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 = [ 1.04628964 -0.4585966 ], value = 1

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

/opt/hostedtoolcache/Python/3.14.2/x64/lib/python3.14/site-packages/keras/src/export/tf2onnx_lib.py:8: FutureWarning: In the future `np.object` will be defined as the corresponding NumPy scalar.
  if not hasattr(np, "object"):

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: 0.6450 - loss: 0.6669

Epoch 2/200

4/4 - 0s - 6ms/step - accuracy: 0.7000 - loss: 0.6363

Epoch 3/200

4/4 - 0s - 6ms/step - accuracy: 0.7250 - loss: 0.6152

Epoch 4/200

4/4 - 0s - 6ms/step - accuracy: 0.7450 - loss: 0.5966

Epoch 5/200

4/4 - 0s - 6ms/step - accuracy: 0.7650 - loss: 0.5778

Epoch 6/200

4/4 - 0s - 6ms/step - accuracy: 0.7750 - loss: 0.5596

Epoch 7/200

4/4 - 0s - 6ms/step - accuracy: 0.8050 - loss: 0.5411

Epoch 8/200

4/4 - 0s - 6ms/step - accuracy: 0.8200 - loss: 0.5231

Epoch 9/200

4/4 - 0s - 6ms/step - accuracy: 0.8250 - loss: 0.5055

Epoch 10/200

4/4 - 0s - 6ms/step - accuracy: 0.8250 - loss: 0.4895

Epoch 11/200

4/4 - 0s - 6ms/step - accuracy: 0.8300 - loss: 0.4736

Epoch 12/200

4/4 - 0s - 6ms/step - accuracy: 0.8300 - loss: 0.4588

Epoch 13/200

4/4 - 0s - 6ms/step - accuracy: 0.8300 - loss: 0.4431

Epoch 14/200

4/4 - 0s - 6ms/step - accuracy: 0.8300 - loss: 0.4283

Epoch 15/200

4/4 - 0s - 6ms/step - accuracy: 0.8300 - loss: 0.4144

Epoch 16/200

4/4 - 0s - 6ms/step - accuracy: 0.8350 - loss: 0.4013

Epoch 17/200

4/4 - 0s - 27ms/step - accuracy: 0.8450 - loss: 0.3891

Epoch 18/200

4/4 - 0s - 5ms/step - accuracy: 0.8500 - loss: 0.3779

Epoch 19/200

4/4 - 0s - 6ms/step - accuracy: 0.8500 - loss: 0.3680

Epoch 20/200

4/4 - 0s - 6ms/step - accuracy: 0.8500 - loss: 0.3572

Epoch 21/200

4/4 - 0s - 5ms/step - accuracy: 0.8600 - loss: 0.3484

Epoch 22/200

4/4 - 0s - 5ms/step - accuracy: 0.8600 - loss: 0.3395

Epoch 23/200

4/4 - 0s - 5ms/step - accuracy: 0.8600 - loss: 0.3316

Epoch 24/200

4/4 - 0s - 11ms/step - accuracy: 0.8650 - loss: 0.3246

Epoch 25/200

4/4 - 0s - 5ms/step - accuracy: 0.8650 - loss: 0.3185

Epoch 26/200

4/4 - 0s - 7ms/step - accuracy: 0.8650 - loss: 0.3135

Epoch 27/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.3069

Epoch 28/200

4/4 - 0s - 7ms/step - accuracy: 0.8700 - loss: 0.3030

Epoch 29/200

4/4 - 0s - 7ms/step - accuracy: 0.8700 - loss: 0.2975

Epoch 30/200

4/4 - 0s - 22ms/step - accuracy: 0.8700 - loss: 0.2933

Epoch 31/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2908

Epoch 32/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2866

Epoch 33/200

4/4 - 0s - 5ms/step - accuracy: 0.8750 - loss: 0.2834

Epoch 34/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.2835

Epoch 35/200

4/4 - 0s - 5ms/step - accuracy: 0.8750 - loss: 0.2781

Epoch 36/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2754

Epoch 37/200

4/4 - 0s - 5ms/step - accuracy: 0.8700 - loss: 0.2731

Epoch 38/200

4/4 - 0s - 5ms/step - accuracy: 0.8750 - loss: 0.2711

Epoch 39/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2686

Epoch 40/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2678

Epoch 41/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2652

Epoch 42/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2628

Epoch 43/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2614

Epoch 44/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2583

Epoch 45/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2592

Epoch 46/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2566

Epoch 47/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2532

Epoch 48/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2531

Epoch 49/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2506

Epoch 50/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2484

Epoch 51/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2468

Epoch 52/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2457

Epoch 53/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2439

Epoch 54/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2427

Epoch 55/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2403

Epoch 56/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2404

Epoch 57/200

4/4 - 0s - 40ms/step - accuracy: 0.8850 - loss: 0.2376

Epoch 58/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2358

Epoch 59/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2339

Epoch 60/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2331

Epoch 61/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2301

Epoch 62/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2303

Epoch 63/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2281

Epoch 64/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2261

Epoch 65/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2238

Epoch 66/200

4/4 - 0s - 13ms/step - accuracy: 0.8850 - loss: 0.2217

Epoch 67/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2204

Epoch 68/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2190

Epoch 69/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2172

Epoch 70/200

4/4 - 0s - 8ms/step - accuracy: 0.8900 - loss: 0.2147

Epoch 71/200

4/4 - 0s - 7ms/step - accuracy: 0.9000 - loss: 0.2133

Epoch 72/200

4/4 - 0s - 8ms/step - accuracy: 0.8950 - loss: 0.2117

Epoch 73/200

4/4 - 0s - 23ms/step - accuracy: 0.8950 - loss: 0.2086

Epoch 74/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2091

Epoch 75/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2068

Epoch 76/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.2040

Epoch 77/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2017

Epoch 78/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1999

Epoch 79/200

4/4 - 0s - 5ms/step - accuracy: 0.9100 - loss: 0.1985

Epoch 80/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.1963

Epoch 81/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.1941

Epoch 82/200

4/4 - 0s - 7ms/step - accuracy: 0.9100 - loss: 0.1927

Epoch 83/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1895

Epoch 84/200

4/4 - 0s - 5ms/step - accuracy: 0.9100 - loss: 0.1893

Epoch 85/200

4/4 - 0s - 5ms/step - accuracy: 0.9100 - loss: 0.1868

Epoch 86/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1842

Epoch 87/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.1834

Epoch 88/200

4/4 - 0s - 5ms/step - accuracy: 0.9100 - loss: 0.1820

Epoch 89/200

4/4 - 0s - 5ms/step - accuracy: 0.9100 - loss: 0.1781

Epoch 90/200

4/4 - 0s - 5ms/step - accuracy: 0.9100 - loss: 0.1764

Epoch 91/200

4/4 - 0s - 5ms/step - accuracy: 0.9100 - loss: 0.1791

Epoch 92/200

4/4 - 0s - 5ms/step - accuracy: 0.9250 - loss: 0.1724

Epoch 93/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1703

Epoch 94/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1692

Epoch 95/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1658

Epoch 96/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1640

Epoch 97/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1639

Epoch 98/200

4/4 - 0s - 5ms/step - accuracy: 0.9250 - loss: 0.1601

Epoch 99/200

4/4 - 0s - 5ms/step - accuracy: 0.9300 - loss: 0.1574

Epoch 100/200

4/4 - 0s - 5ms/step - accuracy: 0.9300 - loss: 0.1559

Epoch 101/200

4/4 - 0s - 45ms/step - accuracy: 0.9300 - loss: 0.1539

Epoch 102/200

4/4 - 0s - 7ms/step - accuracy: 0.9300 - loss: 0.1512

Epoch 103/200

4/4 - 0s - 7ms/step - accuracy: 0.9300 - loss: 0.1495

Epoch 104/200

4/4 - 0s - 7ms/step - accuracy: 0.9300 - loss: 0.1471

Epoch 105/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1449

Epoch 106/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1442

Epoch 107/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1420

Epoch 108/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1390

Epoch 109/200

4/4 - 0s - 5ms/step - accuracy: 0.9300 - loss: 0.1375

Epoch 110/200

4/4 - 0s - 13ms/step - accuracy: 0.9350 - loss: 0.1349

Epoch 111/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1326

Epoch 112/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1300

Epoch 113/200

4/4 - 0s - 8ms/step - accuracy: 0.9350 - loss: 0.1288

Epoch 114/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1294

Epoch 115/200

4/4 - 0s - 7ms/step - accuracy: 0.9450 - loss: 0.1238

Epoch 116/200

4/4 - 0s - 7ms/step - accuracy: 0.9400 - loss: 0.1224

Epoch 117/200

4/4 - 0s - 22ms/step - accuracy: 0.9450 - loss: 0.1195

Epoch 118/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1178

Epoch 119/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1155

Epoch 120/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1134

Epoch 121/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1115

Epoch 122/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1100

Epoch 123/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1073

Epoch 124/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1051

Epoch 125/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1042

Epoch 126/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1015

Epoch 127/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1004

Epoch 128/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.0973

Epoch 129/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.0957

Epoch 130/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.0936

Epoch 131/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.0918

Epoch 132/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.0901

Epoch 133/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.0901

Epoch 134/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.0897

Epoch 135/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0854

Epoch 136/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.0847

Epoch 137/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0820

Epoch 138/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0816

Epoch 139/200

4/4 - 0s - 5ms/step - accuracy: 0.9850 - loss: 0.0802

Epoch 140/200

4/4 - 0s - 5ms/step - accuracy: 0.9850 - loss: 0.0775

Epoch 141/200

4/4 - 0s - 5ms/step - accuracy: 0.9800 - loss: 0.0772

Epoch 142/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0762

Epoch 143/200

4/4 - 0s - 5ms/step - accuracy: 0.9850 - loss: 0.0739

Epoch 144/200

4/4 - 0s - 5ms/step - accuracy: 0.9800 - loss: 0.0723

Epoch 145/200

4/4 - 0s - 47ms/step - accuracy: 0.9850 - loss: 0.0704

Epoch 146/200

4/4 - 0s - 5ms/step - accuracy: 0.9800 - loss: 0.0702

Epoch 147/200

4/4 - 0s - 6ms/step - accuracy: 0.9850 - loss: 0.0684

Epoch 148/200

4/4 - 0s - 5ms/step - accuracy: 0.9800 - loss: 0.0681

Epoch 149/200

4/4 - 0s - 5ms/step - accuracy: 0.9850 - loss: 0.0660

Epoch 150/200

4/4 - 0s - 5ms/step - accuracy: 0.9850 - loss: 0.0647

Epoch 151/200

4/4 - 0s - 6ms/step - accuracy: 0.9850 - loss: 0.0626

Epoch 152/200

4/4 - 0s - 6ms/step - accuracy: 0.9850 - loss: 0.0622

Epoch 153/200

4/4 - 0s - 6ms/step - accuracy: 0.9850 - loss: 0.0605

Epoch 154/200

4/4 - 0s - 14ms/step - accuracy: 0.9850 - loss: 0.0596

Epoch 155/200

4/4 - 0s - 6ms/step - accuracy: 0.9850 - loss: 0.0589

Epoch 156/200

4/4 - 0s - 6ms/step - accuracy: 0.9850 - loss: 0.0585

Epoch 157/200

4/4 - 0s - 9ms/step - accuracy: 0.9900 - loss: 0.0556

Epoch 158/200

4/4 - 0s - 8ms/step - accuracy: 0.9950 - loss: 0.0542

Epoch 159/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0539

Epoch 160/200

4/4 - 0s - 9ms/step - accuracy: 0.9900 - loss: 0.0523

Epoch 161/200

4/4 - 0s - 21ms/step - accuracy: 0.9850 - loss: 0.0523

Epoch 162/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0512

Epoch 163/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0501

Epoch 164/200

4/4 - 0s - 6ms/step - accuracy: 1.0000 - loss: 0.0483

Epoch 165/200

4/4 - 0s - 5ms/step - accuracy: 0.9900 - loss: 0.0477

Epoch 166/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0467

Epoch 167/200

4/4 - 0s - 5ms/step - accuracy: 1.0000 - loss: 0.0451

Epoch 168/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0451

Epoch 169/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0445

Epoch 170/200

4/4 - 0s - 6ms/step - accuracy: 1.0000 - loss: 0.0424

Epoch 171/200

4/4 - 0s - 6ms/step - accuracy: 1.0000 - loss: 0.0416

Epoch 172/200

4/4 - 0s - 5ms/step - accuracy: 0.9950 - loss: 0.0413

Epoch 173/200

4/4 - 0s - 6ms/step - accuracy: 1.0000 - loss: 0.0409

Epoch 174/200

4/4 - 0s - 6ms/step - accuracy: 1.0000 - loss: 0.0395

Epoch 175/200

4/4 - 0s - 6ms/step - accuracy: 1.0000 - loss: 0.0391

Epoch 176/200

4/4 - 0s - 6ms/step - accuracy: 1.0000 - loss: 0.0386

Epoch 177/200

4/4 - 0s - 6ms/step - accuracy: 1.0000 - loss: 0.0374

Epoch 178/200

4/4 - 0s - 6ms/step - accuracy: 1.0000 - loss: 0.0363

Epoch 179/200

4/4 - 0s - 6ms/step - accuracy: 1.0000 - loss: 0.0359

Epoch 180/200

4/4 - 0s - 6ms/step - accuracy: 1.0000 - loss: 0.0351

Epoch 181/200

4/4 - 0s - 6ms/step - accuracy: 1.0000 - loss: 0.0340

Epoch 182/200

4/4 - 0s - 6ms/step - accuracy: 1.0000 - loss: 0.0344

Epoch 183/200

4/4 - 0s - 6ms/step - accuracy: 1.0000 - loss: 0.0330

Epoch 184/200

4/4 - 0s - 5ms/step - accuracy: 1.0000 - loss: 0.0320

Epoch 185/200

4/4 - 0s - 6ms/step - accuracy: 1.0000 - loss: 0.0322

Epoch 186/200

4/4 - 0s - 6ms/step - accuracy: 1.0000 - loss: 0.0321

Epoch 187/200

4/4 - 0s - 5ms/step - accuracy: 1.0000 - loss: 0.0303

Epoch 188/200

4/4 - 0s - 54ms/step - accuracy: 1.0000 - loss: 0.0294

Epoch 189/200

4/4 - 0s - 6ms/step - accuracy: 1.0000 - loss: 0.0290

Epoch 190/200

4/4 - 0s - 6ms/step - accuracy: 1.0000 - loss: 0.0289

Epoch 191/200

4/4 - 0s - 5ms/step - accuracy: 1.0000 - loss: 0.0284

Epoch 192/200

4/4 - 0s - 5ms/step - accuracy: 1.0000 - loss: 0.0278

Epoch 193/200

4/4 - 0s - 6ms/step - accuracy: 1.0000 - loss: 0.0270

Epoch 194/200

4/4 - 0s - 6ms/step - accuracy: 1.0000 - loss: 0.0264

Epoch 195/200

4/4 - 0s - 5ms/step - accuracy: 1.0000 - loss: 0.0260

Epoch 196/200

4/4 - 0s - 5ms/step - accuracy: 1.0000 - loss: 0.0254

Epoch 197/200

4/4 - 0s - 16ms/step - accuracy: 1.0000 - loss: 0.0250

Epoch 198/200

4/4 - 0s - 6ms/step - accuracy: 1.0000 - loss: 0.0243

Epoch 199/200

4/4 - 0s - 6ms/step - accuracy: 1.0000 - loss: 0.0241

Epoch 200/200

4/4 - 0s - 9ms/step - accuracy: 1.0000 - loss: 0.0238

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

score = 0.023014333099126816
accuracy = 1.0

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 5ms/step


1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step

array([[3.4656636e-16]], 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 0x7fc42e0496d0>