# SVM with Python | Support Vector Machines (SVM) Vector Machines Machine Learning | KGP Talkie

## What is Support Vector Machines (SVM)

We will start our discussion with little introduction about `SVM`

. `Support Vector Machine`

(SVM) is a supervised `binary`

classification algorithm. Given a set of points of two types in `N-dimensional`

place SVM generates a `(N−1) dimensional`

hyperplane to separate those points into two groups.

A `SVM`

classifier would attempt to draw a `straight line`

separating the `two sets`

of data, and thereby create a `model`

for `classification`

. For `two dimensional`

data like that shown here, this is a task we could do by hand. But immediately we see a problem: there is `more than one`

possible dividing line that can perfectly `discriminate`

between the two classes.

- Support Vectors
- Hyperplane
- Margin

## Support Vectors

`Support vectors`

are the data points, which are closest to the `hyperplane`

. These points will define the `separating line`

better by calculating `margins`

. These points are more relevant to the `construction`

of the `classifier`

.

#### Hyperplane

A `hyperplane`

is a decision plane which `separates`

between a set of objects having `different class`

memberships.

#### Margin

A `margin`

is a gap between the two lines on the closest `class points`

. This is calculated as the `perpendicular distance`

from the line to `support vectors`

or closest points. If the `margin`

is larger in between the `classes`

, then it is considered a `good margin`

, a smaller margin is a `bad margin`

.

## How SVM works?

- Generate
`hyperplanes`

which segregates the classes in the best way. Left-hand side figure showing`three hyperplanes`

black, blue and orange. Here, the blue and orange have higher`classification error`

, but the black is separating the two classes correctly.

- Select the right
`hyperplane`

with the maximum`segregation`

from the either nearest data points as shown in the right-hand side figure.

## Separation Planes

- Linear
- Non-Linear

### Dealing with non-linear and inseparable planes

`SVM`

uses a `kernel`

trick to transform the input space to a `higher dimensional`

space

#### Beauty of Kernal

`kernels`

allow us to do stuff in `infinite dimensions`

. Sometimes going to `higher dimension`

is not just computationally `expensive`

, but also `impossible`

. function can be a `mapping`

from `n-dimension`

to `infinite dimension`

which we may have little idea of how to deal with. Then kernel gives us a wonderful shortcut.

#### SVM Kernels

- Linear
- Polynomial
- Radial Basis Function

The `SVM`

algorithm is implemented in practice using a `kernel`

. Kernel helps you to build a more `accurate`

classifier.

- A linear kernel can be used as normal
`dot product`

any two given observations. The product between`two vectors`

is the sum of the`multiplication`

of each pair of`input values`

.Training a SVM with a Linear Kernel is Faster than with any other Kernel. - A
`polynomial kernel`

is a more generalized form of the`linear kernel`

. The polynomial kernel can distinguish curved or nonlinear`input space`

. - The
`Radial basis function (RBF)`

kernel is a popular`kernel function`

commonly used in`Support Vector Machine`

classification.`RBF`

can map an input space in`infinite dimensional`

space.

## Let's Build Model in sklearn

import pandas as pd import seaborn as sns import matplotlib.pyplot as plt import numpy as np

from sklearn import datasets, metrics from sklearn.model_selection import train_test_split from sklearn.preprocessing import StandardScaler

cancer = datasets.load_breast_cancer() cancer.keys() dict_keys(['data', 'target', 'frame', 'target_names', 'DESCR', 'feature_names', 'filename']) print(cancer.DESCR)

.. _breast_cancer_dataset: Breast cancer wisconsin (diagnostic) dataset -------------------------------------------- **Data Set Characteristics:** :Number of Instances: 569 :Number of Attributes: 30 numeric, predictive attributes and the class :Attribute Information: - radius (mean of distances from center to points on the perimeter) - texture (standard deviation of gray-scale values) - perimeter - area - smoothness (local variation in radius lengths) - compactness (perimeter^2 / area - 1.0) - concavity (severity of concave portions of the contour) - concave points (number of concave portions of the contour) - symmetry - fractal dimension ("coastline approximation" - 1) The mean, standard error, and "worst" or largest (mean of the three worst/largest values) of these features were computed for each image, resulting in 30 features. For instance, field 0 is Mean Radius, field 10 is Radius SE, field 20 is Worst Radius. - class: - WDBC-Malignant - WDBC-Benign :Summary Statistics: ===================================== ====== ====== Min Max ===================================== ====== ====== radius (mean): 6.981 28.11 texture (mean): 9.71 39.28 perimeter (mean): 43.79 188.5 area (mean): 143.5 2501.0 smoothness (mean): 0.053 0.163 compactness (mean): 0.019 0.345 concavity (mean): 0.0 0.427 concave points (mean): 0.0 0.201 symmetry (mean): 0.106 0.304 fractal dimension (mean): 0.05 0.097 radius (standard error): 0.112 2.873 texture (standard error): 0.36 4.885 perimeter (standard error): 0.757 21.98 area (standard error): 6.802 542.2 smoothness (standard error): 0.002 0.031 compactness (standard error): 0.002 0.135 concavity (standard error): 0.0 0.396 concave points (standard error): 0.0 0.053 symmetry (standard error): 0.008 0.079 fractal dimension (standard error): 0.001 0.03 radius (worst): 7.93 36.04 texture (worst): 12.02 49.54 perimeter (worst): 50.41 251.2 area (worst): 185.2 4254.0 smoothness (worst): 0.071 0.223 compactness (worst): 0.027 1.058 concavity (worst): 0.0 1.252 concave points (worst): 0.0 0.291 symmetry (worst): 0.156 0.664 fractal dimension (worst): 0.055 0.208 ===================================== ====== ====== :Missing Attribute Values: None :Class Distribution: 212 - Malignant, 357 - Benign

cancer.target_names array(['malignant', 'benign'], dtype='<U9') cancer.feature_names[: 5]

array(['mean radius', 'mean texture', 'mean perimeter', 'mean area', 'mean smoothness'], dtype='<U23')

cancer.feature_names.shape

(30,)

X = cancer.data y = cancer.target X.shape, y.shape

((569, 30), (569,))

Let's print the slicing array of x , y:

X[: 2]

array([[1.799e+01, 1.038e+01, 1.228e+02, 1.001e+03, 1.184e-01, 2.776e-01, 3.001e-01, 1.471e-01, 2.419e-01, 7.871e-02, 1.095e+00, 9.053e-01, 8.589e+00, 1.534e+02, 6.399e-03, 4.904e-02, 5.373e-02, 1.587e-02, 3.003e-02, 6.193e-03, 2.538e+01, 1.733e+01, 1.846e+02, 2.019e+03, 1.622e-01, 6.656e-01, 7.119e-01, 2.654e-01, 4.601e-01, 1.189e-01], [2.057e+01, 1.777e+01, 1.329e+02, 1.326e+03, 8.474e-02, 7.864e-02, 8.690e-02, 7.017e-02, 1.812e-01, 5.667e-02, 5.435e-01, 7.339e-01, 3.398e+00, 7.408e+01, 5.225e-03, 1.308e-02, 1.860e-02, 1.340e-02, 1.389e-02, 3.532e-03, 2.499e+01, 2.341e+01, 1.588e+02, 1.956e+03, 1.238e-01, 1.866e-01, 2.416e-01, 1.860e-01, 2.750e-01, 8.902e-02]])

y[: 10]

array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])

## Standardization

`Standardization`

of a dataset is a common requirement for many `machine learning`

estimators: they might behave badly if the individual feature do not more or less look like standard `normally distributed`

data (e.g. Gaussian with `0`

mean and `unit`

variance).

The idea behind `StandardScaler()`

is that it will transform your data such that its `distribution`

will have a `mean`

value `0`

and `standard deviation`

of `1`

.

scaler = StandardScaler() X_scaled = scaler.fit_transform(X) X_scaled[2:2]

array([], shape=(0, 30), dtype=float64)

## Split the data and build the model

X_train, X_test, y_train, y_test = train_test_split(X_scaled, y, test_size = 0.2, random_state = 1, stratify = y)

### Linear kernel

Let’s create a `Linear Kernel`

SVM using the `sklearn`

library of Python. Linear Kernel is used when the data is `Linearly`

separable, that is, it can be separated using a `single Line`

. It is one of the most common kernels to be used. It is mostly used when there are a Large number of Features in a particular Data Set.

from sklearn import svm

clf = svm.SVC(kernel='linear') clf.fit(X_train, y_train) y_predict = clf.predict(X_test) print('Accuracy: ', metrics.accuracy_score(y_test, y_predict)) print('Precision: ', metrics.precision_score(y_test, y_predict)) print('Recall: ', metrics.recall_score(y_test, y_predict)) print('Confusion Matrix') mat = metrics.confusion_matrix(y_test, y_predict) sns.heatmap(mat, square = True, annot = True, fmt = 'd', cbar = False, xticklabels=cancer.target_names, yticklabels=cancer.target_names) plt.xlabel('Predicted Label') plt.ylabel('True Label') plt.show()

Accuracy: 0.9649122807017544 Precision: 0.9594594594594594 Recall: 0.9861111111111112 Confusion Matrix

### np.unique()

This function returns an `array of unique elements`

in the input array. The function can be able to return a `tuple of array of unique vales`

and an array of associated indices. Nature of the indices depend upon the type of `return`

parameter in the function call.

Let's see the following code:

element, count = np.unique(y_test, return_counts=True) element, count

(array([0, 1]), array([42, 72], dtype=int64))

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 1, stratify = y) clf = svm.SVC(kernel='linear') clf.fit(X_train, y_train) y_predict = clf.predict(X_test) print('Accuracy: ', metrics.accuracy_score(y_test, y_predict))

Accuracy: 0.9649122807017544

## Polynomial Kernel

The `Polynomial kernel`

is a `non-stationary`

kernel. Polynomial kernels are well suited for problems where all the training data is `normalized`

. In the case of this kernel, you also have to pass a value for the `degree`

parameter of the SVC class. This basically is the `degree`

of the polynomial.

Take a look at how we can use a `polynomial`

kernel to implement kernel SVM:

clf = svm.SVC(kernel='poly', degree = 5, gamma = 100) clf.fit(X_train, y_train) y_predict = clf.predict(X_test) print('Accuracy: ', metrics.accuracy_score(y_test, y_predict)) print('Precision: ', metrics.precision_score(y_test, y_predict)) print('Recall: ', metrics.recall_score(y_test, y_predict)) print('Confusion Matrix') mat = metrics.confusion_matrix(y_test, y_predict) sns.heatmap(mat, square = True, annot = True, fmt = 'd', cbar = False, xticklabels=cancer.target_names, yticklabels=cancer.target_names) plt.xlabel('Predicted Label') plt.ylabel('True Label') plt.show()

Accuracy: 0.631578947368421 Precision: 0.631578947368421 Recall: 1.0 Confusion Matrix

## Sigmoid Kernel

Finally, let's use a `sigmoid kernel`

for implementing Kernel SVM.The `sigmoid kernel`

was quite popular for support vector machines due to its origin from `neural networks`

.To use the `sigmoid kernel`

, you have to specify `'sigmoid'`

as value for the kernel parameter of the SVC class.

Take a look at the following script.

clf = svm.SVC(kernel='sigmoid', gamma = 200, C = 10000) clf.fit(X_train, y_train) y_predict = clf.predict(X_test) print('Accuracy: ', metrics.accuracy_score(y_test, y_predict)) print('Precision: ', metrics.precision_score(y_test, y_predict)) print('Recall: ', metrics.recall_score(y_test, y_predict)) print('Confusion Matrix') mat = metrics.confusion_matrix(y_test, y_predict) sns.heatmap(mat, square = True, annot = True, fmt = 'd', cbar = False, xticklabels=cancer.target_names, yticklabels=cancer.target_names) plt.xlabel('Predicted Label') plt.ylabel('True Label') plt.show()

Accuracy: 0.631578947368421 Precision: 0.631578947368421 Recall: 1.0 Confusion Matrix

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