Using SVM with sklearn library, I would like to plot the data with each labels representing its color. I don't want to color the points but filling area with colors.
I have now :
d_pred, d_train_std, d_test_std, l_train, l_test
d_pred are the labels predicted.
I would plot d_pred with d_train_std with shape : (70000,2) where X-axis are the first column and Y-Axis the second column.
Thank you.
You cannot visualize the decision surface for a lot of features. This is because the dimensions will be too many and there is no way to visualize an N-dimensional surface.
However, you can use 2 features and plot nice decision surfaces as follows.
I have also written an article about this here:
https://towardsdatascience.com/support-vector-machines-svm-clearly-explained-a-python-tutorial-for-classification-problems-29c539f3ad8?source=friends_link&sk=80f72ab272550d76a0cc3730d7c8af35
Case 1: 2D plot for 2 features and using the iris dataset
from sklearn.svm import SVC
import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm, datasets
iris = datasets.load_iris()
X = iris.data[:, :2] # we only take the first two features.
y = iris.target
def make_meshgrid(x, y, h=.02):
x_min, x_max = x.min() - 1, x.max() + 1
y_min, y_max = y.min() - 1, y.max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
return xx, yy
def plot_contours(ax, clf, xx, yy, **params):
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)
out = ax.contourf(xx, yy, Z, **params)
return out
model = svm.SVC(kernel='linear')
clf = model.fit(X, y)
fig, ax = plt.subplots()
# title for the plots
title = ('Decision surface of linear SVC ')
# Set-up grid for plotting.
X0, X1 = X[:, 0], X[:, 1]
xx, yy = make_meshgrid(X0, X1)
plot_contours(ax, clf, xx, yy, cmap=plt.cm.coolwarm, alpha=0.8)
ax.scatter(X0, X1, c=y, cmap=plt.cm.coolwarm, s=20, edgecolors='k')
ax.set_ylabel('y label here')
ax.set_xlabel('x label here')
ax.set_xticks(())
ax.set_yticks(())
ax.set_title(title)
ax.legend()
plt.show()
Case 2: 3D plot for 3 features and using the iris dataset
from sklearn.svm import SVC
import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm, datasets
from mpl_toolkits.mplot3d import Axes3D
iris = datasets.load_iris()
X = iris.data[:, :3] # we only take the first three features.
Y = iris.target
#make it binary classification problem
X = X[np.logical_or(Y==0,Y==1)]
Y = Y[np.logical_or(Y==0,Y==1)]
model = svm.SVC(kernel='linear')
clf = model.fit(X, Y)
# The equation of the separating plane is given by all x so that np.dot(svc.coef_[0], x) + b = 0.
# Solve for w3 (z)
z = lambda x,y: (-clf.intercept_[0]-clf.coef_[0][0]*x -clf.coef_[0][1]*y) / clf.coef_[0][2]
tmp = np.linspace(-5,5,30)
x,y = np.meshgrid(tmp,tmp)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot3D(X[Y==0,0], X[Y==0,1], X[Y==0,2],'ob')
ax.plot3D(X[Y==1,0], X[Y==1,1], X[Y==1,2],'sr')
ax.plot_surface(x, y, z(x,y))
ax.view_init(30, 60)
plt.show()
It can be difficult to get the function in 3D. An easy way to get a visualization is to get a large amount of points that cover your point space and run them through your learned function (my_model.predict), keep the points that hit inside the function, and visualize them. The more you add the more defined the boundary will be.
Here's my code that does what #Christian Tuchez describes:
outputs = my_clf.predict(1_test)
hits = []
for i in range(outputs.size):
if outputs[i] == 1:
hits.append(i) # save the index where it's 1
This saves the index of all the points that hit in the function (saved in the "hits" list). You can probably accomplish this without a loop, I just found it easiest for me.
Then to display just those points, you'd write something like this:
ax.scatter(1_test[hits[:], 0], 1_test[hits[:], 1], 1_test[hits[:], 2], c="cyan", s=2, edgecolor=None)
Related
I have an assignment in which I need to compare my own multi-class logistic regression and the built-in SKlearn one.
As part of it, I need to plot the decision boundaries of each, on the same figure (for 2,3, and 4 classes separately).
This is my model's decision boundaries for 3 classes:
Made with this code:
x1_min, x1_max = X[:,0].min()-.5, X[:,0].max()+.5
x2_min, x2_max = X[:,1].min()-.5, X[:,1].max()+.5
xx1, xx2 = np.meshgrid(np.linspace(x1_min, x1_max), np.linspace(x2_min, x2_max))
grid = np.c_[xx1.ravel(), xx2.ravel()]
for i in range(len(ws)):
probs = ol.predict_prob(grid, ws[i]).reshape(xx1.shape)
plt.contour(xx1, xx2, probs, [0.5], linewidths=1, colors='green')
where
ol - is my Own Linear regression
ws - the current weights
That's how I tried to plot the Sklearn boundaries:
for i in range(len(clf.coef_)):
w = clf.coef_[i]
a = -w[0] / w[1]
xx = np.linspace(x1_min, x1_max)
yy = a * xx - (clf.intercept_[0]) / w[1]
plt.plot(xx, yy, 'k-')
Resulting
I understand that it's due to the 1dim vs 2dim grids, but I can't understand how to solve it.
I also tried to use the built-in DecisionBoundaryDisplay but I couldn't figure out how to plot it with my boundaries + it doesn't plot only the lines but also the whole background is painted in the corresponding color.
A couple fixes:
Change clf.intercept_[1] to clf.intercept_[i]
If the xlimits and ylimits in the plot look strange, you can constrain them.
ax.set_xlim([x1_min, x1_max])
ax.set_ylim([x2_min, x2_max])
MRE:
import matplotlib.pyplot as plt
import numpy as np
from sklearn.datasets import make_blobs
from sklearn.linear_model import LogisticRegression
X, y = make_blobs(n_features=2, centers=3, random_state=42)
fig, ax = plt.subplots(1, 2)
x1_min, x1_max = X[:,0].min()-.5, X[:,0].max()+.5
x2_min, x2_max = X[:,1].min()-.5, X[:,1].max()+.5
def draw_coef_lines(clf, X, y, ax, title):
for i in range(len(clf.coef_)):
w = clf.coef_[i]
a = -w[0] / w[1]
xx = np.linspace(x1_min, x1_max)
yy = a * xx - (clf.intercept_[i]) / w[1]
ax.plot(xx, yy, 'k-')
ax.scatter(X[:, 0], X[:, 1], c=y)
ax.set_xlim([x1_min, x1_max])
ax.set_ylim([x2_min, x2_max])
ax.set_title(title)
clf1 = LogisticRegression().fit(X, y)
clf2 = LogisticRegression(multi_class="ovr").fit(X, y)
draw_coef_lines(clf1, X, y, ax[0], "Multinomial")
draw_coef_lines(clf2, X, y, ax[1], "OneVsRest")
plt.show()
I have some trouble plotting the image which is in my head.
I want to visualize the Kernel-trick with Support Vector Machines. So I made some two-dimensional data consisting of two circles (an inner and an outer circle) which should be separated by a hyperplane. Obviously this isn't possible in two dimensions - so I transformed them into 3D. Let n be the number of samples. Now I have an (n,3)-array (3 columns, n rows) X of data points and an (n,1)-array y with labels. Using sklearn I get the linear classifier via
clf = svm.SVC(kernel='linear', C=1000)
clf.fit(X, y)
I already plot the data points as scatter plot via
plt.scatter(X[:, 0], X[:, 1], c=y, s=30, cmap=plt.cm.Paired)
Now I want to plot the separating hyperplane as surface plot. My problem here is the missing explicit representation of the hyperplane because the decision function only yields an implicit hyperplane via decision_function = 0. Therefore I need to plot the level set (of level 0) of an 4-dimensional object.
Since I'm not a python expert I would appreciate if somebody could help me out! And I know that this isn't really the "style" of using a SVM but I need this image as an illustration for my thesis.
Edit: my current "code"
import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm
from sklearn.datasets import make_blobs, make_circles
from tikzplotlib import save as tikz_save
plt.close('all')
# we create 50 separable points
#X, y = make_blobs(n_samples=40, centers=2, random_state=6)
X, y = make_circles(n_samples=50, factor=0.5, random_state=4, noise=.05)
X2, y2 = make_circles(n_samples=50, factor=0.2, random_state=5, noise=.08)
X = np.append(X,X2, axis=0)
y = np.append(y,y2, axis=0)
# shifte X to [0,2]x[0,2]
X = np.array([[item[0] + 1, item[1] + 1] for item in X])
X[X<0] = 0.01
clf = svm.SVC(kernel='rbf', C=1000)
clf.fit(X, y)
plt.scatter(X[:, 0], X[:, 1], c=y, s=30, cmap=plt.cm.Paired)
# plot the decision function
ax = plt.gca()
xlim = ax.get_xlim()
ylim = ax.get_ylim()
# create grid to evaluate model
xx = np.linspace(xlim[0], xlim[1], 30)
yy = np.linspace(ylim[0], ylim[1], 30)
YY, XX = np.meshgrid(yy, xx)
xy = np.vstack([XX.ravel(), YY.ravel()]).T
Z = clf.decision_function(xy).reshape(XX.shape)
# plot decision boundary and margins
ax.contour(XX, YY, Z, colors='k', levels=[-1, 0, 1], alpha=0.5, linestyles=['--','-','--'])
# plot support vectors
ax.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1], s=100,
linewidth=1, facecolors='none', edgecolors='k')
################## KERNEL TRICK - 3D ##################
trans_X = np.array([[item[0]**2, item[1]**2, np.sqrt(2*item[0]*item[1])] for item in X])
fig = plt.figure()
ax = plt.axes(projection ="3d")
# creating scatter plot
ax.scatter3D(trans_X[:,0],trans_X[:,1],trans_X[:,2], c = y, cmap=plt.cm.Paired)
clf2 = svm.SVC(kernel='linear', C=1000)
clf2.fit(trans_X, y)
ax = plt.gca(projection='3d')
xlim = ax.get_xlim()
ylim = ax.get_ylim()
zlim = ax.get_zlim()
### from here i don't know what to do ###
xx = np.linspace(xlim[0], xlim[1], 3)
yy = np.linspace(ylim[0], ylim[1], 3)
zz = np.linspace(zlim[0], zlim[1], 3)
ZZ, YY, XX = np.meshgrid(zz, yy, xx)
xyz = np.vstack([XX.ravel(), YY.ravel(), ZZ.ravel()]).T
Z = clf2.decision_function(xyz).reshape(XX.shape)
#ax.contour(XX, YY, ZZ, Z, colors='k', levels=[-1, 0, 1], alpha=0.5, linestyles=['--','-','--'])
Desired Output
I want to get something like that.
In general I want to reconstruct what they do in this article, especially "Non-linear transformations".
Part of your question is addressed in this question on linear-kernel SVM. It's a partial answer, because only linear kernels can be represented this way, i.e. thanks to hyperplane coordinates accessible via the estimator when using linear kernel.
Another solution is to find the isosurface with marching_cubes
This solution involves installing the scikit-image toolkit (https://scikit-image.org) which allows to find an isosurface of a given value (here, I considered 0 since it represents the distance to the hyperplane) from the mesh grid of the 3D coordinates.
In the code below (copied from yours), I implement the idea for any kernel (in the example, I used the RBF kernel), and the output is shown beneath the code. Please consider my footnote about 3D plotting with matplotlib, which may be another issue in your case.
import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm
from skimage import measure
from sklearn.datasets import make_blobs, make_circles
from tikzplotlib import save as tikz_save
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
plt.close('all')
# we create 50 separable points
#X, y = make_blobs(n_samples=40, centers=2, random_state=6)
X, y = make_circles(n_samples=50, factor=0.5, random_state=4, noise=.05)
X2, y2 = make_circles(n_samples=50, factor=0.2, random_state=5, noise=.08)
X = np.append(X,X2, axis=0)
y = np.append(y,y2, axis=0)
# shifte X to [0,2]x[0,2]
X = np.array([[item[0] + 1, item[1] + 1] for item in X])
X[X<0] = 0.01
clf = svm.SVC(kernel='rbf', C=1000)
clf.fit(X, y)
plt.scatter(X[:, 0], X[:, 1], c=y, s=30, cmap=plt.cm.Paired)
# plot the decision function
ax = plt.gca()
xlim = ax.get_xlim()
ylim = ax.get_ylim()
# create grid to evaluate model
xx = np.linspace(xlim[0], xlim[1], 30)
yy = np.linspace(ylim[0], ylim[1], 30)
YY, XX = np.meshgrid(yy, xx)
xy = np.vstack([XX.ravel(), YY.ravel()]).T
Z = clf.decision_function(xy).reshape(XX.shape)
# plot decision boundary and margins
ax.contour(XX, YY, Z, colors='k', levels=[-1, 0, 1], alpha=0.5, linestyles=['--','-','--'])
# plot support vectors
ax.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1], s=100,
linewidth=1, facecolors='none', edgecolors='k')
################## KERNEL TRICK - 3D ##################
trans_X = np.array([[item[0]**2, item[1]**2, np.sqrt(2*item[0]*item[1])] for item in X])
fig = plt.figure()
ax = plt.axes(projection ="3d")
# creating scatter plot
ax.scatter3D(trans_X[:,0],trans_X[:,1],trans_X[:,2], c = y, cmap=plt.cm.Paired)
clf2 = svm.SVC(kernel='rbf', C=1000)
clf2.fit(trans_X, y)
z = lambda x,y: (-clf2.intercept_[0]-clf2.coef_[0][0]*x-clf2.coef_[0][1]*y) / clf2.coef_[0][2]
ax = plt.gca(projection='3d')
xlim = ax.get_xlim()
ylim = ax.get_ylim()
zlim = ax.get_zlim()
### from here i don't know what to do ###
xx = np.linspace(xlim[0], xlim[1], 50)
yy = np.linspace(ylim[0], ylim[1], 50)
zz = np.linspace(zlim[0], zlim[1], 50)
XX ,YY, ZZ = np.meshgrid(xx, yy, zz)
xyz = np.vstack([XX.ravel(), YY.ravel(), ZZ.ravel()]).T
Z = clf2.decision_function(xyz).reshape(XX.shape)
# find isosurface with marching cubes
dx = xx[1] - xx[0]
dy = yy[1] - yy[0]
dz = zz[1] - zz[0]
verts, faces, _, _ = measure.marching_cubes_lewiner(Z, 0, spacing=(1, 1, 1), step_size=2)
verts *= np.array([dx, dy, dz])
verts -= np.array([xlim[0], ylim[0], zlim[0]])
# add as Poly3DCollection
mesh = Poly3DCollection(verts[faces])
mesh.set_facecolor('g')
mesh.set_edgecolor('none')
mesh.set_alpha(0.3)
ax.add_collection3d(mesh)
ax.view_init(20, -45)
plt.savefig('kerneltrick')
Running the code produces the following image with Matplotlib, where the green semi-transparent surface represents the non-linear decision boundary.
Footnote: 3D plotting with matplotlib
Note that Matplotlib 3D is not able to manage the "depth" of objects in some cases, because it can be in conflict with the zorder of this object. This is the reason why sometimes the hyperplane look to be plotted "on top of" the points, even it should be "behind". This issue is a known bug discussed in the matplotlib 3d documentation and in this answer.
If you want to have better rendering results, you may want to use Mayavi, as recommended by the Matplotlib developers, or any other 3D Python plotting library.
I am working with scikit-learn's breast cancer dataset, consisting of 30 features.
Following this tutorial for the much less depressing iris dataset, I figured how to plot the decision surface separating the "benign" and "malignant" categories, when considering the dataset's first two features (mean radius and mean texture).
This is what I get:
But how to represent the hyperplane computed when using all features in the dataset?
I am aware that I cannot plot a graph in 30 dimensions, but I would like to "project" the hyperplane created when running svm.SVC(kernel='linear', C=1).fit(X_train, y_train) onto the 2D scatter plot showing mean texture against mean radius.
I read about using PCA to reduce dimensionality, but I suspect that fitting a "reduced" dataset is not the same as projecting the hyperplane computed over all 30 features onto a 2D plot.
Here is my code so far:
from sklearn import datasets
import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split
from sklearn import svm
import numpy as np
#Load dataset
cancer = datasets.load_breast_cancer()
# Split dataset into training set and test set
X_train, X_test, y_train, y_test = train_test_split(cancer.data, cancer.target, test_size=0.3,random_state=109) # 70% training and 30% test
h = .02 # mesh step
C = 1.0 # Regularisation
clf = svm.SVC(kernel='linear', C=C).fit(X_train[:,:2], y_train) # Linear Kernel
x_min, x_max = X_train[:, 0].min() - 1, X_train[:, 0].max() + 1
y_min, y_max = X_train[:, 1].min() - 1, X_train[:, 1].max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)
plt.contourf(xx, yy, Z, cmap=plt.cm.coolwarm, alpha=0.8)
scat=plt.scatter(X_train[:, 0], X_train[:, 1], c=y_train)
legend1 = plt.legend(*scat.legend_elements(),
loc="upper right", title="diagnostic")
plt.xlabel('mean_radius')
plt.ylabel('mean_texture')
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max())
plt.show()
You cannot visualize the decision surface for a lot of features. This is because the dimensions will be too many and there is no way to visualize an N-dimensional surface.
I have also written an article about this here:
https://towardsdatascience.com/support-vector-machines-svm-clearly-explained-a-python-tutorial-for-classification-problems-29c539f3ad8?source=friends_link&sk=80f72ab272550d76a0cc3730d7c8af35
However, you can use 2 features and plot nice decision surfaces as follows.
Case 1: 2D plot for 2 features and using the iris dataset
from sklearn.svm import SVC
import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm, datasets
iris = datasets.load_iris()
X = iris.data[:, :2] # we only take the first two features.
y = iris.target
def make_meshgrid(x, y, h=.02):
x_min, x_max = x.min() - 1, x.max() + 1
y_min, y_max = y.min() - 1, y.max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
return xx, yy
def plot_contours(ax, clf, xx, yy, **params):
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)
out = ax.contourf(xx, yy, Z, **params)
return out
model = svm.SVC(kernel='linear')
clf = model.fit(X, y)
fig, ax = plt.subplots()
# title for the plots
title = ('Decision surface of linear SVC ')
# Set-up grid for plotting.
X0, X1 = X[:, 0], X[:, 1]
xx, yy = make_meshgrid(X0, X1)
plot_contours(ax, clf, xx, yy, cmap=plt.cm.coolwarm, alpha=0.8)
ax.scatter(X0, X1, c=y, cmap=plt.cm.coolwarm, s=20, edgecolors='k')
ax.set_ylabel('y label here')
ax.set_xlabel('x label here')
ax.set_xticks(())
ax.set_yticks(())
ax.set_title(title)
ax.legend()
plt.show()
Case 2: 3D plot for 3 features and using the iris dataset
from sklearn.svm import SVC
import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm, datasets
from mpl_toolkits.mplot3d import Axes3D
iris = datasets.load_iris()
X = iris.data[:, :3] # we only take the first three features.
Y = iris.target
#make it binary classification problem
X = X[np.logical_or(Y==0,Y==1)]
Y = Y[np.logical_or(Y==0,Y==1)]
model = svm.SVC(kernel='linear')
clf = model.fit(X, Y)
# The equation of the separating plane is given by all x so that np.dot(svc.coef_[0], x) + b = 0.
# Solve for w3 (z)
z = lambda x,y: (-clf.intercept_[0]-clf.coef_[0][0]*x -clf.coef_[0][1]*y) / clf.coef_[0][2]
tmp = np.linspace(-5,5,30)
x,y = np.meshgrid(tmp,tmp)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot3D(X[Y==0,0], X[Y==0,1], X[Y==0,2],'ob')
ax.plot3D(X[Y==1,0], X[Y==1,1], X[Y==1,2],'sr')
ax.plot_surface(x, y, z(x,y))
ax.view_init(30, 60)
plt.show()
You can't plot the 30-dim data without any transformation to 2-d.
https://github.com/tmadl/highdimensional-decision-boundary-plot
What is a Voronoi Tessellation?
Given a set P := {p1, ..., pn} of sites, a Voronoi Tessellation is a subdivision of the space into n cells, one for each site in P, with the property that a point q lies in the cell corresponding to a site pi iff d(pi, q) < d(pj, q) for i distinct from j. The segments in a Voronoi Tessellation correspond to all points in the plane equidistant to the two nearest sites. Voronoi Tessellations have applications in computer science. - https://philogb.github.io/blog/2010/02/12/voronoi-tessellation/
In geometry, a centroidal Voronoi tessellation (CVT) is a special type of Voronoi tessellation or Voronoi diagram. A Voronoi tessellation is called centroidal when the generating point of each Voronoi cell is also its centroid, i.e. the arithmetic mean or center of mass. It can be viewed as an optimal partition corresponding to an optimal distribution of generators. A number of algorithms can be used to generate centroidal Voronoi tessellations, including Lloyd's algorithm for K-means clustering or Quasi-Newton methods like BFGS. - Wiki
import numpy as np, matplotlib.pyplot as plt
from sklearn.neighbors.classification import KNeighborsClassifier
from sklearn.datasets.base import load_breast_cancer
from sklearn.manifold.t_sne import TSNE
from sklearn import svm
bcd = load_breast_cancer()
X,y = bcd.data, bcd.target
X_Train_embedded = TSNE(n_components=2).fit_transform(X)
print(X_Train_embedded.shape)
h = .02 # mesh step
C = 1.0 # Regularisation
clf = svm.SVC(kernel='linear', C=C) # Linear Kernel
clf = clf.fit(X,y)
y_predicted = clf.predict(X)
resolution = 100 # 100x100 background pixels
X2d_xmin, X2d_xmax = np.min(X_Train_embedded[:,0]), np.max(X_Train_embedded[:,0])
X2d_ymin, X2d_ymax = np.min(X_Train_embedded[:,1]), np.max(X_Train_embedded[:,1])
xx, yy = np.meshgrid(np.linspace(X2d_xmin, X2d_xmax, resolution), np.linspace(X2d_ymin, X2d_ymax, resolution))
# approximate Voronoi tesselation on resolution x resolution grid using 1-NN
background_model = KNeighborsClassifier(n_neighbors=1).fit(X_Train_embedded, y_predicted)
voronoiBackground = background_model.predict(np.c_[xx.ravel(), yy.ravel()])
voronoiBackground = voronoiBackground.reshape((resolution, resolution))
#plot
plt.contourf(xx, yy, voronoiBackground)
plt.scatter(X_Train_embedded[:,0], X_Train_embedded[:,1], c=y)
plt.show()
From my wine-dataset, I am trying to plot a decision boundary between 2 columns which is described by the snippet:
X0, X1 = X[:, 10], Y
I have taken the following code from scikit svm plot tutorial and modified to replace with my variable names/index. However when I run the following code, I get an error saying:
ValueError: X.shape[1] = 2 should be equal to 11, the number of features at training time
with error stack as:
Traceback (most recent call last):
File "test-wine.py", line 120, in <module>
cmap=plt.cm.coolwarm, alpha=0.8)
File "test-wine.py", line 96, in plot_contours
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
File "/home/suhail/anaconda3/envs/ml/lib/python3.5/site-packages/sklearn/svm/base.py", line 548, in predict
y = super(BaseSVC, self).predict(X)
File "/home/suhail/anaconda3/envs/ml/lib/python3.5/site-packages/sklearn/svm/base.py", line 308, in predict
X = self._validate_for_predict(X)
File "/home/suhail/anaconda3/envs/ml/lib/python3.5/site-packages/sklearn/svm/base.py", line 459, in _validate_for_predict
(n_features, self.shape_fit_[1]))
ValueError: X.shape[1] = 2 should be equal to 11, the number of features at training time
I cannot understand the reason for the above error. Here is the code that I have modified.
import pandas as pd
from sklearn.svm import SVC
import matplotlib.pyplot as plt
import numpy as np
data = pd.read_csv('winequality-red.csv').values
x_data_shape = data.shape[0]
y_data_shape = data.shape[1]
X = data[:, 0:y_data_shape-1]
Y = data[:, y_data_shape-1]
############### PLOT DECISION BOUNDARY SVM #############
def make_meshgrid(x, y, h=.02):
"""Create a mesh of points to plot in
Parameters
----------
x: data to base x-axis meshgrid on
y: data to base y-axis meshgrid on
h: stepsize for meshgrid, optional
Returns
-------
xx, yy : ndarray
"""
x_min, x_max = x.min() - 1, x.max() + 1
y_min, y_max = y.min() - 1, y.max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
return xx, yy
def plot_contours(ax, clf, xx, yy, **params):
"""Plot the decision boundaries for a classifier.
Parameters
----------
ax: matplotlib axes object
clf: a classifier
xx: meshgrid ndarray
yy: meshgrid ndarray
params: dictionary of params to pass to contourf, optional
"""
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)
out = ax.contourf(xx, yy, Z, **params)
return out
C = 1.0 # SVM regularization parameter
models = (SVC(kernel='linear', C=C),
SVC(kernel='rbf', gamma=0.7, C=C),
SVC(kernel='poly', degree=3, C=C))
models = (clf.fit(X, Y) for clf in models)
titles = ('SVC with linear kernel',
'SVC with RBF kernel',
'SVC with polynomial (degree 3) kernel')
fig, sub = plt.subplots(2, 2)
plt.subplots_adjust(wspace=0.4, hspace=0.4)
X0, X1 = X[:, 10], Y
xx, yy = make_meshgrid(X0, X1)
for clf, title, ax in zip(models, titles, sub.flatten()):
plot_contours(ax, clf, xx, yy,
cmap=plt.cm.coolwarm, alpha=0.8)
ax.scatter(X0, X1, c=Y, cmap=plt.cm.coolwarm, s=20, edgecolors='k')
ax.set_xlim(xx.min(), xx.max())
ax.set_ylim(yy.min(), yy.max())
ax.set_xlabel('Alcohol Content')
ax.set_ylabel('Quality')
ax.set_xticks(())
ax.set_yticks(())
ax.set_title(title)
plt.show()
What could be the reason for this error?
You trained the classifiers with all 11 features,
but you provide only 2 features for the evaluation of the classifier which happens when Z = clf.predict(np.c_[xx.ravel(), yy.ravel()]) is called from within the plot_contours method.
To evaluate a classifier trained with 11 features, you need to provide all 11 features. This is what your error message indicates.
So in order to make the snippet work for you, you should limit yourself to two features (otherwise plotting two-dimensional decision boundaries does not make sense anyway), e.g by using
X = data[:, :2]
Y = data[:, y_data_shape-1]
when reading your data.
Note that the example you referred to also uses only two features:
# import some data to play with
iris = datasets.load_iris()
# Take the first two features. We could avoid this by using a two-dim dataset
X = iris.data[:, :2]
y = iris.target
I am currently performing multi class SVM with linear kernel using python's scikit library.
The sample training data and testing data are as given below:
Model data:
x = [[20,32,45,33,32,44,0],[23,32,45,12,32,66,11],[16,32,45,12,32,44,23],[120,2,55,62,82,14,81],[30,222,115,12,42,64,91],[220,12,55,222,82,14,181],[30,222,315,12,222,64,111]]
y = [0,0,0,1,1,2,2]
I want to plot the decision boundary and visualize the datasets. Can someone please help to plot this type of data.
The data given above is just mock data so feel free to change the values.
It would be helpful if at least if you could suggest the steps that are to followed.
Thanks in advance
You have to choose only 2 features to do this. The reason is that you cannot plot a 7D plot. After selecting the 2 features use only these for the visualization of the decision surface.
(I have also written an article about this here: https://towardsdatascience.com/support-vector-machines-svm-clearly-explained-a-python-tutorial-for-classification-problems-29c539f3ad8?source=friends_link&sk=80f72ab272550d76a0cc3730d7c8af35)
Now, the next question that you would ask: How can I choose these 2 features?. Well, there are a lot of ways. You could do a univariate F-value (feature ranking) test and see what features/variables are the most important. Then you could use these for the plot. Also, we could reduce the dimensionality from 7 to 2 using PCA for example.
2D plot for 2 features and using the iris dataset
from sklearn.svm import SVC
import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm, datasets
iris = datasets.load_iris()
# Select 2 features / variable for the 2D plot that we are going to create.
X = iris.data[:, :2] # we only take the first two features.
y = iris.target
def make_meshgrid(x, y, h=.02):
x_min, x_max = x.min() - 1, x.max() + 1
y_min, y_max = y.min() - 1, y.max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
return xx, yy
def plot_contours(ax, clf, xx, yy, **params):
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)
out = ax.contourf(xx, yy, Z, **params)
return out
model = svm.SVC(kernel='linear')
clf = model.fit(X, y)
fig, ax = plt.subplots()
# title for the plots
title = ('Decision surface of linear SVC ')
# Set-up grid for plotting.
X0, X1 = X[:, 0], X[:, 1]
xx, yy = make_meshgrid(X0, X1)
plot_contours(ax, clf, xx, yy, cmap=plt.cm.coolwarm, alpha=0.8)
ax.scatter(X0, X1, c=y, cmap=plt.cm.coolwarm, s=20, edgecolors='k')
ax.set_ylabel('y label here')
ax.set_xlabel('x label here')
ax.set_xticks(())
ax.set_yticks(())
ax.set_title(title)
ax.legend()
plt.show()
EDIT: Apply PCA to reduce dimensionality.
from sklearn.svm import SVC
import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm, datasets
from sklearn.decomposition import PCA
iris = datasets.load_iris()
X = iris.data
y = iris.target
pca = PCA(n_components=2)
Xreduced = pca.fit_transform(X)
def make_meshgrid(x, y, h=.02):
x_min, x_max = x.min() - 1, x.max() + 1
y_min, y_max = y.min() - 1, y.max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
return xx, yy
def plot_contours(ax, clf, xx, yy, **params):
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)
out = ax.contourf(xx, yy, Z, **params)
return out
model = svm.SVC(kernel='linear')
clf = model.fit(Xreduced, y)
fig, ax = plt.subplots()
# title for the plots
title = ('Decision surface of linear SVC ')
# Set-up grid for plotting.
X0, X1 = Xreduced[:, 0], Xreduced[:, 1]
xx, yy = make_meshgrid(X0, X1)
plot_contours(ax, clf, xx, yy, cmap=plt.cm.coolwarm, alpha=0.8)
ax.scatter(X0, X1, c=y, cmap=plt.cm.coolwarm, s=20, edgecolors='k')
ax.set_ylabel('PC2')
ax.set_xlabel('PC1')
ax.set_xticks(())
ax.set_yticks(())
ax.set_title('Decison surface using the PCA transformed/projected features')
ax.legend()
plt.show()
EDIT 1 (April 15th, 2020):
Case: 3D plot for 3 features and using the iris dataset
from sklearn.svm import SVC
import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm, datasets
from mpl_toolkits.mplot3d import Axes3D
iris = datasets.load_iris()
X = iris.data[:, :3] # we only take the first three features.
Y = iris.target
#make it binary classification problem
X = X[np.logical_or(Y==0,Y==1)]
Y = Y[np.logical_or(Y==0,Y==1)]
model = svm.SVC(kernel='linear')
clf = model.fit(X, Y)
# The equation of the separating plane is given by all x so that np.dot(svc.coef_[0], x) + b = 0.
# Solve for w3 (z)
z = lambda x,y: (-clf.intercept_[0]-clf.coef_[0][0]*x -clf.coef_[0][1]*y) / clf.coef_[0][2]
tmp = np.linspace(-5,5,30)
x,y = np.meshgrid(tmp,tmp)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot3D(X[Y==0,0], X[Y==0,1], X[Y==0,2],'ob')
ax.plot3D(X[Y==1,0], X[Y==1,1], X[Y==1,2],'sr')
ax.plot_surface(x, y, z(x,y))
ax.view_init(30, 60)
plt.show()
You can use mlxtend. It's quite clean.
First do a pip install mlxtend, and then:
from sklearn.svm import SVC
import matplotlib.pyplot as plt
from mlxtend.plotting import plot_decision_regions
svm = SVC(C=0.5, kernel='linear')
svm.fit(X, y)
plot_decision_regions(X, y, clf=svm, legend=2)
plt.show()
Where X is a two-dimensional data matrix, and y is the associated vector of training labels.