In [1]:

import numpy as np
rng = np.random.default_rng()

import matplotlib.pyplot as plt
from matplotlib.colors import ListedColormap, TABLEAU_COLORS
import seaborn as sns

# load mlp from github
!git clone https://github.com/StephenTGibson/homemade-artificial-neural-networks.git &> /dev/null
import sys
sys.path.append('/content/homemade-artificial-neural-networks')
import multilayerPerceptron as mlp

Create a dataset

Non-linearly separable
2D for plotting

In [67]:

objectsPerClass = 10
variables = 2
classes = 4
data = mlp.createDataset_clouds(objectsPerClass, variables, classes, step=1.5)

sns.scatterplot(
    x=data[:, 0],
    y=data[:, 1],
    hue=data[:, 2],
    palette='tab10',
)
plt.show()

Define the network
Layers take following args: number inputs, number outputs, activation function

In [68]:

model = mlp.MultilayerPerceptron(
    mlp.Layer(variables, 6, 'sigmoid'),
    [
     mlp.Layer(6, 6, 'sigmoid'),
    ],
    mlp.Layer(6, classes, 'softmax'),
    learningRate=0.001,
    momentum=0.99,
    lossFunction=mlp.multiCrossEntropy,
    )

Train the network (online SGD)

In [69]:

epochs = 2000

history = model.train(data, epochs)
print(f'Final mean loss: {(history[-1]):.3g}')

predictions = model.test(data[:, :-1])
correct = (data[:, -1] == predictions) * 1.

print(f'Final training accuracy: {(100 * correct.sum() / data.shape[0]):.1f}%')

Epoch: 0
Classification accuracy: 32.5%
Epoch: 400
Classification accuracy: 82.5%
Epoch: 800
Classification accuracy: 85.0%
Epoch: 1200
Classification accuracy: 85.0%
Epoch: 1600
Classification accuracy: 87.5%
Final mean loss: 0.271
Final training accuracy: 87.5%

Plot training loss and learnt decision boundary

In [70]:

# colours for mesh plot
keys = [num for num in range(len(TABLEAU_COLORS))]
vals = [color for color in TABLEAU_COLORS.keys()]
cDict = dict(zip(keys, vals))
cMap = ListedColormap([cDict[num] for num in range(classes)])

In [71]:

fig, axs = plt.subplots(1, 2, figsize=(12, 6), constrained_layout=True)

axs[0].plot(history)

xMesh, yMesh, labelsMesh, confidenceMesh = mlp.createDecisionBoundaryMesh('multiClass', model, data)

axs[1].pcolormesh(xMesh, yMesh, labelsMesh, cmap=cMap, shading='auto')
axs[1].pcolormesh(xMesh, yMesh, confidenceMesh, cmap='Greys', alpha=0.5, shading='auto')

sns.scatterplot(
        ax=axs[1],
        x=data[:, 0],
        y=data[:, 1],
        hue=data[:, -1],
        style=correct,
        palette=cDict,
        markers={0: 'X', 1: 'o'},
        edgecolor='black',
        linewidth=1.5,
        )
axs[1].get_legend().remove()
plt.show()

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