diff --git a/exercises/02450Toolbox_Python/Scripts/ex3_1_2.py b/exercises/02450Toolbox_Python/Scripts/ex3_1_2.py
index 98d81d30af0dc3e90ed0b06be631b75d063ee994..2a818546aef751bad53b318dc9c980c80851adfd 100644
--- a/exercises/02450Toolbox_Python/Scripts/ex3_1_2.py
+++ b/exercises/02450Toolbox_Python/Scripts/ex3_1_2.py
@@ -2,7 +2,7 @@
# (requires data structures from ex. 3.1.1)
# Imports the numpy and xlrd package, then runs the ex3_1_1 code
from ex3_1_1 import *
-from matplotlib.pyplot import figure, legend, plot, show, title, xlabel, ylabel
+import matplotlib.pyplot as plt
# Data attributes to be plotted
i = 0
@@ -10,25 +10,23 @@ j = 1
##
# Make a simple plot of the i'th attribute against the j'th attribute
-# Notice that X is of matrix type (but it will also work with a numpy array)
-# X = np.array(X) #Try to uncomment this line
-plot(X[:, i], X[:, j], "o")
+plt.plot(X[:, i], X[:, j], "o")
##
# Make another more fancy plot that includes legend, class labels,
# attribute names, and a title.
-f = figure()
-title("NanoNose data")
+f = plt.figure()
+plt.title("NanoNose data")
for c in range(C):
# select indices belonging to class c:
- class_mask = y == c
- plot(X[class_mask, i], X[class_mask, j], "o", alpha=0.3)
+ class_mask = y == c
+ plt.plot(X[class_mask, i], X[class_mask, j], "o", alpha=0.3)
-legend(classNames)
-xlabel(attributeNames[i])
-ylabel(attributeNames[j])
+plt.legend(classNames)
+plt.xlabel(attributeNames[i])
+plt.ylabel(attributeNames[j])
# Output result to screen
-show()
+plt.show()
print("Ran Exercise 3.1.2")
diff --git a/exercises/02450Toolbox_Python/Scripts/ex3_1_3.py b/exercises/02450Toolbox_Python/Scripts/ex3_1_3.py
index 947bd45c321d6e26fe347bdd7c252ba4f3ba5ac9..d7a229c8bc50c3cb05fbd876151f10b8d9aad900 100644
--- a/exercises/02450Toolbox_Python/Scripts/ex3_1_3.py
+++ b/exercises/02450Toolbox_Python/Scripts/ex3_1_3.py
@@ -2,15 +2,22 @@
# (requires data structures from ex. 3.1.1)
import matplotlib.pyplot as plt
from ex3_1_1 import *
-from scipy.linalg import svd
+from scipy.linalg import svd
# Subtract mean value from data
+# Note: Here we use Y to in teh book we often use X with a hat-symbol on top.
Y = X - np.ones((N, 1)) * X.mean(axis=0)
# PCA by computing SVD of Y
-U, S, V = svd(Y, full_matrices=False)
+# Note: Here we call the Sigma matrix in the SVD S for notational convinience
+U, S, Vh = svd(Y, full_matrices=False)
-# Compute variance explained by principal components
+# scipy.linalg.svd returns "Vh", which is the Hermitian (transpose)
+# of the vector V. So, for us to obtain the correct V, we transpose:
+V = Vh.T
+
+# Compute variance explained by principal components
+# Note: This is an important equation, see Eq. 3.18 on page 40 in the book.
rho = (S * S) / (S * S).sum()
threshold = 0.9
diff --git a/exercises/02450Toolbox_Python/Scripts/ex3_1_4.py b/exercises/02450Toolbox_Python/Scripts/ex3_1_4.py
index 6c6e8c9547048f8c304e2361ccbadb7da535e268..75c7d53ac8690bdc91c9cf2e14d511fb5b65bca6 100644
--- a/exercises/02450Toolbox_Python/Scripts/ex3_1_4.py
+++ b/exercises/02450Toolbox_Python/Scripts/ex3_1_4.py
@@ -1,7 +1,7 @@
# exercise 3.1.4
# (requires data structures from ex. 3.1.1)
from ex3_1_1 import *
-from matplotlib.pyplot import figure, legend, plot, show, title, xlabel, ylabel
+import matplotlib.pyplot as plt
from scipy.linalg import svd
# Subtract mean value from data
@@ -14,6 +14,8 @@ U, S, Vh = svd(Y, full_matrices=False)
V = Vh.T
# Project the centered data onto principal component space
+# Note: Make absolutely sure you understand what the @ symbol
+# does by inspecing the numpy documentation!
Z = Y @ V
# Indices of the principal components to be plotted
@@ -21,18 +23,18 @@ i = 0
j = 1
# Plot PCA of the data
-f = figure()
-title("NanoNose data: PCA")
+f = plt.figure()
+plt.title("NanoNose data: PCA")
# Z = array(Z)
for c in range(C):
# select indices belonging to class c:
class_mask = y == c
- plot(Z[class_mask, i], Z[class_mask, j], "o", alpha=0.5)
-legend(classNames)
-xlabel("PC{0}".format(i + 1))
-ylabel("PC{0}".format(j + 1))
+ plt.plot(Z[class_mask, i], Z[class_mask, j], "o", alpha=0.5)
+plt.legend(classNames)
+plt.xlabel("PC{0}".format(i + 1))
+plt.ylabel("PC{0}".format(j + 1))
# Output result to screen
-show()
+plt.show()
print("Ran Exercise 3.1.4")
diff --git a/exercises/02450Toolbox_Python/Scripts/ex3_1_5.py b/exercises/02450Toolbox_Python/Scripts/ex3_1_5.py
index 19a444591042a9c057de09fd9834b6a1464cbb4f..b11e1afa463cc5143375ae6d7f4c5abea244ee37 100644
--- a/exercises/02450Toolbox_Python/Scripts/ex3_1_5.py
+++ b/exercises/02450Toolbox_Python/Scripts/ex3_1_5.py
@@ -14,11 +14,12 @@ N, M = X.shape
# percent of the variance. Let's look at their coefficients:
pcs = [0, 1, 2]
legendStrs = ["PC" + str(e + 1) for e in pcs]
-c = ["r", "g", "b"]
bw = 0.2
r = np.arange(1, M + 1)
+
for i in pcs:
plt.bar(r + i * bw, V[:, i], width=bw)
+
plt.xticks(r + bw, attributeNames)
plt.xlabel("Attributes")
plt.ylabel("Component coefficients")
@@ -48,6 +49,5 @@ print(all_water_data[0, :])
# coefficient and the attribute!
# You can determine the projection by (remove comments):
-print("...and its projection onto PC2")
-print(all_water_data[0, :] @ V[:, 1])
-# Try to explain why?
+# print("...and its projection onto PC2")
+# print(all_water_data[0, :] @ V[:, 1])
diff --git a/exercises/02450Toolbox_Python/Scripts/ex3_1_6.py b/exercises/02450Toolbox_Python/Scripts/ex3_1_6.py
index 3045c7912e4b7912bf888484d56fe0fba6ce3080..493c29fbcd5015a1aabad606d8ee45f46ef40f61 100644
--- a/exercises/02450Toolbox_Python/Scripts/ex3_1_6.py
+++ b/exercises/02450Toolbox_Python/Scripts/ex3_1_6.py
@@ -65,7 +65,7 @@ for k in range(2):
for c in range(C):
plt.plot(Z[y == c, i], Z[y == c, j], ".", alpha=0.5)
plt.xlabel("PC" + str(i + 1))
- plt.xlabel("PC" + str(j + 1))
+ plt.ylabel("PC" + str(j + 1))
plt.title(titles[k] + "\n" + "Projection")
plt.legend(classNames)
plt.axis("equal")
diff --git a/exercises/02450Toolbox_Python/Scripts/ex3_2_1.py b/exercises/02450Toolbox_Python/Scripts/ex3_2_1.py
index 88cd3ccb7a1c413fccfe4e9444494d953167118e..69537b2142db1aae35b63578c4e02c57aca9cc2e 100644
--- a/exercises/02450Toolbox_Python/Scripts/ex3_2_1.py
+++ b/exercises/02450Toolbox_Python/Scripts/ex3_2_1.py
@@ -1,7 +1,7 @@
## exercise 3.2.1
import importlib_resources
import numpy as np
-from matplotlib.pyplot import cm, figure, imshow, show, subplot, title, xlabel, yticks
+import matplotlib.pyplot as plt
from scipy.io import loadmat
filename = importlib_resources.files("dtuimldmtools").joinpath("data/zipdata.mat")
@@ -19,19 +19,19 @@ y = traindata[:, 0]
# Visualize the i'th digit as a vector
-f = figure()
-subplot(4, 1, 4)
-imshow(np.expand_dims(X[i, :], axis=0), extent=(0, 256, 0, 10), cmap=cm.gray_r)
-xlabel("Pixel number")
-title("Digit in vector format")
-yticks([])
+f = plt.figure()
+plt.subplot(4, 1, 4)
+plt.imshow(np.expand_dims(X[i, :], axis=0), extent=(0, 256, 0, 10), cmap=plt.cm.gray_r)
+plt.xlabel("Pixel number")
+plt.title("Digit in vector format")
+plt.yticks([])
# Visualize the i'th digit as an image
-subplot(2, 1, 1)
+plt.subplot(2, 1, 1)
I = np.reshape(X[i, :], (16, 16))
-imshow(I, extent=(0, 16, 0, 16), cmap=cm.gray_r)
-title("Digit as an image")
+plt.imshow(I, extent=(0, 16, 0, 16), cmap=plt.cm.gray_r)
+plt.title("Digit as an image")
-show()
+plt.show()
diff --git a/exercises/02450Toolbox_Python/Scripts/ex3_2_2.py b/exercises/02450Toolbox_Python/Scripts/ex3_2_2.py
index e0b1f0857b4a66ec97aaea0653f689c4225bf740..44a2c874d78c2935dadb20ee2e5578eb919aa0e5 100644
--- a/exercises/02450Toolbox_Python/Scripts/ex3_2_2.py
+++ b/exercises/02450Toolbox_Python/Scripts/ex3_2_2.py
@@ -1,20 +1,8 @@
# exercise 3.2.2
import importlib_resources
import numpy as np
-import scipy.linalg as linalg
-from matplotlib.pyplot import (
- cm,
- figure,
- imshow,
- legend,
- plot,
- show,
- subplot,
- title,
- xlabel,
- ylabel,
- yticks,
-)
+from scipy.linalg import svd
+import matplotlib.pyplot as plt
from scipy.io import loadmat
filename = importlib_resources.files("dtuimldmtools").joinpath("data/zipdata.mat")
@@ -26,7 +14,6 @@ K = 16
# Digits to visualize
nD = range(6)
-
# Load Matlab data file to python dict structure
# and extract variables of interest
traindata = loadmat(filename)["traindata"]
@@ -45,73 +32,76 @@ classDict = dict(zip(classNames, classValues))
class_mask = np.zeros(N).astype(bool)
for v in n:
cmsk = y == v
+ # Use the logical OR operator ("|") to select rows
+ # already in class_mask OR cmsk
class_mask = class_mask | cmsk
X = X[class_mask, :]
y = y[class_mask]
N = X.shape[0]
# Center the data (subtract mean column values)
-Xc = X - np.ones((N, 1)) * X.mean(0)
+Y = X - np.ones((N, 1)) * X.mean(0)
# PCA by computing SVD of Y
-U, S, V = linalg.svd(Xc, full_matrices=False)
+U, S, Vh = svd(Y, full_matrices=False) #NOTE: Change to Vh
# U = mat(U)
-V = V.T
+V = Vh.T
# Compute variance explained by principal components
rho = (S * S) / (S * S).sum()
# Project data onto principal component space
-Z = Xc @ V
+Z = Y @ V
# Plot variance explained
-figure()
-plot(rho, "o-")
-title("Variance explained by principal components")
-xlabel("Principal component")
-ylabel("Variance explained value")
+plt.figure()
+plt.plot(rho, "o-")
+plt.title("Variance explained by principal components")
+plt.xlabel("Principal component")
+plt.ylabel("Variance explained value")
# Plot PCA of the data
-f = figure()
-title("pixel vectors of handwr. digits projected on PCs")
+f = plt.figure()
+plt.title("pixel vectors of handwr. digits projected on PCs")
for c in n:
# select indices belonging to class c:
class_mask = y == c
- plot(Z[class_mask, 0], Z[class_mask, 1], "o")
-legend(classNames)
-xlabel("PC1")
-ylabel("PC2")
+ plt.plot(Z[class_mask, 0], Z[class_mask, 1], "o")
+plt.legend(classNames)
+plt.xlabel("PC1")
+plt.ylabel("PC2")
# Visualize the reconstructed data from the first K principal components
# Select randomly D digits.
-figure(figsize=(10, 3))
+plt.figure(figsize=(10, 3))
W = Z[:, range(K)] @ V[:, range(K)].T
D = len(nD)
for d in range(D):
+ # Select random digit index
digit_ix = np.random.randint(0, N)
- subplot(2, D, int(d + 1))
+ plt.subplot(2, D, int(d + 1))
+ # Reshape the digit from vector to 16x16 array
I = np.reshape(X[digit_ix, :], (16, 16))
- imshow(I, cmap=cm.gray_r)
- title("Original")
- subplot(2, D, D + d + 1)
+ plt.imshow(I, cmap=plt.cm.gray_r)
+ plt.title("Original")
+ plt.subplot(2, D, D + d + 1)
+ # Reshape the digit from vector to 16x16 array
I = np.reshape(W[digit_ix, :] + X.mean(0), (16, 16))
- imshow(I, cmap=cm.gray_r)
- title("Reconstr.")
+ plt.imshow(I, cmap=plt.cm.gray_r)
+ plt.title("Reconstr.")
# Visualize the pricipal components
-figure(figsize=(8, 6))
+plt.figure(figsize=(8, 6))
for k in range(K):
N1 = int(np.ceil(np.sqrt(K)))
N2 = int(np.ceil(K / N1))
- subplot(N2, N1, int(k + 1))
+ plt.subplot(N2, N1, int(k + 1))
I = np.reshape(V[:, k], (16, 16))
- imshow(I, cmap=cm.hot)
- title("PC{0}".format(k + 1))
+ plt.imshow(I, cmap=plt.cm.hot)
+ plt.title("PC{0}".format(k + 1))
# output to screen
-show()
-
-
+plt.show()
diff --git a/exercises/02450Toolbox_Python/Scripts/ex3_3_1.py b/exercises/02450Toolbox_Python/Scripts/ex3_3_1.py
index a3104d8dff87096bb3acbd6998ea6d97df7ac26e..081970c7e159bd7b60471ad584021cb8e7a868a0 100644
--- a/exercises/02450Toolbox_Python/Scripts/ex3_3_1.py
+++ b/exercises/02450Toolbox_Python/Scripts/ex3_3_1.py
@@ -2,8 +2,8 @@
import importlib_resources
import numpy as np
-import scipy.linalg as linalg
-from matplotlib.pyplot import figure, plot, show, xlabel, ylabel
+from scipy.linalg import svd
+import matplotlib.pyplot as plt
from scipy.io import loadmat
from sklearn.neighbors import KNeighborsClassifier
@@ -21,13 +21,13 @@ ytest = mat_data["testdata"][:, 0]
N, M = X.shape
Ntest = Xtest.shape[0] # or Xtest[:,0].shape
-# Subtract the mean from the data
+# Subtract the mean of X from the data
Y = X - np.ones((N, 1)) * X.mean(0)
Ytest = Xtest - np.ones((Ntest, 1)) * X.mean(0)
# Obtain the PCA solution by calculate the SVD of Y
-U, S, V = linalg.svd(Y, full_matrices=False)
-V = V.T
+U, S, Vh = svd(Y, full_matrices=False)
+V = Vh.T
# Repeat classification for different values of K
@@ -49,8 +49,8 @@ for k in K:
print("K={0}: Error rate: {1:.1f}%".format(k, er))
# Visualize error rates vs. number of principal components considered
-figure()
-plot(K, error_rates, "o-")
-xlabel("Number of principal components K")
-ylabel("Error rate [%]")
-show()
+plt.figure()
+plt.plot(K, error_rates, "o-")
+plt.xlabel("Number of principal components K")
+plt.ylabel("Error rate [%]")
+plt.show()