Clustering

Clustering seeks to group data into clusters based on their properties and then allow us to predict which cluster a new member belongs.

import numpy as np
import matplotlib.pyplot as plt

Preparing the data

We’ll use a dataset generator that is part of scikit-learn called make_moons. This generates data that falls into 2 different sets with a shape that looks like half-moons.

from sklearn import datasets

def generate_data():
    xvec, val = datasets.make_moons(200, noise=0.15)

    # encode the output to be 2 elements
    x = []
    v = []
    for xv, vv in zip(xvec, val):
        x.append(np.array(xv))
        v.append(vv)

    return np.array(x), np.array(v)

Tip

By adjusting the noise parameter, we can blur the boundary between the two datasets, making the classification harder.

x, v = generate_data()

Let’s look at a point and it’s value

print(f"x = {x[0]}, value = {v[0]}")

x = [-1.1053184   0.27590723], value = 0

Now let’s plot the data

def plot_data(x, v):
    xpt = [q[0] for q in x]
    ypt = [q[1] for q in x]

    fig, ax = plt.subplots()
    ax.scatter(xpt, ypt, s=40, c=v, cmap="viridis")
    ax.set_aspect("equal")
    return fig

fig = plot_data(x, v)

We want to partition this domain into 2 regions, such that when we come in with a new point, we know which group it belongs to.

Constructing the network

First we setup and train our network

from keras.models import Sequential
from keras.layers import Input, Dense, Dropout, Activation
from keras.optimizers import RMSprop

model = Sequential()
model.add(Input((2,)))
model.add(Dense(50, activation="relu"))
model.add(Dense(20, activation="relu"))
model.add(Dense(1, activation="sigmoid"))

rms = RMSprop()
model.compile(loss='binary_crossentropy',
              optimizer=rms, metrics=['accuracy'])

model.summary()

Model: "sequential"

┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
┃ Layer (type)                    ┃ Output Shape           ┃       Param # ┃
┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
│ dense (Dense)                   │ (None, 50)             │           150 │
├─────────────────────────────────┼────────────────────────┼───────────────┤
│ dense_1 (Dense)                 │ (None, 20)             │         1,020 │
├─────────────────────────────────┼────────────────────────┼───────────────┤
│ dense_2 (Dense)                 │ (None, 1)              │            21 │
└─────────────────────────────────┴────────────────────────┴───────────────┘

 Total params: 1,191 (4.65 KB)

 Trainable params: 1,191 (4.65 KB)

 Non-trainable params: 0 (0.00 B)

Training

Important

We seem to need a lot of epochs here to get a good result

results = model.fit(x, v, batch_size=50, epochs=200, verbose=2)

Epoch 1/200

4/4 - 0s - 6ms/step - accuracy: 0.6400 - loss: 0.6688

Epoch 2/200

4/4 - 0s - 6ms/step - accuracy: 0.7150 - loss: 0.6355

Epoch 3/200

4/4 - 0s - 6ms/step - accuracy: 0.7300 - loss: 0.6107

Epoch 4/200

4/4 - 0s - 6ms/step - accuracy: 0.7700 - loss: 0.5886

Epoch 5/200

4/4 - 0s - 6ms/step - accuracy: 0.7800 - loss: 0.5690

Epoch 6/200

4/4 - 0s - 6ms/step - accuracy: 0.8000 - loss: 0.5503

Epoch 7/200

4/4 - 0s - 6ms/step - accuracy: 0.8000 - loss: 0.5341

Epoch 8/200

4/4 - 0s - 5ms/step - accuracy: 0.8050 - loss: 0.5190

Epoch 9/200

4/4 - 0s - 5ms/step - accuracy: 0.8100 - loss: 0.5047

Epoch 10/200

4/4 - 0s - 5ms/step - accuracy: 0.8100 - loss: 0.4910

Epoch 11/200

4/4 - 0s - 6ms/step - accuracy: 0.8250 - loss: 0.4774

Epoch 12/200

4/4 - 0s - 6ms/step - accuracy: 0.8250 - loss: 0.4644

Epoch 13/200

4/4 - 0s - 6ms/step - accuracy: 0.8300 - loss: 0.4522

Epoch 14/200

4/4 - 0s - 6ms/step - accuracy: 0.8350 - loss: 0.4402

Epoch 15/200

4/4 - 0s - 5ms/step - accuracy: 0.8400 - loss: 0.4288

Epoch 16/200

4/4 - 0s - 5ms/step - accuracy: 0.8450 - loss: 0.4166

Epoch 17/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.4054

Epoch 18/200

4/4 - 0s - 6ms/step - accuracy: 0.8500 - loss: 0.3951

Epoch 19/200

4/4 - 0s - 6ms/step - accuracy: 0.8500 - loss: 0.3845

Epoch 20/200

4/4 - 0s - 5ms/step - accuracy: 0.8600 - loss: 0.3739

Epoch 21/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3654

Epoch 22/200

4/4 - 0s - 7ms/step - accuracy: 0.8600 - loss: 0.3557

Epoch 23/200

4/4 - 0s - 5ms/step - accuracy: 0.8600 - loss: 0.3463

Epoch 24/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3377

Epoch 25/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3310

Epoch 26/200

4/4 - 0s - 5ms/step - accuracy: 0.8600 - loss: 0.3232

Epoch 27/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3157

Epoch 28/200

4/4 - 0s - 5ms/step - accuracy: 0.8600 - loss: 0.3093

Epoch 29/200

4/4 - 0s - 5ms/step - accuracy: 0.8750 - loss: 0.3027

Epoch 30/200

4/4 - 0s - 5ms/step - accuracy: 0.8650 - loss: 0.2979

Epoch 31/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2919

Epoch 32/200

4/4 - 0s - 5ms/step - accuracy: 0.8750 - loss: 0.2871

Epoch 33/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2813

Epoch 34/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2767

Epoch 35/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2730

Epoch 36/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2684

Epoch 37/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2638

Epoch 38/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2603

Epoch 39/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2560

Epoch 40/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2533

Epoch 41/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2501

Epoch 42/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2464

Epoch 43/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2430

Epoch 44/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2431

Epoch 45/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2378

Epoch 46/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2364

Epoch 47/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2353

Epoch 48/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2321

Epoch 49/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2293

Epoch 50/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2298

Epoch 51/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2251

Epoch 52/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2240

Epoch 53/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2221

Epoch 54/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2215

Epoch 55/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2197

Epoch 56/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2169

Epoch 57/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2165

Epoch 58/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2138

Epoch 59/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2132

Epoch 60/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2111

Epoch 61/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2109

Epoch 62/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2098

Epoch 63/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2073

Epoch 64/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.2052

Epoch 65/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2051

Epoch 66/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2052

Epoch 67/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2026

Epoch 68/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.2016

Epoch 69/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.1983

Epoch 70/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.1970

Epoch 71/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.1974

Epoch 72/200

4/4 - 0s - 5ms/step - accuracy: 0.9100 - loss: 0.1949

Epoch 73/200

4/4 - 0s - 5ms/step - accuracy: 0.9100 - loss: 0.1936

Epoch 74/200

4/4 - 0s - 7ms/step - accuracy: 0.9050 - loss: 0.1927

Epoch 75/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.1908

Epoch 76/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.1886

Epoch 77/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.1870

Epoch 78/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.1864

Epoch 79/200

4/4 - 0s - 5ms/step - accuracy: 0.9150 - loss: 0.1854

Epoch 80/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1827

Epoch 81/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1814

Epoch 82/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1806

Epoch 83/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.1794

Epoch 84/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.1762

Epoch 85/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1761

Epoch 86/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1751

Epoch 87/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1719

Epoch 88/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1702

Epoch 89/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1736

Epoch 90/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1677

Epoch 91/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1672

Epoch 92/200

4/4 - 0s - 5ms/step - accuracy: 0.9250 - loss: 0.1666

Epoch 93/200

4/4 - 0s - 5ms/step - accuracy: 0.9300 - loss: 0.1637

Epoch 94/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1622

Epoch 95/200

4/4 - 0s - 5ms/step - accuracy: 0.9400 - loss: 0.1607

Epoch 96/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1591

Epoch 97/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1574

Epoch 98/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1566

Epoch 99/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1573

Epoch 100/200

4/4 - 0s - 7ms/step - accuracy: 0.9450 - loss: 0.1530

Epoch 101/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1520

Epoch 102/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1503

Epoch 103/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1490

Epoch 104/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1466

Epoch 105/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1460

Epoch 106/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1454

Epoch 107/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1426

Epoch 108/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1414

Epoch 109/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1419

Epoch 110/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1383

Epoch 111/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1374

Epoch 112/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1361

Epoch 113/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1349

Epoch 114/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1328

Epoch 115/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.1312

Epoch 116/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.1307

Epoch 117/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1298

Epoch 118/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1296

Epoch 119/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1256

Epoch 120/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.1244

Epoch 121/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1225

Epoch 122/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.1234

Epoch 123/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1194

Epoch 124/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.1183

Epoch 125/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.1174

Epoch 126/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.1156

Epoch 127/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1148

Epoch 128/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1143

Epoch 129/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.1122

Epoch 130/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.1091

Epoch 131/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.1085

Epoch 132/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.1069

Epoch 133/200

4/4 - 0s - 7ms/step - accuracy: 0.9650 - loss: 0.1049

Epoch 134/200

4/4 - 0s - 7ms/step - accuracy: 0.9700 - loss: 0.1039

Epoch 135/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1031

Epoch 136/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.1015

Epoch 137/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.0996

Epoch 138/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0986

Epoch 139/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.0983

Epoch 140/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.0962

Epoch 141/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0941

Epoch 142/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0929

Epoch 143/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0907

Epoch 144/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0897

Epoch 145/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.0880

Epoch 146/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0864

Epoch 147/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0853

Epoch 148/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0854

Epoch 149/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0836

Epoch 150/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0804

Epoch 151/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.0792

Epoch 152/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0782

Epoch 153/200

4/4 - 0s - 5ms/step - accuracy: 0.9800 - loss: 0.0776

Epoch 154/200

4/4 - 0s - 5ms/step - accuracy: 0.9800 - loss: 0.0748

Epoch 155/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.0763

Epoch 156/200

4/4 - 0s - 5ms/step - accuracy: 0.9800 - loss: 0.0721

Epoch 157/200

4/4 - 0s - 5ms/step - accuracy: 0.9800 - loss: 0.0716

Epoch 158/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.0706

Epoch 159/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0694

Epoch 160/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0687

Epoch 161/200

4/4 - 0s - 5ms/step - accuracy: 0.9800 - loss: 0.0669

Epoch 162/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0671

Epoch 163/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.0647

Epoch 164/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.0634

Epoch 165/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.0619

Epoch 166/200

4/4 - 0s - 5ms/step - accuracy: 0.9800 - loss: 0.0611

Epoch 167/200

4/4 - 0s - 7ms/step - accuracy: 0.9800 - loss: 0.0597

Epoch 168/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.0587

Epoch 169/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.0574

Epoch 170/200

4/4 - 0s - 6ms/step - accuracy: 0.9850 - loss: 0.0592

Epoch 171/200

4/4 - 0s - 6ms/step - accuracy: 0.9850 - loss: 0.0555

Epoch 172/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.0547

Epoch 173/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.0533

Epoch 174/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.0522

Epoch 175/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.0521

Epoch 176/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0504

Epoch 177/200

4/4 - 0s - 6ms/step - accuracy: 0.9850 - loss: 0.0491

Epoch 178/200

4/4 - 0s - 6ms/step - accuracy: 0.9850 - loss: 0.0507

Epoch 179/200

4/4 - 0s - 6ms/step - accuracy: 0.9850 - loss: 0.0473

Epoch 180/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0468

Epoch 181/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0464

Epoch 182/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0460

Epoch 183/200

4/4 - 0s - 5ms/step - accuracy: 0.9900 - loss: 0.0441

Epoch 184/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0433

Epoch 185/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0440

Epoch 186/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0429

Epoch 187/200

4/4 - 0s - 5ms/step - accuracy: 0.9900 - loss: 0.0418

Epoch 188/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0408

Epoch 189/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0408

Epoch 190/200

4/4 - 0s - 5ms/step - accuracy: 0.9900 - loss: 0.0394

Epoch 191/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0388

Epoch 192/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0378

Epoch 193/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0376

Epoch 194/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0366

Epoch 195/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0356

Epoch 196/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0352

Epoch 197/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0352

Epoch 198/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0342

Epoch 199/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0334

Epoch 200/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0332

score = model.evaluate(x, v, verbose=0)
print(f"score = {score[0]}")
print(f"accuracy = {score[1]}")

score = 0.03187823295593262
accuracy = 0.9900000095367432

Predicting

Let’s look at a prediction. We need to feed in a single point as an array of shape (N, 2), where N is the number of points

res = model.predict(np.array([[-2, 2]]))
res

1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step


1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step

array([[4.866069e-12]], dtype=float32)

We see that we get a floating point number. We will need to convert this to 0 or 1 by rounding.

Let’s plot the partitioning

M = 256
N = 256

xmin = -1.75
xmax = 2.5
ymin = -1.25
ymax = 1.75

xpt = np.linspace(xmin, xmax, M)
ypt = np.linspace(ymin, ymax, N)

To make the prediction go faster, we want to feed in a vector of these points, of the form:

[[xpt[0], ypt[0]],
 [xpt[1], ypt[1]],
 ...
]

We can see that this packs them into the vector

pairs = np.array(np.meshgrid(xpt, ypt)).T.reshape(-1, 2)
pairs[0]

array([-1.75, -1.25])

Now we do the prediction. We will get a vector out, which we reshape to match the original domain.

res = model.predict(pairs, verbose=0)
res.shape = (M, N)

Finally, round to 0 or 1

domain = np.where(res > 0.5, 1, 0)

and we can plot the data

fig, ax = plt.subplots()
ax.imshow(domain.T, origin="lower",
          extent=[xmin, xmax, ymin, ymax], alpha=0.25)
xpt = [q[0] for q in x]
ypt = [q[1] for q in x]

ax.scatter(xpt, ypt, s=40, c=v, cmap="viridis")

<matplotlib.collections.PathCollection at 0x7fe8c577f110>