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 = [ 0.36160058 -0.00204808], 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

2025-09-11 22:13:21.542605: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:31] Could not find cuda drivers on your machine, GPU will not be used.
2025-09-11 22:13:21.587700: I tensorflow/core/platform/cpu_feature_guard.cc:210] This TensorFlow binary is optimized to use available CPU instructions in performance-critical operations.
To enable the following instructions: AVX2 FMA, in other operations, rebuild TensorFlow with the appropriate compiler flags.

2025-09-11 22:13:23.226040: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:31] Could not find cuda drivers on your machine, GPU will not be used.

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

2025-09-11 22:13:23.525295: E external/local_xla/xla/stream_executor/cuda/cuda_platform.cc:51] failed call to cuInit: INTERNAL: CUDA error: Failed call to cuInit: UNKNOWN ERROR (303)

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 - 115ms/step - accuracy: 0.6200 - loss: 0.6802

Epoch 2/200

4/4 - 0s - 6ms/step - accuracy: 0.7450 - loss: 0.6297

Epoch 3/200

4/4 - 0s - 6ms/step - accuracy: 0.8200 - loss: 0.5984

Epoch 4/200

4/4 - 0s - 6ms/step - accuracy: 0.8200 - loss: 0.5731

Epoch 5/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.5500

Epoch 6/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.5282

Epoch 7/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.5082

Epoch 8/200

4/4 - 0s - 6ms/step - accuracy: 0.8450 - loss: 0.4892

Epoch 9/200

4/4 - 0s - 6ms/step - accuracy: 0.8450 - loss: 0.4718

Epoch 10/200

4/4 - 0s - 6ms/step - accuracy: 0.8400 - loss: 0.4556

Epoch 11/200

4/4 - 0s - 6ms/step - accuracy: 0.8450 - loss: 0.4399

Epoch 12/200

4/4 - 0s - 6ms/step - accuracy: 0.8400 - loss: 0.4257

Epoch 13/200

4/4 - 0s - 6ms/step - accuracy: 0.8400 - loss: 0.4121

Epoch 14/200

4/4 - 0s - 6ms/step - accuracy: 0.8400 - loss: 0.3990

Epoch 15/200

4/4 - 0s - 6ms/step - accuracy: 0.8400 - loss: 0.3873

Epoch 16/200

4/4 - 0s - 6ms/step - accuracy: 0.8400 - loss: 0.3752

Epoch 17/200

4/4 - 0s - 6ms/step - accuracy: 0.8500 - loss: 0.3650

Epoch 18/200

4/4 - 0s - 6ms/step - accuracy: 0.8450 - loss: 0.3554

Epoch 19/200

4/4 - 0s - 6ms/step - accuracy: 0.8500 - loss: 0.3468

Epoch 20/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.3385

Epoch 21/200

4/4 - 0s - 6ms/step - accuracy: 0.8500 - loss: 0.3314

Epoch 22/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3253

Epoch 23/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3188

Epoch 24/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3128

Epoch 25/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3090

Epoch 26/200

4/4 - 0s - 6ms/step - accuracy: 0.8500 - loss: 0.3042

Epoch 27/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2994

Epoch 28/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2961

Epoch 29/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2922

Epoch 30/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.2898

Epoch 31/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.2870

Epoch 32/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2827

Epoch 33/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2799

Epoch 34/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.2792

Epoch 35/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2757

Epoch 36/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.2732

Epoch 37/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2707

Epoch 38/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2680

Epoch 39/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2673

Epoch 40/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2655

Epoch 41/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2627

Epoch 42/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2601

Epoch 43/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2609

Epoch 44/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2568

Epoch 45/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2547

Epoch 46/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2548

Epoch 47/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2512

Epoch 48/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2494

Epoch 49/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2485

Epoch 50/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2458

Epoch 51/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2446

Epoch 52/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2429

Epoch 53/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2422

Epoch 54/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2385

Epoch 55/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2381

Epoch 56/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2351

Epoch 57/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2336

Epoch 58/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2339

Epoch 59/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2336

Epoch 60/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2286

Epoch 61/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2282

Epoch 62/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2264

Epoch 63/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2246

Epoch 64/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2227

Epoch 65/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2210

Epoch 66/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2197

Epoch 67/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2177

Epoch 68/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2181

Epoch 69/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2151

Epoch 70/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2128

Epoch 71/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2144

Epoch 72/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2097

Epoch 73/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2081

Epoch 74/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2068

Epoch 75/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2050

Epoch 76/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2035

Epoch 77/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2040

Epoch 78/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2013

Epoch 79/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.1995

Epoch 80/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1965

Epoch 81/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1968

Epoch 82/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1957

Epoch 83/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1936

Epoch 84/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1917

Epoch 85/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1886

Epoch 86/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1875

Epoch 87/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1855

Epoch 88/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1859

Epoch 89/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1822

Epoch 90/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1829

Epoch 91/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1797

Epoch 92/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1771

Epoch 93/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1752

Epoch 94/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1732

Epoch 95/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1754

Epoch 96/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.1699

Epoch 97/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1678

Epoch 98/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1696

Epoch 99/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.1645

Epoch 100/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.1652

Epoch 101/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1608

Epoch 102/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1601

Epoch 103/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1590

Epoch 104/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1562

Epoch 105/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1577

Epoch 106/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1525

Epoch 107/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1506

Epoch 108/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1513

Epoch 109/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1469

Epoch 110/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1453

Epoch 111/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1457

Epoch 112/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1433

Epoch 113/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1412

Epoch 114/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1414

Epoch 115/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1404

Epoch 116/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1365

Epoch 117/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1344

Epoch 118/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1331

Epoch 119/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1314

Epoch 120/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1298

Epoch 121/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1284

Epoch 122/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1272

Epoch 123/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1248

Epoch 124/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1221

Epoch 125/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1206

Epoch 126/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.1205

Epoch 127/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1175

Epoch 128/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1163

Epoch 129/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.1142

Epoch 130/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.1114

Epoch 131/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.1112

Epoch 132/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.1089

Epoch 133/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.1070

Epoch 134/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.1064

Epoch 135/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.1038

Epoch 136/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.1013

Epoch 137/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.0988

Epoch 138/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0973

Epoch 139/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.0958

Epoch 140/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0950

Epoch 141/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.0908

Epoch 142/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.0889

Epoch 143/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.0872

Epoch 144/200

4/4 - 0s - 6ms/step - accuracy: 0.9850 - loss: 0.0879

Epoch 145/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.0843

Epoch 146/200

4/4 - 0s - 6ms/step - accuracy: 0.9850 - loss: 0.0826

Epoch 147/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.0800

Epoch 148/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.0790

Epoch 149/200

4/4 - 0s - 6ms/step - accuracy: 0.9850 - loss: 0.0785

Epoch 150/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.0780

Epoch 151/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.0761

Epoch 152/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0730

Epoch 153/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0720

Epoch 154/200

4/4 - 0s - 6ms/step - accuracy: 0.9850 - loss: 0.0699

Epoch 155/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0680

Epoch 156/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0668

Epoch 157/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0658

Epoch 158/200

4/4 - 0s - 6ms/step - accuracy: 0.9850 - loss: 0.0651

Epoch 159/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0638

Epoch 160/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0615

Epoch 161/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0603

Epoch 162/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0588

Epoch 163/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0581

Epoch 164/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0568

Epoch 165/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0552

Epoch 166/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0531

Epoch 167/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0523

Epoch 168/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0516

Epoch 169/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0500

Epoch 170/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0495

Epoch 171/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0479

Epoch 172/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0473

Epoch 173/200

4/4 - 0s - 6ms/step - accuracy: 0.9900 - loss: 0.0457

Epoch 174/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0462

Epoch 175/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0440

Epoch 176/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0433

Epoch 177/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0424

Epoch 178/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0413

Epoch 179/200

4/4 - 0s - 8ms/step - accuracy: 0.9950 - loss: 0.0400

Epoch 180/200

4/4 - 0s - 7ms/step - accuracy: 0.9950 - loss: 0.0397

Epoch 181/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0389

Epoch 182/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0383

Epoch 183/200

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

Epoch 184/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0361

Epoch 185/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0354

Epoch 186/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0344

Epoch 187/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0342

Epoch 188/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0328

Epoch 189/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0323

Epoch 190/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0318

Epoch 191/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0325

Epoch 192/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0307

Epoch 193/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0306

Epoch 194/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0293

Epoch 195/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0284

Epoch 196/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0278

Epoch 197/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0276

Epoch 198/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0275

Epoch 199/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0267

Epoch 200/200

4/4 - 0s - 6ms/step - accuracy: 0.9950 - loss: 0.0259

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

score = 0.02486642636358738
accuracy = 0.9950000047683716

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 30ms/step


1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 40ms/step

array([[1.980287e-17]], 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 0x7f0e60b7b410>