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 = [2.20225073 0.11862178], 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

2025-04-30 17:08:07.908152: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2025-04-30 17:08:07.911440: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2025-04-30 17:08:07.920234: 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 00:00:1746032887.935110    4788 cuda_dnn.cc:8579] Unable to register cuDNN factory: Attempting to register factory for plugin cuDNN when one has already been registered
E0000 00:00:1746032887.939288    4788 cuda_blas.cc:1407] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered
W0000 00:00:1746032887.951234    4788 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
W0000 00:00:1746032887.951256    4788 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
W0000 00:00:1746032887.951258    4788 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
W0000 00:00:1746032887.951260    4788 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
2025-04-30 17:08:07.955769: 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"))

2025-04-30 17:08:09.920449: 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 - 122ms/step - accuracy: 0.4700 - loss: 0.6921

Epoch 2/200

4/4 - 0s - 7ms/step - accuracy: 0.7800 - loss: 0.6535

Epoch 3/200

4/4 - 0s - 7ms/step - accuracy: 0.8050 - loss: 0.6254

Epoch 4/200

4/4 - 0s - 7ms/step - accuracy: 0.8350 - loss: 0.6004

Epoch 5/200

4/4 - 0s - 7ms/step - accuracy: 0.8450 - loss: 0.5771

Epoch 6/200

4/4 - 0s - 7ms/step - accuracy: 0.8450 - loss: 0.5547

Epoch 7/200

4/4 - 0s - 8ms/step - accuracy: 0.8450 - loss: 0.5336

Epoch 8/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.5132

Epoch 9/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.4942

Epoch 10/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.4759

Epoch 11/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.4591

Epoch 12/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.4436

Epoch 13/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.4288

Epoch 14/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.4148

Epoch 15/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.4025

Epoch 16/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.3910

Epoch 17/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.3805

Epoch 18/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.3706

Epoch 19/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.3627

Epoch 20/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.3537

Epoch 21/200

4/4 - 0s - 7ms/step - accuracy: 0.8550 - loss: 0.3464

Epoch 22/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.3396

Epoch 23/200

4/4 - 0s - 7ms/step - accuracy: 0.8550 - loss: 0.3342

Epoch 24/200

4/4 - 0s - 7ms/step - accuracy: 0.8650 - loss: 0.3281

Epoch 25/200

4/4 - 0s - 7ms/step - accuracy: 0.8650 - loss: 0.3222

Epoch 26/200

4/4 - 0s - 7ms/step - accuracy: 0.8650 - loss: 0.3169

Epoch 27/200

4/4 - 0s - 7ms/step - accuracy: 0.8650 - loss: 0.3124

Epoch 28/200

4/4 - 0s - 7ms/step - accuracy: 0.8650 - loss: 0.3083

Epoch 29/200

4/4 - 0s - 7ms/step - accuracy: 0.8650 - loss: 0.3045

Epoch 30/200

4/4 - 0s - 7ms/step - accuracy: 0.8650 - loss: 0.3013

Epoch 31/200

4/4 - 0s - 7ms/step - accuracy: 0.8650 - loss: 0.2987

Epoch 32/200

4/4 - 0s - 7ms/step - accuracy: 0.8650 - loss: 0.2966

Epoch 33/200

4/4 - 0s - 7ms/step - accuracy: 0.8650 - loss: 0.2932

Epoch 34/200

4/4 - 0s - 7ms/step - accuracy: 0.8650 - loss: 0.2900

Epoch 35/200

4/4 - 0s - 7ms/step - accuracy: 0.8700 - loss: 0.2900

Epoch 36/200

4/4 - 0s - 7ms/step - accuracy: 0.8650 - loss: 0.2867

Epoch 37/200

4/4 - 0s - 7ms/step - accuracy: 0.8700 - loss: 0.2841

Epoch 38/200

4/4 - 0s - 7ms/step - accuracy: 0.8700 - loss: 0.2820

Epoch 39/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2795

Epoch 40/200

4/4 - 0s - 7ms/step - accuracy: 0.8750 - loss: 0.2807

Epoch 41/200

4/4 - 0s - 10ms/step - accuracy: 0.8750 - loss: 0.2763

Epoch 42/200

4/4 - 0s - 7ms/step - accuracy: 0.8700 - loss: 0.2745

Epoch 43/200

4/4 - 0s - 7ms/step - accuracy: 0.8700 - loss: 0.2755

Epoch 44/200

4/4 - 0s - 7ms/step - accuracy: 0.8750 - loss: 0.2711

Epoch 45/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2697

Epoch 46/200

4/4 - 0s - 7ms/step - accuracy: 0.8750 - loss: 0.2687

Epoch 47/200

4/4 - 0s - 7ms/step - accuracy: 0.8750 - loss: 0.2667

Epoch 48/200

4/4 - 0s - 7ms/step - accuracy: 0.8700 - loss: 0.2643

Epoch 49/200

4/4 - 0s - 7ms/step - accuracy: 0.8700 - loss: 0.2632

Epoch 50/200

4/4 - 0s - 7ms/step - accuracy: 0.8750 - loss: 0.2616

Epoch 51/200

4/4 - 0s - 7ms/step - accuracy: 0.8700 - loss: 0.2620

Epoch 52/200

4/4 - 0s - 7ms/step - accuracy: 0.8750 - loss: 0.2577

Epoch 53/200

4/4 - 0s - 7ms/step - accuracy: 0.8750 - loss: 0.2564

Epoch 54/200

4/4 - 0s - 7ms/step - accuracy: 0.8750 - loss: 0.2550

Epoch 55/200

4/4 - 0s - 7ms/step - accuracy: 0.8750 - loss: 0.2540

Epoch 56/200

4/4 - 0s - 7ms/step - accuracy: 0.8750 - loss: 0.2519

Epoch 57/200

4/4 - 0s - 7ms/step - accuracy: 0.8800 - loss: 0.2506

Epoch 58/200

4/4 - 0s - 7ms/step - accuracy: 0.8750 - loss: 0.2483

Epoch 59/200

4/4 - 0s - 7ms/step - accuracy: 0.8800 - loss: 0.2471

Epoch 60/200

4/4 - 0s - 7ms/step - accuracy: 0.8800 - loss: 0.2452

Epoch 61/200

4/4 - 0s - 7ms/step - accuracy: 0.8800 - loss: 0.2431

Epoch 62/200

4/4 - 0s - 7ms/step - accuracy: 0.8750 - loss: 0.2414

Epoch 63/200

4/4 - 0s - 7ms/step - accuracy: 0.8800 - loss: 0.2400

Epoch 64/200

4/4 - 0s - 7ms/step - accuracy: 0.8750 - loss: 0.2384

Epoch 65/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2354

Epoch 66/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2341

Epoch 67/200

4/4 - 0s - 7ms/step - accuracy: 0.8900 - loss: 0.2311

Epoch 68/200

4/4 - 0s - 7ms/step - accuracy: 0.9050 - loss: 0.2296

Epoch 69/200

4/4 - 0s - 7ms/step - accuracy: 0.9000 - loss: 0.2266

Epoch 70/200

4/4 - 0s - 7ms/step - accuracy: 0.9000 - loss: 0.2258

Epoch 71/200

4/4 - 0s - 7ms/step - accuracy: 0.9050 - loss: 0.2239

Epoch 72/200

4/4 - 0s - 7ms/step - accuracy: 0.9000 - loss: 0.2212

Epoch 73/200

4/4 - 0s - 7ms/step - accuracy: 0.9050 - loss: 0.2186

Epoch 74/200

4/4 - 0s - 8ms/step - accuracy: 0.9000 - loss: 0.2172

Epoch 75/200

4/4 - 0s - 9ms/step - accuracy: 0.9050 - loss: 0.2156

Epoch 76/200

4/4 - 0s - 7ms/step - accuracy: 0.9050 - loss: 0.2117

Epoch 77/200

4/4 - 0s - 7ms/step - accuracy: 0.9050 - loss: 0.2104

Epoch 78/200

4/4 - 0s - 7ms/step - accuracy: 0.9050 - loss: 0.2084

Epoch 79/200

4/4 - 0s - 7ms/step - accuracy: 0.9050 - loss: 0.2071

Epoch 80/200

4/4 - 0s - 7ms/step - accuracy: 0.8950 - loss: 0.2053

Epoch 81/200

4/4 - 0s - 7ms/step - accuracy: 0.9100 - loss: 0.2026

Epoch 82/200

4/4 - 0s - 7ms/step - accuracy: 0.9100 - loss: 0.1995

Epoch 83/200

4/4 - 0s - 7ms/step - accuracy: 0.9100 - loss: 0.1988

Epoch 84/200

4/4 - 0s - 7ms/step - accuracy: 0.9050 - loss: 0.1976

Epoch 85/200

4/4 - 0s - 7ms/step - accuracy: 0.9100 - loss: 0.1930

Epoch 86/200

4/4 - 0s - 7ms/step - accuracy: 0.9100 - loss: 0.1912

Epoch 87/200

4/4 - 0s - 7ms/step - accuracy: 0.9100 - loss: 0.1889

Epoch 88/200

4/4 - 0s - 7ms/step - accuracy: 0.9100 - loss: 0.1871

Epoch 89/200

4/4 - 0s - 7ms/step - accuracy: 0.9150 - loss: 0.1845

Epoch 90/200

4/4 - 0s - 7ms/step - accuracy: 0.9050 - loss: 0.1830

Epoch 91/200

4/4 - 0s - 7ms/step - accuracy: 0.9200 - loss: 0.1804

Epoch 92/200

4/4 - 0s - 7ms/step - accuracy: 0.9250 - loss: 0.1785

Epoch 93/200

4/4 - 0s - 7ms/step - accuracy: 0.9250 - loss: 0.1765

Epoch 94/200

4/4 - 0s - 7ms/step - accuracy: 0.9250 - loss: 0.1749

Epoch 95/200

4/4 - 0s - 7ms/step - accuracy: 0.9250 - loss: 0.1717

Epoch 96/200

4/4 - 0s - 7ms/step - accuracy: 0.9250 - loss: 0.1720

Epoch 97/200

4/4 - 0s - 7ms/step - accuracy: 0.9250 - loss: 0.1673

Epoch 98/200

4/4 - 0s - 7ms/step - accuracy: 0.9250 - loss: 0.1670

Epoch 99/200

4/4 - 0s - 7ms/step - accuracy: 0.9300 - loss: 0.1635

Epoch 100/200

4/4 - 0s - 7ms/step - accuracy: 0.9350 - loss: 0.1616

Epoch 101/200

4/4 - 0s - 7ms/step - accuracy: 0.9300 - loss: 0.1597

Epoch 102/200

4/4 - 0s - 7ms/step - accuracy: 0.9300 - loss: 0.1575

Epoch 103/200

4/4 - 0s - 7ms/step - accuracy: 0.9350 - loss: 0.1562

Epoch 104/200

4/4 - 0s - 7ms/step - accuracy: 0.9350 - loss: 0.1546

Epoch 105/200

4/4 - 0s - 7ms/step - accuracy: 0.9450 - loss: 0.1517

Epoch 106/200

4/4 - 0s - 7ms/step - accuracy: 0.9400 - loss: 0.1499

Epoch 107/200

4/4 - 0s - 7ms/step - accuracy: 0.9400 - loss: 0.1474

Epoch 108/200

4/4 - 0s - 9ms/step - accuracy: 0.9350 - loss: 0.1481

Epoch 109/200

4/4 - 0s - 7ms/step - accuracy: 0.9400 - loss: 0.1434

Epoch 110/200

4/4 - 0s - 7ms/step - accuracy: 0.9400 - loss: 0.1440

Epoch 111/200

4/4 - 0s - 7ms/step - accuracy: 0.9450 - loss: 0.1403

Epoch 112/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1388

Epoch 113/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1381

Epoch 114/200

4/4 - 0s - 7ms/step - accuracy: 0.9400 - loss: 0.1344

Epoch 115/200

4/4 - 0s - 7ms/step - accuracy: 0.9400 - loss: 0.1331

Epoch 116/200

4/4 - 0s - 7ms/step - accuracy: 0.9450 - loss: 0.1320

Epoch 117/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1300

Epoch 118/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1278

Epoch 119/200

4/4 - 0s - 7ms/step - accuracy: 0.9450 - loss: 0.1257

Epoch 120/200

4/4 - 0s - 7ms/step - accuracy: 0.9400 - loss: 0.1247

Epoch 121/200

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

Epoch 122/200

4/4 - 0s - 7ms/step - accuracy: 0.9400 - loss: 0.1207

Epoch 123/200

4/4 - 0s - 7ms/step - accuracy: 0.9450 - loss: 0.1190

Epoch 124/200

4/4 - 0s - 7ms/step - accuracy: 0.9450 - loss: 0.1186

Epoch 125/200

4/4 - 0s - 7ms/step - accuracy: 0.9400 - loss: 0.1156

Epoch 126/200

4/4 - 0s - 7ms/step - accuracy: 0.9450 - loss: 0.1149

Epoch 127/200

4/4 - 0s - 7ms/step - accuracy: 0.9500 - loss: 0.1122

Epoch 128/200

4/4 - 0s - 7ms/step - accuracy: 0.9500 - loss: 0.1111

Epoch 129/200

4/4 - 0s - 7ms/step - accuracy: 0.9500 - loss: 0.1096

Epoch 130/200

4/4 - 0s - 7ms/step - accuracy: 0.9450 - loss: 0.1082

Epoch 131/200

4/4 - 0s - 7ms/step - accuracy: 0.9500 - loss: 0.1065

Epoch 132/200

4/4 - 0s - 7ms/step - accuracy: 0.9500 - loss: 0.1045

Epoch 133/200

4/4 - 0s - 7ms/step - accuracy: 0.9550 - loss: 0.1035

Epoch 134/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1026

Epoch 135/200

4/4 - 0s - 7ms/step - accuracy: 0.9500 - loss: 0.1002

Epoch 136/200

4/4 - 0s - 7ms/step - accuracy: 0.9600 - loss: 0.0995

Epoch 137/200

4/4 - 0s - 7ms/step - accuracy: 0.9550 - loss: 0.0994

Epoch 138/200

4/4 - 0s - 7ms/step - accuracy: 0.9550 - loss: 0.0968

Epoch 139/200

4/4 - 0s - 7ms/step - accuracy: 0.9650 - loss: 0.0951

Epoch 140/200

4/4 - 0s - 7ms/step - accuracy: 0.9600 - loss: 0.0946

Epoch 141/200

4/4 - 0s - 8ms/step - accuracy: 0.9650 - loss: 0.0929

Epoch 142/200

4/4 - 0s - 10ms/step - accuracy: 0.9700 - loss: 0.0912

Epoch 143/200

4/4 - 0s - 7ms/step - accuracy: 0.9600 - loss: 0.0920

Epoch 144/200

4/4 - 0s - 7ms/step - accuracy: 0.9650 - loss: 0.0893

Epoch 145/200

4/4 - 0s - 7ms/step - accuracy: 0.9650 - loss: 0.0885

Epoch 146/200

4/4 - 0s - 7ms/step - accuracy: 0.9700 - loss: 0.0876

Epoch 147/200

4/4 - 0s - 7ms/step - accuracy: 0.9700 - loss: 0.0863

Epoch 148/200

4/4 - 0s - 7ms/step - accuracy: 0.9800 - loss: 0.0850

Epoch 149/200

4/4 - 0s - 7ms/step - accuracy: 0.9750 - loss: 0.0846

Epoch 150/200

4/4 - 0s - 7ms/step - accuracy: 0.9800 - loss: 0.0829

Epoch 151/200

4/4 - 0s - 7ms/step - accuracy: 0.9700 - loss: 0.0813

Epoch 152/200

4/4 - 0s - 7ms/step - accuracy: 0.9750 - loss: 0.0807

Epoch 153/200

4/4 - 0s - 7ms/step - accuracy: 0.9700 - loss: 0.0822

Epoch 154/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0789

Epoch 155/200

4/4 - 0s - 6ms/step - accuracy: 0.9850 - loss: 0.0793

Epoch 156/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0772

Epoch 157/200

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

Epoch 158/200

4/4 - 0s - 6ms/step - accuracy: 0.9850 - loss: 0.0762

Epoch 159/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0742

Epoch 160/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0740

Epoch 161/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0739

Epoch 162/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0719

Epoch 163/200

4/4 - 0s - 8ms/step - accuracy: 0.9850 - loss: 0.0710

Epoch 164/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0710

Epoch 165/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0700

Epoch 166/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0681

Epoch 167/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0673

Epoch 168/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0684

Epoch 169/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0665

Epoch 170/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0655

Epoch 171/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0651

Epoch 172/200

4/4 - 0s - 6ms/step - accuracy: 0.9850 - loss: 0.0656

Epoch 173/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0639

Epoch 174/200

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

Epoch 175/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0623

Epoch 176/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0621

Epoch 177/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0615

Epoch 178/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0615

Epoch 179/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0592

Epoch 180/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0597

Epoch 181/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0584

Epoch 182/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0577

Epoch 183/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0574

Epoch 184/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0565

Epoch 185/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0579

Epoch 186/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0564

Epoch 187/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0548

Epoch 188/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0549

Epoch 189/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0545

Epoch 190/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0535

Epoch 191/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0528

Epoch 192/200

4/4 - 0s - 6ms/step - accuracy: 0.9850 - loss: 0.0521

Epoch 193/200

4/4 - 0s - 6ms/step - accuracy: 0.9850 - loss: 0.0522

Epoch 194/200

4/4 - 0s - 6ms/step - accuracy: 0.9850 - loss: 0.0520

Epoch 195/200

4/4 - 0s - 6ms/step - accuracy: 0.9850 - loss: 0.0523

Epoch 196/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0503

Epoch 197/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0493

Epoch 198/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0502

Epoch 199/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0494

Epoch 200/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0499

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

score = 0.047401219606399536
accuracy = 0.9850000143051147

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 32ms/step


1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 42ms/step

array([[1.335973e-18]], 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 0x7f2c88349450>