Clustering

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 = [ 0.63410601 -0.37232508], 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)
../_images/1ab38431dc816df3b630793c134f082dd069ea179708120d0891020537f28f87.png

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

2025-12-04 16:04:18.637156: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:31] Could not find cuda drivers on your machine, GPU will not be used.
2025-12-04 16:04:18.682594: 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.

2025-12-04 16:04:20.312388: 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"))

2025-12-04 16:04:20.620012: 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 - 114ms/step - accuracy: 0.4750 - loss: 0.6943

Epoch 2/200

4/4 - 0s - 6ms/step - accuracy: 0.7450 - loss: 0.6599

Epoch 3/200

4/4 - 0s - 6ms/step - accuracy: 0.7950 - loss: 0.6368

Epoch 4/200

4/4 - 0s - 6ms/step - accuracy: 0.7950 - loss: 0.6156

Epoch 5/200

4/4 - 0s - 6ms/step - accuracy: 0.8050 - loss: 0.5978

Epoch 6/200

4/4 - 0s - 6ms/step - accuracy: 0.8050 - loss: 0.5812

Epoch 7/200

4/4 - 0s - 6ms/step - accuracy: 0.8050 - loss: 0.5649

Epoch 8/200

4/4 - 0s - 6ms/step - accuracy: 0.8150 - loss: 0.5487

Epoch 9/200

4/4 - 0s - 6ms/step - accuracy: 0.8200 - loss: 0.5323

Epoch 10/200

4/4 - 0s - 6ms/step - accuracy: 0.8250 - loss: 0.5161

Epoch 11/200

4/4 - 0s - 6ms/step - accuracy: 0.8250 - loss: 0.4999

Epoch 12/200

4/4 - 0s - 6ms/step - accuracy: 0.8300 - loss: 0.4828

Epoch 13/200

4/4 - 0s - 6ms/step - accuracy: 0.8300 - loss: 0.4666

Epoch 14/200

4/4 - 0s - 6ms/step - accuracy: 0.8350 - loss: 0.4520

Epoch 15/200

4/4 - 0s - 6ms/step - accuracy: 0.8350 - loss: 0.4378

Epoch 16/200

4/4 - 0s - 6ms/step - accuracy: 0.8400 - loss: 0.4238

Epoch 17/200

4/4 - 0s - 6ms/step - accuracy: 0.8400 - loss: 0.4109

Epoch 18/200

4/4 - 0s - 6ms/step - accuracy: 0.8450 - loss: 0.3983

Epoch 19/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.3869

Epoch 20/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.3759

Epoch 21/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.3651

Epoch 22/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3552

Epoch 23/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.3470

Epoch 24/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.3400

Epoch 25/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3317

Epoch 26/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.3253

Epoch 27/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.3194

Epoch 28/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3144

Epoch 29/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.3089

Epoch 30/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.3041

Epoch 31/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.2998

Epoch 32/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.2964

Epoch 33/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2935

Epoch 34/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2889

Epoch 35/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2867

Epoch 36/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.2836

Epoch 37/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2807

Epoch 38/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2800

Epoch 39/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2760

Epoch 40/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2741

Epoch 41/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2722

Epoch 42/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.2706

Epoch 43/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2678

Epoch 44/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2655

Epoch 45/200

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

Epoch 46/200

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

Epoch 47/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2612

Epoch 48/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2583

Epoch 49/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2584

Epoch 50/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2567

Epoch 51/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2537

Epoch 52/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2527

Epoch 53/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2506

Epoch 54/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2488

Epoch 55/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2477

Epoch 56/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2462

Epoch 57/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2446

Epoch 58/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2424

Epoch 59/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2430

Epoch 60/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2394

Epoch 61/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2381

Epoch 62/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2359

Epoch 63/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2346

Epoch 64/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2333

Epoch 65/200

4/4 - 0s - 7ms/step - accuracy: 0.8950 - loss: 0.2343

Epoch 66/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2296

Epoch 67/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2283

Epoch 68/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2264

Epoch 69/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2249

Epoch 70/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.2249

Epoch 71/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2217

Epoch 72/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2221

Epoch 73/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2193

Epoch 74/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2179

Epoch 75/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.2167

Epoch 76/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.2163

Epoch 77/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.2137

Epoch 78/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.2114

Epoch 79/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.2113

Epoch 80/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.2084

Epoch 81/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.2070

Epoch 82/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.2051

Epoch 83/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.2039

Epoch 84/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.2028

Epoch 85/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.2023

Epoch 86/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.2003

Epoch 87/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1977

Epoch 88/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1966

Epoch 89/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1932

Epoch 90/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1922

Epoch 91/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1910

Epoch 92/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1886

Epoch 93/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1870

Epoch 94/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1859

Epoch 95/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1833

Epoch 96/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1809

Epoch 97/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1807

Epoch 98/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1775

Epoch 99/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1769

Epoch 100/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1748

Epoch 101/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1744

Epoch 102/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1707

Epoch 103/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1709

Epoch 104/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1681

Epoch 105/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1681

Epoch 106/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1663

Epoch 107/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1649

Epoch 108/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1612

Epoch 109/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1605

Epoch 110/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1582

Epoch 111/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1571

Epoch 112/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1559

Epoch 113/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1578

Epoch 114/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1519

Epoch 115/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1522

Epoch 116/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1502

Epoch 117/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1482

Epoch 118/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1464

Epoch 119/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1491

Epoch 120/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1451

Epoch 121/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1436

Epoch 122/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1415

Epoch 123/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1403

Epoch 124/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1384

Epoch 125/200

4/4 - 0s - 7ms/step - accuracy: 0.9350 - loss: 0.1374

Epoch 126/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1369

Epoch 127/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1351

Epoch 128/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1325

Epoch 129/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1313

Epoch 130/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1308

Epoch 131/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1299

Epoch 132/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1276

Epoch 133/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1255

Epoch 134/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1243

Epoch 135/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1240

Epoch 136/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1209

Epoch 137/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1207

Epoch 138/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1202

Epoch 139/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1171

Epoch 140/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1167

Epoch 141/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1145

Epoch 142/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1145

Epoch 143/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1133

Epoch 144/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1113

Epoch 145/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1099

Epoch 146/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1088

Epoch 147/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1077

Epoch 148/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1061

Epoch 149/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1049

Epoch 150/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1057

Epoch 151/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1028

Epoch 152/200

4/4 - 0s - 7ms/step - accuracy: 0.9600 - loss: 0.1028

Epoch 153/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1013

Epoch 154/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1000

Epoch 155/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.0982

Epoch 156/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.0981

Epoch 157/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.0965

Epoch 158/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.0953

Epoch 159/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.0947

Epoch 160/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.0925

Epoch 161/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.0940

Epoch 162/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.0935

Epoch 163/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.0897

Epoch 164/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.0912

Epoch 165/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.0892

Epoch 166/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.0886

Epoch 167/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.0863

Epoch 168/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.0860

Epoch 169/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.0850

Epoch 170/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0841

Epoch 171/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.0840

Epoch 172/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0818

Epoch 173/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.0811

Epoch 174/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.0815

Epoch 175/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0790

Epoch 176/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.0800

Epoch 177/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0772

Epoch 178/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0775

Epoch 179/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0768

Epoch 180/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0749

Epoch 181/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.0753

Epoch 182/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0737

Epoch 183/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0739

Epoch 184/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0725

Epoch 185/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0722

Epoch 186/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0708

Epoch 187/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0703

Epoch 188/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.0688

Epoch 189/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0694

Epoch 190/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0679

Epoch 191/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0666

Epoch 192/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0663

Epoch 193/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0650

Epoch 194/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0650

Epoch 195/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0632

Epoch 196/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0632

Epoch 197/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0652

Epoch 198/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0610

Epoch 199/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0610

Epoch 200/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0601

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

score = 0.05888679623603821
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 30ms/step


1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 40ms/step

array([[4.3344662e-15]], 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 0x7f553408add0>
../_images/e4ec0af99432a73bc380abf67b42593c25300348f3f4ab91f8e6aef9f2796ce6.png
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