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 = [ 1.45633693 -0.4060936 ], 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

2025-06-10 23:59:10.945382: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2025-06-10 23:59:10.948576: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2025-06-10 23:59:10.957268: E external/local_xla/xla/stream_executor/cuda/cuda_fft.cc:467] Unable to register cuFFT factory: Attempting to register factory for plugin cuFFT when one has already been registered
WARNING: All log messages before absl::InitializeLog() is called are written to STDERR
E0000 00:00:1749599950.971409    4941 cuda_dnn.cc:8579] Unable to register cuDNN factory: Attempting to register factory for plugin cuDNN when one has already been registered
E0000 00:00:1749599950.975564    4941 cuda_blas.cc:1407] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered
W0000 00:00:1749599950.987192    4941 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
W0000 00:00:1749599950.987202    4941 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
W0000 00:00:1749599950.987204    4941 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
W0000 00:00:1749599950.987205    4941 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
2025-06-10 23:59:10.991210: 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.

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

2025-06-10 23:59:12.800821: 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 - 116ms/step - accuracy: 0.5350 - loss: 0.6960

Epoch 2/200

4/4 - 0s - 6ms/step - accuracy: 0.7850 - loss: 0.6527

Epoch 3/200

4/4 - 0s - 6ms/step - accuracy: 0.8150 - loss: 0.6279

Epoch 4/200

4/4 - 0s - 6ms/step - accuracy: 0.8250 - loss: 0.6069

Epoch 5/200

4/4 - 0s - 6ms/step - accuracy: 0.8250 - loss: 0.5887

Epoch 6/200

4/4 - 0s - 6ms/step - accuracy: 0.8200 - loss: 0.5710

Epoch 7/200

4/4 - 0s - 6ms/step - accuracy: 0.8200 - loss: 0.5536

Epoch 8/200

4/4 - 0s - 6ms/step - accuracy: 0.8100 - loss: 0.5366

Epoch 9/200

4/4 - 0s - 6ms/step - accuracy: 0.8150 - loss: 0.5185

Epoch 10/200

4/4 - 0s - 6ms/step - accuracy: 0.8200 - loss: 0.4999

Epoch 11/200

4/4 - 0s - 6ms/step - accuracy: 0.8250 - loss: 0.4830

Epoch 12/200

4/4 - 0s - 6ms/step - accuracy: 0.8350 - loss: 0.4668

Epoch 13/200

4/4 - 0s - 6ms/step - accuracy: 0.8300 - loss: 0.4528

Epoch 14/200

4/4 - 0s - 6ms/step - accuracy: 0.8350 - loss: 0.4379

Epoch 15/200

4/4 - 0s - 6ms/step - accuracy: 0.8300 - loss: 0.4249

Epoch 16/200

4/4 - 0s - 6ms/step - accuracy: 0.8300 - loss: 0.4117

Epoch 17/200

4/4 - 0s - 6ms/step - accuracy: 0.8400 - loss: 0.3993

Epoch 18/200

4/4 - 0s - 6ms/step - accuracy: 0.8400 - loss: 0.3874

Epoch 19/200

4/4 - 0s - 6ms/step - accuracy: 0.8400 - loss: 0.3759

Epoch 20/200

4/4 - 0s - 6ms/step - accuracy: 0.8450 - loss: 0.3656

Epoch 21/200

4/4 - 0s - 6ms/step - accuracy: 0.8400 - loss: 0.3565

Epoch 22/200

4/4 - 0s - 6ms/step - accuracy: 0.8450 - loss: 0.3461

Epoch 23/200

4/4 - 0s - 6ms/step - accuracy: 0.8500 - loss: 0.3380

Epoch 24/200

4/4 - 0s - 6ms/step - accuracy: 0.8500 - loss: 0.3298

Epoch 25/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3233

Epoch 26/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3164

Epoch 27/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3108

Epoch 28/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3057

Epoch 29/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.3020

Epoch 30/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2966

Epoch 31/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.2939

Epoch 32/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.2899

Epoch 33/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2870

Epoch 34/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2833

Epoch 35/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.2805

Epoch 36/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.2777

Epoch 37/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2758

Epoch 38/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.2733

Epoch 39/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.2715

Epoch 40/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.2691

Epoch 41/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2667

Epoch 42/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2656

Epoch 43/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.2665

Epoch 44/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2630

Epoch 45/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2605

Epoch 46/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2597

Epoch 47/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2579

Epoch 48/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2573

Epoch 49/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2556

Epoch 50/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2542

Epoch 51/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2523

Epoch 52/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2530

Epoch 53/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2502

Epoch 54/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2522

Epoch 55/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2479

Epoch 56/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2483

Epoch 57/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2460

Epoch 58/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2445

Epoch 59/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2457

Epoch 60/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2460

Epoch 61/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2432

Epoch 62/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2417

Epoch 63/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2410

Epoch 64/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2436

Epoch 65/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2399

Epoch 66/200

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

Epoch 67/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2381

Epoch 68/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2374

Epoch 69/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2358

Epoch 70/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2389

Epoch 71/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2350

Epoch 72/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2364

Epoch 73/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2337

Epoch 74/200

4/4 - 0s - 8ms/step - accuracy: 0.8800 - loss: 0.2328

Epoch 75/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2331

Epoch 76/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2335

Epoch 77/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2328

Epoch 78/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2310

Epoch 79/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2297

Epoch 80/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2287

Epoch 81/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2289

Epoch 82/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2285

Epoch 83/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2286

Epoch 84/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2264

Epoch 85/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2253

Epoch 86/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2281

Epoch 87/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2268

Epoch 88/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2239

Epoch 89/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2232

Epoch 90/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2239

Epoch 91/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2230

Epoch 92/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2218

Epoch 93/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2230

Epoch 94/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2216

Epoch 95/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2194

Epoch 96/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2184

Epoch 97/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2194

Epoch 98/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2193

Epoch 99/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2199

Epoch 100/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2165

Epoch 101/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2165

Epoch 102/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2156

Epoch 103/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2139

Epoch 104/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2159

Epoch 105/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2170

Epoch 106/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2123

Epoch 107/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2141

Epoch 108/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2116

Epoch 109/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2103

Epoch 110/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2119

Epoch 111/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2091

Epoch 112/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2096

Epoch 113/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2083

Epoch 114/200

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

Epoch 115/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2066

Epoch 116/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2060

Epoch 117/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2057

Epoch 118/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.2051

Epoch 119/200

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

Epoch 120/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2025

Epoch 121/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2013

Epoch 122/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2017

Epoch 123/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1997

Epoch 124/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1998

Epoch 125/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1991

Epoch 126/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1997

Epoch 127/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.1971

Epoch 128/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.1961

Epoch 129/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.1976

Epoch 130/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1950

Epoch 131/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.1938

Epoch 132/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.1951

Epoch 133/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1978

Epoch 134/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1911

Epoch 135/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1939

Epoch 136/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.1893

Epoch 137/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.1927

Epoch 138/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1888

Epoch 139/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.1882

Epoch 140/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.1864

Epoch 141/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1886

Epoch 142/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.1850

Epoch 143/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.1877

Epoch 144/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.1857

Epoch 145/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1848

Epoch 146/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1819

Epoch 147/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.1830

Epoch 148/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1801

Epoch 149/200

4/4 - 0s - 8ms/step - accuracy: 0.9050 - loss: 0.1809

Epoch 150/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1782

Epoch 151/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1795

Epoch 152/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1781

Epoch 153/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.1774

Epoch 154/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.1757

Epoch 155/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1753

Epoch 156/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.1746

Epoch 157/200

4/4 - 0s - 7ms/step - accuracy: 0.9100 - loss: 0.1750

Epoch 158/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1722

Epoch 159/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.1725

Epoch 160/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.1703

Epoch 161/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1726

Epoch 162/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1686

Epoch 163/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1689

Epoch 164/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1682

Epoch 165/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1676

Epoch 166/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1655

Epoch 167/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1659

Epoch 168/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1642

Epoch 169/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.1650

Epoch 170/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1615

Epoch 171/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1618

Epoch 172/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1598

Epoch 173/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1589

Epoch 174/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1587

Epoch 175/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1587

Epoch 176/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1569

Epoch 177/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1570

Epoch 178/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1549

Epoch 179/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1538

Epoch 180/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1545

Epoch 181/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1529

Epoch 182/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1508

Epoch 183/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1495

Epoch 184/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1491

Epoch 185/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1474

Epoch 186/200

4/4 - 0s - 9ms/step - accuracy: 0.9300 - loss: 0.1472

Epoch 187/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1481

Epoch 188/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1448

Epoch 189/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1445

Epoch 190/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1459

Epoch 191/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1446

Epoch 192/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1402

Epoch 193/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1405

Epoch 194/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1411

Epoch 195/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1397

Epoch 196/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1384

Epoch 197/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1360

Epoch 198/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1358

Epoch 199/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1346

Epoch 200/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1330

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

score = 0.13195249438285828
accuracy = 0.949999988079071

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 31ms/step


1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step

array([[6.2307455e-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 0x7faf00990190>