolor')
plt.scatter(verginicaSeries.sWidth , verginicaSeries.pLength, s=35, marker='o', color='blue', label='Iris-virginica')
plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
plt.title('Distribution for Sepal Width and Petal Length')
plt.xlabel('Sepal Width')
plt.ylabel('Petal Length')
<matplotlib.text.Text at 0x114367910>
Based on the drawn decision boundaries on the scatter plot, the regularized logistic regression implemented in sklearn to classify Setosa from the rest of flowers does not make any error.
# import the first couple of feature
X = getData[['sLength','sWidth']]
#Reference SciKit-Learn documentation: http://scikit-learn.org/stable/auto_examples/linear_model/plot_iris_logistic.html
#Define a function based on the Logistic Regression code to loop through different label values
def logregLoopRegularized(Y):
from sklearn import linear_model
h = .02 # step size in the mesh
logreg = linear_model.LogisticRegression(C=1e5)
# Neighbours Classifier to fit the data.
logreg.fit(X, Y)
#Score
score = logreg.score(X, Y)
print 'The score for this iteration is'
print score
# Plot the decision boundary. Assign a color to each point in the mesh [x_min, m_max]x[y_min, y_max].
x_min, x_max = X['sLength'].min() - .5, X['sLength'].max() + .5
y_min, y_max = X['sWidth'].min() - .5, X['sWidth'].max() + .5
xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
#Predict
Z = logreg.predict(np.c_[xx.ravel(), yy.ravel()])
# Plot result
Z = Z.reshape(xx.shape)
pl.figure(1, figsize=(16, 9))
pl.pcolormesh(xx, yy, Z, cmap=pl.cm.Paired)
pl.xlim(xx.min(), xx.max())
pl.ylim(yy.min(), yy.max())
# Plot training points
pl.scatter(X['sLength'], X['sWidth'], c=Y, edgecolors='k', cmap=pl.cm.Paired)
pl.xlabel('Length')
pl.ylabel('Width')
#Loop through label values and plot boundries dynamically changing the plot title
for i in range(1,4):
Y = getData.newLabel==i
logregLoopRegularized(Y)
if i == 1:
T='Setosa classification from the rest of flowers for C=1e5'
elif i == 2:
T='Versicolor classification from the rest of flowers for C=1e5'
else:
T='Verginica classification from the rest of flowers for C=1e5'
pl.title(T)
pl.xticks(())
pl.yticks(())
pl.show()
i=i+1
The score for this iteration is
1.0
The score for this iteration is
0.713333333333
The score for this iteration is
0.806666666667
Based on the drawn decision boundaries on the scatter plot, the logistic regression implemented in sklearn to classify Virginica the rest of flowers makes 31 (21+10) errors for C=1 as compared to 22 (14+8) errors for C=1e5.
#Reference SciKit-Learn documentation: http://scikit-learn.org/stable/auto_examples/linear_model/plot_iris_logistic.html
#Define a function based on the Logistic Regression code to loop through different label values
def logregLoop(Y):
from sklearn import linear_model
h = .02 # step size in the mesh
#for C = 1
logreg = linear_model.LogisticRegression(C=1)
#Neighbours Classifier to fit the data.
logreg.fit(X, Y)
score = logreg.score(X, Y)
print 'The score for this iteration is'
print score
# Plot decision boundary. Assign a color to each point in the mesh [x_min, m_max]x[y_min, y_max].
x_min, x_max = X['sLength'].min() - .5, X['sLength'].max() + .5
y_min, y_max = X['sWidth'].min() - .5, X['sWidth'].max() + .5
xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
#Predict
Z = logreg.predict(np.c_[xx.ravel(), yy.ravel()])
#Plot results
Z = Z.reshape(xx.shape)
pl.figure(1, figsize=(16, 9))
pl.pcolormesh(xx, yy, Z, cmap=pl.cm.Paired)
pl.xlim(xx.min(), xx.max())
pl.ylim(yy.min(), yy.max())
# Plot training points
pl.scatter(X['sLength'], X['sWidth'], c=Y, edgecolors='k', cmap=pl.cm.Paired)
pl.xlabel('Length')
pl.ylabel('Width')
Y = getData.newLabel==3
logregLoop(Y)
pl.title('Virginica classification from the rest of flowers for C=1')
pl.xticks(())
pl.yticks(())
pl.show()
The score for this iteration is
0.726666666667
2.5 Infer errors made by a polynomial model for classfying Verginica based on the decision boundries and scatter plot
Y = getData.newLabel
#Reference SciKit-Learn documentation: http://scikit-learn.org/stable/auto_examples/linear_model/plot_iris_logistic.html
def logregLoopRegularizedPolynomial(Y, P):
from sklearn import linear_model
h = .02 # step size in the mesh
newX = np.power(X, P)
logreg = linear_model.LogisticRegression(C=1e5)
# Neighbours Classifier and fit the data.
logreg.fit(newX, Y)
score = logreg.score(newX, Y)
print 'The score for this iteration is'
print score
# Plot the decision boundary. For that, we will assign a color to each
# point in the mesh [x_min, m_max]x[y_min, y_max].
x_min, x_max = newX['sLength'].min() - .5, newX['sLength'].max() + .5
y_min, y_max = newX['sWidth'].min() - .5, newX['sWidth'].max() + .5
xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
Z = logreg.predict(np.c_[xx.ravel(), yy.ravel()])
# Put the result into a color plot
Z = Z.reshape(xx.shape)
pl.figure(1, figsize=(16, 9))
pl.pcolormesh(xx, yy, Z, cmap=pl.cm.Paired)
# Plot also the training points
pl.scatter(newX['sLength'], newX['sWidth'], c=Y, edgecolors='k', cmap=pl.cm.Paired)
pl.xlabel('Length')
pl.ylabel('Width')
pl.title('Classification for all Classes')
pl.xlim(xx.min(), xx.max())
pl.ylim(yy.min(), yy.max())
#Loop through power values 2 & 3 and plot boundries dynamically changing the plot title
for i in range(2,4):
Y = getData.newLabel==3
P = i
logregLoopRegularizedPolynomial(Y, P)
if i == 2:
T='Verginica classification from the rest of flowers when the features are raised to the power 2'
else:
T='Verginica classification from the rest of flowers when the features are raised to the power 3'
pl.title(T)
pl.xticks(())
pl.yticks(())
pl.show()
i=i+1
The score for this iteration is
0.806666666667
The score for this iteration is
0.8
#Loop through power values 4 &5 and plot boundries dynamically changing the plot title
for i in range(4,6):
Y = getData.newLabel==3
P = i
#logregLoopRegularizedPolynomial(Y, P)
#CAUTION takes a very long time to run
if i == 4:
T='Verginica classification from the rest of flowers when the features are raised to the power 4'
else:
T='Verginica classification from the rest of flowers when the features are raised to the power 5'
pl.title(T)
pl.xticks(())
pl.yticks(())
pl.show()
i=i+1
#Loop through power value 6 and plot boundries dynamically changing the plot title
Y = getData.newLabel==3
P = i
#logregLoopRegularizedPolynomial(Y, P)
#Caution takes a very long time to run
T='Verginica classification from the rest of flowers when the features are raised to the power 6'
pl.title(T)
pl.xticks(())
pl.yticks(())
pl.show()
import numpy as np
# map the LED outputs
dataLED = np.array([[1,1,1,1,1,1,1,0],
[1,0,1,1,0,0,0,0],
[1,1,1,0,1,1,0,1],
[1,1,1,1,1,0,0,1],
[1,0,0,1,0,0,1,1],
[1,1,0,1,1,0,1,1],
[1,0,0,1,1,1,1,1],
[1,1,1,1,0,0,0,0],
[1,1,1,1,1,1,1,1],
[1,1,1,1,1,0,1,1]])
#setup the known classification for odd/even number.
expect = np.array([[-1],[1],[-1],[1],[-1],[1],[-1],[1], [-1],[1]])
#initialize the weights
W = np.array([[1],[1],[1],[1],[1],[1],[1],[1]])
def train(data,weights):
print('Incoming data ')
print data
dataSize= len(data)
print('This is the number of rows ')
print dataSize
print('This is the size of the weights ')
# print wSize
for x in range(dataSize):
print('LED row number is ')
print(x)
row = data[x]
print('LED binary code is ')
print row
print('Confirm shape of incoming row')
print row.shape
print('Confirm shape of incoming weights ')
print(W.shape)
dotSUM = np.dot(row,W)
print ('This is the sum after the dot product ')
print dotSUM
if dotSUM > 0:
predicted = 1
else:
predicted = -1
print ('The predicted value was ')
print predicted
expected = expect[x]
print ('The expected value was ')
print expected
if expected*predicted < 0:
#update weights
print('Thia the array ')
arrayRow = np.asarray(row)
print arrayRow.shape
wSize = weights.size
for i in range (wSize):
print('This it the W coming in ')
print W[i]
W[i] += expected*arrayRow[i]
print ('This is the updated W ')
print W
print ('This is the final weights ')
newWeight = W
print newWeight
###if newWeight == train(trainLED, newWeight):'''
#print('Convergence reached ')
#train for LED data
trainLED = dataLED
train(trainLED,W)
Incoming data
[[1 1 1 1 1 1 1 0]
[1 0 1 1 0 0 0 0]
[1 1 1 0 1 1 0 1]
[1 1 1 1 1 0 0 1]
[1 0 0 1 0 0 1 1]
[1 1 0 1 1 0 1 1]
[1 0 0 1 1 1 1 1]
[1 1 1 1 0 0 0 0]
[1 1 1 1 1 1 1 1]
[1 1 1 1 1 0 1 1]]
This is the number of rows
10
This is the size of the weights
LED row number is
0
LED binary code is
[1 1 1 1 1 1 1 0]
Confirm shape of incoming row
(8,)
Confirm shape of incoming weights
(8, 1)
This is the sum after the dot product
[7]
The predicted value was
1
The expected value was
[-1]
Thia the array
(8,)
This it the W coming in
[1]
This is the updated W
[[0]
[1]
[1]
[1]
[1]
[1]
[1]
[1]]
This it the W coming in
[1]
This is the updated W
[[0]
[0]
[1]
[1]
[1]
[1]
[1]
[1]]
This it the W coming in
[1]
This is the updated W
[[0]
[0]
[0]
[1]
[1]
[1]
[1]
[1]]
This it the W coming in
[1]
This is the updated W
[[0]
[0]
[0]
[0]
[1]
[1]
[1]
[1]]
This it the W coming in
[1]
This is the updated W
[[0]
[0]
[0]
[0]
[0]
[1]
[1]
[1]]
This it the W coming in
[1]
This is the updated W
[[0]
[0]
[0]
[0]
[0]
[0]
[1]
[1]]
This it the W coming in
[1]
This is the updated W
[[0]
[0]
[0]
[0]
[0]
[0]
[0]
[1]]
This it the W coming in
[1]
This is the updated W
[[0]
[0]
[0]
[0]
[0]
[0]
[0]
[1]]
LED row number is
1
LED binary code is
[1 0 1 1 0 0 0 0]
Confirm shape of incoming row
(8,)
Confirm shape of incoming weights
(8, 1)
This is the sum after the dot product
[0]
The predicted value was
-1
The expected value was
[1]
Thia the array
(8,)
This it the W coming in
[0]
This is the updated W
[[1]
[0]
[0]
[0]
[0]
[0]
[0]
[1]]
This it the W coming in
[0]
This is the updated W
[[1]
[0]
[0]
[0]
[0]
[0]
[0]
[1]]
This it the W coming in
[0]
This is the updated W
[[1]
[0]
[1]
[0]
[0]
[0]
[0]
[1]]
This it the W coming in
[0]
This is the updated W
[[1]
[0]
[1]
[1]
[0]
[0]
[0]
[1]]
This it the W coming in
[0]
This is the updated W
[[1]
[0]
[1]
[1]
[0]
[0]
[0]
[1]]
This it the W coming in
[0]
This is the updated W
[[1]
[0]
[1]
[1]
[0]
[0]
[0]
[1]]
This it the W coming in
[0]
This is the updated W
[[1]
[0]
[1]
[1]
[0]
[0]
[0]
[1]]
This it the W coming in
[1]
This is the updated W
[[1]
[0]
[1]
[1]
[0]
[0]
[0]
[1]]
LED row number is
2
LED binary code is
[1 1 1 0 1 1 0 1]
Confirm shape of incoming row
(8,)
Confirm shape of incoming weights
(8, 1)
This is the sum after the dot product
[3]
The predicted value was
1
The expected value was
[-1]
Thia the array
(8,)
This it the W coming in
[1]
This is the updated W
[[0]
[0]
[1]
[1]
[0]
[0]
[0]
[1]]
This it the W coming in
[0]
This is the updated W
[[ 0]
[-1]
[ 1]
[ 1]
[ 0]
[ 0]
[ 0]
[ 1]]
This it the W coming in
[1]
This is the updated W
[[ 0]
[-1]
[ 0]
[ 1]
[ 0]
[ 0]
[ 0]
[ 1]]
This it the W coming in
[1]
This is the updated W
[[ 0]
[-1]
[ 0]
[ 1]
[ 0]
[ 0]
[ 0]
[ 1]]
This it the W coming in
[0]
This is the updated W
[[ 0]
[-1]
[ 0]
[ 1]
[-1]
[ 0]
[ 0]
[ 1]]
This it the W coming in
[0]
This is the updated W
[[ 0]
[-1]
[ 0]
[ 1]
[-1]
[-1]
[ 0]
[ 1]]
This it the W coming in
[0]
This is the updated W
[[ 0]
[-1]
[ 0]
[ 1]
[-1]
[-1]
[ 0]
[ 1]]
This it the W coming in
[1]
This is the updated W
[[ 0]
[-1]
[ 0]
[ 1]
[-1]
[-1]
[ 0]
[ 0]]
LED row number is
3
LED binary code is
[1 1 1 1 1 0 0 1]
Confirm shape of incoming row
(8,)
Confirm shape of incoming weights
(8, 1)
This is the sum after the dot product
[-1]
The predicted value was
-1
The expected value was
[1]
Thia the array
(8,)
This it the W coming in
[0]
This is the updated W
[[ 1]
[-1]
[ 0]
[ 1]
[-1]
[-1]
[ 0]
[ 0]]
This it the W coming in
[-1]
This is the updated W
[[ 1]
[ 0]
[ 0]
[ 1]
[-1]
[-1]
[ 0]
[ 0]]
This it the W coming in
[0]
This is the updated W
[[ 1]
[ 0]
[ 1]
[ 1]
[-1]
[-1]
[ 0]
[ 0]]
This it the W coming in
[1]
This is the updated W
[[ 1]
[ 0]
[ 1]
[ 2]
[-1]
[-1]
[ 0]
[ 0]]
This it the W coming in
[-1]
This is the updated W
[[ 1]
[ 0]
[ 1]
[ 2]
[ 0]
[-1]
[ 0]
[ 0]]
This it the W coming in
[-1]
This is the updated W
[[ 1]
[ 0]
[ 1]
[ 2]
[ 0]
[-1]
[ 0]
[ 0]]
This it the W coming in
[0]
This is the updated W
[[ 1]
[ 0]
[ 1]
[ 2]
[ 0]
[-1]
[ 0]
[ 0]]
This it the W coming in
[0]
This is the updated W
[[ 1]
[ 0]
[ 1]
[ 2]
[ 0]
[-1]
[ 0]
[ 1]]
LED row number is
4
LED binary code is
[1 0 0 1 0 0 1 1]
Confirm shape of incoming row
(8,)
Confirm shape of incoming weights
(8, 1)
This is the sum after the dot product
[4]
The predicted value was
1
The expected value was
[-1]
Thia the array
(8,)
This it the W coming in
[1]
This is the updated W
[[ 0]
[ 0]
[ 1]
[ 2]
[ 0]
[-1]
[ 0]
[ 1]]
This it the W coming in
[0]
This is the updated W
[[ 0]
[ 0]
[ 1]
[ 2]
[ 0]
[-1]
[ 0]
[ 1]]
This it the W coming in
[1]
This is the updated W
[[ 0]
[ 0]
[ 1]
[ 2]
[ 0]
[-1]
[ 0]
[ 1]]
This it the W coming in
[2]
This is the updated W
[[ 0]
[ 0]
[ 1]
[ 1]
[ 0]
[-1]
[ 0]
[ 1]]
This it the W coming in
[0]
This is the updated W
[[ 0]
[ 0]
[ 1]
[ 1]
[ 0]
[-1]
[ 0]
[ 1]]
This it the W coming in
[-1]
This is the updated W
[[ 0]
[ 0]
[ 1]
[ 1]
[ 0]
[-1]
[ 0]
[ 1]]
This it the W coming in
[0]
This is the updated W
[[ 0]
[ 0]
[ 1]
[ 1]
[ 0]
[-1]
[-1]
[ 1]]
This it the W coming in
[1]
This is the updated W
[[ 0]
[ 0]
[ 1]
[ 1]
[ 0]
[-1]
[-1]
[ 0]]
LED row number is
5
LED binary code is
[1 1 0 1 1 0 1 1]
Confirm shape of incoming row
(8,)
Confirm shape of incoming weights
(8, 1)
This is the sum after the dot product
[0]
The predicted value was
-1
The expected value was
[1]
Thia the array
(8,)
This it the W coming in
[0]
This is the updated W
[[ 1]
[ 0]
[ 1]
[ 1]
[ 0]
[-1]
[-1]
[ 0]]
This it the W coming in
[0]
This is the updated W
[[ 1]
[ 1]
[ 1]
[ 1]
[ 0]
[-1]
[-1]
[ 0]]
This it the W coming in
[1]
This is the updated W
[[ 1]
[ 1]
[ 1]
[ 1]
[ 0]
[-1]
[-1]
[ 0]]
This it the W coming in
[1]
This is the updated W
[[ 1]
[ 1]
[ 1]
[ 2]
[ 0]
[-1]
[-1]
[ 0]]
This it the W coming in
[0]
This is the updated W
[[ 1]
[ 1]
[ 1]
[ 2]
[ 1]
[-1]
[-1]
[ 0]]
This it the W coming in
[-1]
This is the updated W
[[ 1]
[ 1]
[ 1]
[ 2]
[ 1]
[-1]
[-1]
[ 0]]
This it the W coming in
[-1]
This is the updated W
[[ 1]
[ 1]
[ 1]
[ 2]
[ 1]
[-1]
[ 0]
[ 0]]
This it the W coming in
[0]
This is the updated W
[[ 1]
[ 1]
[ 1]
[ 2]
[ 1]
[-1]
[ 0]
[ 1]]
LED row number is
6
LED binary code is
[1 0 0 1 1 1 1 1]
Confirm shape of incoming row
(8,)
Confirm shape of incoming weights
(8, 1)
This is the sum after the dot product
[4]
The predicted value was
1
The expected value was
[-1]
Thia the array
(8,)
This it the W coming in
[1]
This is the updated W
[[ 0]
[ 1]
[ 1]
[ 2]
[ 1]
[-1]
[ 0]
[ 1]]
This it the W coming in
[1]
This is the updated W
[[ 0]
[ 1]
[ 1]
[ 2]
[ 1]
[-1]
[ 0]
[ 1]]
This it the W coming in
[1]
This is the updated W
[[ 0]
[ 1]
[ 1]
[ 2]
[ 1]
[-1]
[ 0]
[ 1]]
This it the W coming in
[2]
This is the updated W
[[ 0]
[ 1]
[ 1]
[ 1]
[ 1]
[-1]
[ 0]
[ 1]]
This it the W coming in
[1]
This is the updated W
[[ 0]
[ 1]
[ 1]
[ 1]
[ 0]
[-1]
[ 0]
[ 1]]
This it the W coming in
[-1]
This is the updated W
[[ 0]
[ 1]
[ 1]
[ 1]
[ 0]
[-2]
[ 0]
[ 1]]
This it the W coming in
[0]
This is the updated W
[[ 0]
[ 1]
[ 1]
[ 1]
[ 0]
[-2]
[-1]
[ 1]]
This it the W coming in
[1]
This is the updated W
[[ 0]
[ 1]
[ 1]
[ 1]
[ 0]
[-2]
[-1]
[ 0]]
LED row number is
7
LED binary code is
[1 1 1 1 0 0 0 0]
Confirm shape of incoming row
(8,)
Confirm shape of incoming weights
(8, 1)
This is the sum after the dot product
[3]
The predicted value was
1
The expected value was
[1]
LED row number is
8
LED binary code is
[1 1 1 1 1 1 1 1]
Confirm shape of incoming row
(8,)
Confirm shape of incoming weights
(8, 1)
This is the sum after the dot product
[0]
The predicted value was
-1
The expected value was
[-1]
LED row number is
9
LED binary code is
[1 1 1 1 1 0 1 1]
Confirm shape of incoming row
(8,)
Confirm shape of incoming weights
(8, 1)
This is the sum after the dot product
[2]
The predicted value was
1
The expected value was
[1]
This is the final weights
[[ 0]
[ 1]
[ 1]
[ 1]
[ 0]
[-2]
[-1]
[ 0]]
Binary coding table that allows to represent each digit with the 7 leds and the intercept L0
# L1 L2 L3 L4 L5 L6 L7 L0
# 0 1 1 1 1 1 1 0 1
# 1 0 1 1 0 0 0 0 1
# 2 1 1 0 1 1 0 1 1
# 3 1 1 1 1 0 0 1 1
# 4 0 0 1 0 0 1 1 1
# 5 1 0 1 1 0 1 1 1
# 6 0 0 1 1 1 1 1 1
# 7 1 1 1 0 0 0 0 1
# 8 1 1 1 1 1 1 1 1
# 9 1 1 1 1 0 1 1 1
function). Run the perceptron algorithm on this dataset and draw your conclusions w.r.t. the convergence of the perceptron.
from pylab import rand
import matplotlib.pyplot as plt
def dataXOR():
#map XOR output
dataXOR = []
dataXOR.append([1,0,0,0,1])
dataXOR.append([1,0,1,1,1])
dataXOR.append([1,1,0,1,-1])
dataXOR.append([0,1,1,1,1])
dataXOR.append([1,1,1,1,-1])
dataXOR.append([1,1,1,0,-1])
dataXOR.append([1,0,1,0,1])
dataXOR.append([0,1,1,0,1])
dataXOR.append([1,0,0,1,1])
dataXOR.append([0,1,0,1,1])
dataXOR.append([1,1,0,0,-1])
dataXOR.append([0,1,0,0,1])
return dataXOR
z = dataXOR()
plt.plot(z)
plt.show()
print z