How To Know If The Function Is Linearly Separable Draw The Decision Region Find Weights And Bias

The idea of linearly separable is easiest to visualize and sympathize in 2 dimensions. Allow the two classes be represented by colors red and green.

A dataset is said to exist linearly separable if it is possible to draw a line that can separate the cerise and greenish points from each other.

Hither are same examples of linearly separable information:

And here are some examples of linearly non-separable information

This concept can be extended to three or more than dimensions as well. For instance, beneath is an example of a iii dimensional dataset that is linearly separable :

In due north dimensions, the separator is a (n-one) dimensional hyper-plane – although it is pretty much incommunicable to visualize for four or more dimensions.

Algebraic definition:

Algebraically, the separator is a linear part, i.east. if data point x is given past (x1, x2), when the separator is a office f(x) = w1*x1 + w2*x2 + b

All points for which f(ten) = 0, are on the separator line. All points for which f(x) > 0 are on one side of the line, and all points for which f(10) < 0 are on the other side.

Generating Linearly Separable Data for test purposes :

# import libraries from sklearn.datasets import make_blobs import matplotlib.pyplot as plt %matplotlib inline  # generate a 2-form classification problem with 1,000 information points, # where each data point is a          ii-D feature vector          (X, y) = make_blobs(n_samples=1000, n_features=2, centers=2,                   cluster_std=1.five, random_state=i) y = y.reshape((y.shape[0], i))  X.shape, y.shape  # plot the (testing) classification information plt.style.use("ggplot") plt.figure() plt.title("Data") plt.scatter(Ten[:, 0], X[:, 1], mark="o", c=y[:, 0], s=30)

This generates information something like this :

lineardata1