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 = [ 0.61485765 -0.51314619], 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

2025-06-27 16:25:41.060893: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2025-06-27 16:25:41.064093: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2025-06-27 16:25:41.072774: 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 00:00:1751041541.087438    4984 cuda_dnn.cc:8579] Unable to register cuDNN factory: Attempting to register factory for plugin cuDNN when one has already been registered
E0000 00:00:1751041541.091603    4984 cuda_blas.cc:1407] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered
W0000 00:00:1751041541.103351    4984 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
W0000 00:00:1751041541.103364    4984 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
W0000 00:00:1751041541.103366    4984 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
W0000 00:00:1751041541.103368    4984 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
2025-06-27 16:25:41.107530: 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"))

2025-06-27 16:25:42.973549: 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 - 110ms/step - accuracy: 0.6150 - loss: 0.6913

Epoch 2/200

4/4 - 0s - 6ms/step - accuracy: 0.7700 - loss: 0.6450

Epoch 3/200

4/4 - 0s - 6ms/step - accuracy: 0.7950 - loss: 0.6172

Epoch 4/200

4/4 - 0s - 10ms/step - accuracy: 0.8300 - loss: 0.5927

Epoch 5/200

4/4 - 0s - 7ms/step - accuracy: 0.8300 - loss: 0.5717

Epoch 6/200

4/4 - 0s - 6ms/step - accuracy: 0.8500 - loss: 0.5525

Epoch 7/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.5343

Epoch 8/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.5172

Epoch 9/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.5011

Epoch 10/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.4868

Epoch 11/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.4728

Epoch 12/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.4608

Epoch 13/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.4490

Epoch 14/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.4377

Epoch 15/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.4281

Epoch 16/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.4181

Epoch 17/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.4096

Epoch 18/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.4010

Epoch 19/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.3933

Epoch 20/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.3854

Epoch 21/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.3788

Epoch 22/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.3722

Epoch 23/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.3659

Epoch 24/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3596

Epoch 25/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3540

Epoch 26/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3488

Epoch 27/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3431

Epoch 28/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3385

Epoch 29/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3333

Epoch 30/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.3293

Epoch 31/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.3246

Epoch 32/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.3203

Epoch 33/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.3164

Epoch 34/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.3128

Epoch 35/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.3090

Epoch 36/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.3059

Epoch 37/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.3016

Epoch 38/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.2986

Epoch 39/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2945

Epoch 40/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2921

Epoch 41/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.2891

Epoch 42/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.2865

Epoch 43/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2850

Epoch 44/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2815

Epoch 45/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.2796

Epoch 46/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2774

Epoch 47/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.2746

Epoch 48/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2725

Epoch 49/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2732

Epoch 50/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2692

Epoch 51/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2665

Epoch 52/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.2649

Epoch 53/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2643

Epoch 54/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2610

Epoch 55/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2607

Epoch 56/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2577

Epoch 57/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2574

Epoch 58/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2543

Epoch 59/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2547

Epoch 60/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2514

Epoch 61/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2526

Epoch 62/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2486

Epoch 63/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2480

Epoch 64/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2477

Epoch 65/200

4/4 - 0s - 7ms/step - accuracy: 0.8600 - loss: 0.2446

Epoch 66/200

4/4 - 0s - 7ms/step - accuracy: 0.8600 - loss: 0.2437

Epoch 67/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2444

Epoch 68/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2409

Epoch 69/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2398

Epoch 70/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2387

Epoch 71/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.2385

Epoch 72/200

4/4 - 0s - 7ms/step - accuracy: 0.8600 - loss: 0.2363

Epoch 73/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.2357

Epoch 74/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.2344

Epoch 75/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2342

Epoch 76/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.2313

Epoch 77/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2311

Epoch 78/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2303

Epoch 79/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2287

Epoch 80/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2270

Epoch 81/200

4/4 - 0s - 7ms/step - accuracy: 0.8800 - loss: 0.2257

Epoch 82/200

4/4 - 0s - 7ms/step - accuracy: 0.8850 - loss: 0.2244

Epoch 83/200

4/4 - 0s - 7ms/step - accuracy: 0.8700 - loss: 0.2253

Epoch 84/200

4/4 - 0s - 7ms/step - accuracy: 0.8850 - loss: 0.2220

Epoch 85/200

4/4 - 0s - 7ms/step - accuracy: 0.8850 - loss: 0.2207

Epoch 86/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2197

Epoch 87/200

4/4 - 0s - 7ms/step - accuracy: 0.8900 - loss: 0.2181

Epoch 88/200

4/4 - 0s - 7ms/step - accuracy: 0.8900 - loss: 0.2217

Epoch 89/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2162

Epoch 90/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2150

Epoch 91/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2146

Epoch 92/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2133

Epoch 93/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2137

Epoch 94/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2128

Epoch 95/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2110

Epoch 96/200

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

Epoch 97/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2077

Epoch 98/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2128

Epoch 99/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2076

Epoch 100/200

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

Epoch 101/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2074

Epoch 102/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2041

Epoch 103/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2027

Epoch 104/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2028

Epoch 105/200

4/4 - 0s - 7ms/step - accuracy: 0.9050 - loss: 0.2016

Epoch 106/200

4/4 - 0s - 7ms/step - accuracy: 0.9100 - loss: 0.1999

Epoch 107/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1998

Epoch 108/200

4/4 - 0s - 7ms/step - accuracy: 0.9100 - loss: 0.1975

Epoch 109/200

4/4 - 0s - 7ms/step - accuracy: 0.9100 - loss: 0.1965

Epoch 110/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1989

Epoch 111/200

4/4 - 0s - 7ms/step - accuracy: 0.9100 - loss: 0.1953

Epoch 112/200

4/4 - 0s - 7ms/step - accuracy: 0.9200 - loss: 0.1968

Epoch 113/200

4/4 - 0s - 7ms/step - accuracy: 0.9200 - loss: 0.1931

Epoch 114/200

4/4 - 0s - 7ms/step - accuracy: 0.9150 - loss: 0.1928

Epoch 115/200

4/4 - 0s - 7ms/step - accuracy: 0.9200 - loss: 0.1935

Epoch 116/200

4/4 - 0s - 7ms/step - accuracy: 0.9200 - loss: 0.1904

Epoch 117/200

4/4 - 0s - 7ms/step - accuracy: 0.9200 - loss: 0.1886

Epoch 118/200

4/4 - 0s - 7ms/step - accuracy: 0.9200 - loss: 0.1884

Epoch 119/200

4/4 - 0s - 7ms/step - accuracy: 0.9250 - loss: 0.1866

Epoch 120/200

4/4 - 0s - 7ms/step - accuracy: 0.9250 - loss: 0.1861

Epoch 121/200

4/4 - 0s - 7ms/step - accuracy: 0.9250 - loss: 0.1839

Epoch 122/200

4/4 - 0s - 7ms/step - accuracy: 0.9300 - loss: 0.1843

Epoch 123/200

4/4 - 0s - 7ms/step - accuracy: 0.9300 - loss: 0.1813

Epoch 124/200

4/4 - 0s - 7ms/step - accuracy: 0.9400 - loss: 0.1826

Epoch 125/200

4/4 - 0s - 7ms/step - accuracy: 0.9450 - loss: 0.1805

Epoch 126/200

4/4 - 0s - 7ms/step - accuracy: 0.9250 - loss: 0.1775

Epoch 127/200

4/4 - 0s - 7ms/step - accuracy: 0.9450 - loss: 0.1767

Epoch 128/200

4/4 - 0s - 7ms/step - accuracy: 0.9350 - loss: 0.1772

Epoch 129/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1778

Epoch 130/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1734

Epoch 131/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1727

Epoch 132/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1725

Epoch 133/200

4/4 - 0s - 7ms/step - accuracy: 0.9450 - loss: 0.1709

Epoch 134/200

4/4 - 0s - 7ms/step - accuracy: 0.9450 - loss: 0.1697

Epoch 135/200

4/4 - 0s - 7ms/step - accuracy: 0.9450 - loss: 0.1679

Epoch 136/200

4/4 - 0s - 7ms/step - accuracy: 0.9400 - loss: 0.1687

Epoch 137/200

4/4 - 0s - 7ms/step - accuracy: 0.9500 - loss: 0.1650

Epoch 138/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1655

Epoch 139/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1657

Epoch 140/200

4/4 - 0s - 7ms/step - accuracy: 0.9500 - loss: 0.1626

Epoch 141/200

4/4 - 0s - 7ms/step - accuracy: 0.9500 - loss: 0.1612

Epoch 142/200

4/4 - 0s - 7ms/step - accuracy: 0.9550 - loss: 0.1592

Epoch 143/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1589

Epoch 144/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1575

Epoch 145/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1575

Epoch 146/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1562

Epoch 147/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1535

Epoch 148/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1514

Epoch 149/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1546

Epoch 150/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1495

Epoch 151/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1495

Epoch 152/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1492

Epoch 153/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1462

Epoch 154/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1450

Epoch 155/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1435

Epoch 156/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1433

Epoch 157/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1411

Epoch 158/200

4/4 - 0s - 7ms/step - accuracy: 0.9600 - loss: 0.1408

Epoch 159/200

4/4 - 0s - 7ms/step - accuracy: 0.9550 - loss: 0.1396

Epoch 160/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1376

Epoch 161/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1357

Epoch 162/200

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

Epoch 163/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1326

Epoch 164/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1327

Epoch 165/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1311

Epoch 166/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1312

Epoch 167/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1279

Epoch 168/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1266

Epoch 169/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1287

Epoch 170/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1239

Epoch 171/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1244

Epoch 172/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1217

Epoch 173/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1214

Epoch 174/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1208

Epoch 175/200

4/4 - 0s - 7ms/step - accuracy: 0.9600 - loss: 0.1193

Epoch 176/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1184

Epoch 177/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1168

Epoch 178/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1168

Epoch 179/200

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

Epoch 180/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1142

Epoch 181/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1145

Epoch 182/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1110

Epoch 183/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1119

Epoch 184/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1100

Epoch 185/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1078

Epoch 186/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1085

Epoch 187/200

4/4 - 0s - 7ms/step - accuracy: 0.9600 - loss: 0.1056

Epoch 188/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1050

Epoch 189/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1048

Epoch 190/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1026

Epoch 191/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.1028

Epoch 192/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.1030

Epoch 193/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1006

Epoch 194/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.1008

Epoch 195/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.0984

Epoch 196/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.0975

Epoch 197/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.0971

Epoch 198/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.0952

Epoch 199/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.0960

Epoch 200/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.0944

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

score = 0.09192071110010147
accuracy = 0.9700000286102295

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([[1.2150591e-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 0x7f53d8e85a50>