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 = [0.443747   1.17143192], value = 0

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/2df2fc089d7600b90ec5a9531d5c26b5eea88ad42ba6d1cd257bb11cb5afdba1.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

2025-12-11 14:14:44.243956: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:31] Could not find cuda drivers on your machine, GPU will not be used.
2025-12-11 14:14:44.244264: I tensorflow/core/util/port.cc:153] oneDNN custom operations are on. You may see slightly different numerical results due to floating-point round-off errors from different computation orders. To turn them off, set the environment variable `TF_ENABLE_ONEDNN_OPTS=0`.
2025-12-11 14:14:44.288319: 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 AVX512F AVX512_VNNI FMA, in other operations, rebuild TensorFlow with the appropriate compiler flags.

2025-12-11 14:14:45.650279: I tensorflow/core/util/port.cc:153] oneDNN custom operations are on. You may see slightly different numerical results due to floating-point round-off errors from different computation orders. To turn them off, set the environment variable `TF_ENABLE_ONEDNN_OPTS=0`.
2025-12-11 14:14:45.650622: 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"))

2025-12-11 14:14:45.915526: 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 - 121ms/step - accuracy: 0.4750 - loss: 0.6900

Epoch 2/200

4/4 - 0s - 7ms/step - accuracy: 0.4950 - loss: 0.6533

Epoch 3/200

4/4 - 0s - 7ms/step - accuracy: 0.6500 - loss: 0.6285

Epoch 4/200

4/4 - 0s - 7ms/step - accuracy: 0.7700 - loss: 0.6077

Epoch 5/200

4/4 - 0s - 7ms/step - accuracy: 0.8150 - loss: 0.5885

Epoch 6/200

4/4 - 0s - 7ms/step - accuracy: 0.8200 - loss: 0.5704

Epoch 7/200

4/4 - 0s - 7ms/step - accuracy: 0.8200 - loss: 0.5535

Epoch 8/200

4/4 - 0s - 7ms/step - accuracy: 0.8200 - loss: 0.5372

Epoch 9/200

4/4 - 0s - 7ms/step - accuracy: 0.8400 - loss: 0.5217

Epoch 10/200

4/4 - 0s - 7ms/step - accuracy: 0.8350 - loss: 0.5063

Epoch 11/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.4909

Epoch 12/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.4760

Epoch 13/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.4614

Epoch 14/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.4475

Epoch 15/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.4329

Epoch 16/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.4195

Epoch 17/200

4/4 - 0s - 7ms/step - accuracy: 0.8450 - loss: 0.4068

Epoch 18/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.3946

Epoch 19/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.3836

Epoch 20/200

4/4 - 0s - 7ms/step - accuracy: 0.8450 - loss: 0.3729

Epoch 21/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.3606

Epoch 22/200

4/4 - 0s - 8ms/step - accuracy: 0.8450 - loss: 0.3505

Epoch 23/200

4/4 - 0s - 7ms/step - accuracy: 0.8450 - loss: 0.3403

Epoch 24/200

4/4 - 0s - 7ms/step - accuracy: 0.8450 - loss: 0.3317

Epoch 25/200

4/4 - 0s - 7ms/step - accuracy: 0.8450 - loss: 0.3234

Epoch 26/200

4/4 - 0s - 7ms/step - accuracy: 0.8450 - loss: 0.3167

Epoch 27/200

4/4 - 0s - 7ms/step - accuracy: 0.8500 - loss: 0.3109

Epoch 28/200

4/4 - 0s - 7ms/step - accuracy: 0.8550 - loss: 0.3056

Epoch 29/200

4/4 - 0s - 7ms/step - accuracy: 0.8600 - loss: 0.2999

Epoch 30/200

4/4 - 0s - 7ms/step - accuracy: 0.8600 - loss: 0.2959

Epoch 31/200

4/4 - 0s - 7ms/step - accuracy: 0.8650 - loss: 0.2914

Epoch 32/200

4/4 - 0s - 7ms/step - accuracy: 0.8600 - loss: 0.2876

Epoch 33/200

4/4 - 0s - 7ms/step - accuracy: 0.8650 - loss: 0.2850

Epoch 34/200

4/4 - 0s - 7ms/step - accuracy: 0.8650 - loss: 0.2811

Epoch 35/200

4/4 - 0s - 7ms/step - accuracy: 0.8700 - loss: 0.2795

Epoch 36/200

4/4 - 0s - 7ms/step - accuracy: 0.8650 - loss: 0.2761

Epoch 37/200

4/4 - 0s - 7ms/step - accuracy: 0.8650 - loss: 0.2745

Epoch 38/200

4/4 - 0s - 7ms/step - accuracy: 0.8650 - loss: 0.2717

Epoch 39/200

4/4 - 0s - 7ms/step - accuracy: 0.8650 - loss: 0.2699

Epoch 40/200

4/4 - 0s - 7ms/step - accuracy: 0.8750 - loss: 0.2679

Epoch 41/200

4/4 - 0s - 7ms/step - accuracy: 0.8650 - loss: 0.2654

Epoch 42/200

4/4 - 0s - 7ms/step - accuracy: 0.8750 - loss: 0.2639

Epoch 43/200

4/4 - 0s - 7ms/step - accuracy: 0.8750 - loss: 0.2637

Epoch 44/200

4/4 - 0s - 7ms/step - accuracy: 0.8700 - loss: 0.2599

Epoch 45/200

4/4 - 0s - 7ms/step - accuracy: 0.8800 - loss: 0.2605

Epoch 46/200

4/4 - 0s - 7ms/step - accuracy: 0.8750 - loss: 0.2593

Epoch 47/200

4/4 - 0s - 7ms/step - accuracy: 0.8750 - loss: 0.2562

Epoch 48/200

4/4 - 0s - 7ms/step - accuracy: 0.8850 - loss: 0.2543

Epoch 49/200

4/4 - 0s - 7ms/step - accuracy: 0.8800 - loss: 0.2526

Epoch 50/200

4/4 - 0s - 7ms/step - accuracy: 0.8850 - loss: 0.2516

Epoch 51/200

4/4 - 0s - 7ms/step - accuracy: 0.8850 - loss: 0.2501

Epoch 52/200

4/4 - 0s - 7ms/step - accuracy: 0.8850 - loss: 0.2478

Epoch 53/200

4/4 - 0s - 7ms/step - accuracy: 0.8850 - loss: 0.2466

Epoch 54/200

4/4 - 0s - 7ms/step - accuracy: 0.8850 - loss: 0.2458

Epoch 55/200

4/4 - 0s - 7ms/step - accuracy: 0.8900 - loss: 0.2433

Epoch 56/200

4/4 - 0s - 7ms/step - accuracy: 0.8850 - loss: 0.2435

Epoch 57/200

4/4 - 0s - 7ms/step - accuracy: 0.8900 - loss: 0.2408

Epoch 58/200

4/4 - 0s - 7ms/step - accuracy: 0.8950 - loss: 0.2392

Epoch 59/200

4/4 - 0s - 7ms/step - accuracy: 0.8900 - loss: 0.2375

Epoch 60/200

4/4 - 0s - 7ms/step - accuracy: 0.8900 - loss: 0.2366

Epoch 61/200

4/4 - 0s - 7ms/step - accuracy: 0.9000 - loss: 0.2377

Epoch 62/200

4/4 - 0s - 7ms/step - accuracy: 0.9000 - loss: 0.2342

Epoch 63/200

4/4 - 0s - 7ms/step - accuracy: 0.8850 - loss: 0.2341

Epoch 64/200

4/4 - 0s - 7ms/step - accuracy: 0.8950 - loss: 0.2333

Epoch 65/200

4/4 - 0s - 7ms/step - accuracy: 0.9000 - loss: 0.2303

Epoch 66/200

4/4 - 0s - 7ms/step - accuracy: 0.9050 - loss: 0.2285

Epoch 67/200

4/4 - 0s - 7ms/step - accuracy: 0.9000 - loss: 0.2268

Epoch 68/200

4/4 - 0s - 7ms/step - accuracy: 0.9000 - loss: 0.2287

Epoch 69/200

4/4 - 0s - 7ms/step - accuracy: 0.9000 - loss: 0.2249

Epoch 70/200

4/4 - 0s - 7ms/step - accuracy: 0.9000 - loss: 0.2264

Epoch 71/200

4/4 - 0s - 7ms/step - accuracy: 0.9050 - loss: 0.2229

Epoch 72/200

4/4 - 0s - 7ms/step - accuracy: 0.9000 - loss: 0.2230

Epoch 73/200

4/4 - 0s - 7ms/step - accuracy: 0.9000 - loss: 0.2194

Epoch 74/200

4/4 - 0s - 7ms/step - accuracy: 0.9000 - loss: 0.2187

Epoch 75/200

4/4 - 0s - 7ms/step - accuracy: 0.9000 - loss: 0.2206

Epoch 76/200

4/4 - 0s - 7ms/step - accuracy: 0.9000 - loss: 0.2163

Epoch 77/200

4/4 - 0s - 7ms/step - accuracy: 0.8950 - loss: 0.2178

Epoch 78/200

4/4 - 0s - 7ms/step - accuracy: 0.9050 - loss: 0.2153

Epoch 79/200

4/4 - 0s - 7ms/step - accuracy: 0.9050 - loss: 0.2152

Epoch 80/200

4/4 - 0s - 7ms/step - accuracy: 0.8950 - loss: 0.2125

Epoch 81/200

4/4 - 0s - 7ms/step - accuracy: 0.9000 - loss: 0.2116

Epoch 82/200

4/4 - 0s - 7ms/step - accuracy: 0.8950 - loss: 0.2107

Epoch 83/200

4/4 - 0s - 7ms/step - accuracy: 0.9100 - loss: 0.2087

Epoch 84/200

4/4 - 0s - 7ms/step - accuracy: 0.9000 - loss: 0.2085

Epoch 85/200

4/4 - 0s - 7ms/step - accuracy: 0.9150 - loss: 0.2065

Epoch 86/200

4/4 - 0s - 7ms/step - accuracy: 0.9100 - loss: 0.2045

Epoch 87/200

4/4 - 0s - 7ms/step - accuracy: 0.9050 - loss: 0.2037

Epoch 88/200

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

Epoch 89/200

4/4 - 0s - 7ms/step - accuracy: 0.9100 - loss: 0.2008

Epoch 90/200

4/4 - 0s - 7ms/step - accuracy: 0.9050 - loss: 0.2003

Epoch 91/200

4/4 - 0s - 7ms/step - accuracy: 0.9050 - loss: 0.2014

Epoch 92/200

4/4 - 0s - 7ms/step - accuracy: 0.9100 - loss: 0.1967

Epoch 93/200

4/4 - 0s - 7ms/step - accuracy: 0.9150 - loss: 0.1958

Epoch 94/200

4/4 - 0s - 7ms/step - accuracy: 0.9200 - loss: 0.1951

Epoch 95/200

4/4 - 0s - 7ms/step - accuracy: 0.9050 - loss: 0.1943

Epoch 96/200

4/4 - 0s - 7ms/step - accuracy: 0.9150 - loss: 0.1920

Epoch 97/200

4/4 - 0s - 7ms/step - accuracy: 0.9100 - loss: 0.1901

Epoch 98/200

4/4 - 0s - 7ms/step - accuracy: 0.9150 - loss: 0.1907

Epoch 99/200

4/4 - 0s - 7ms/step - accuracy: 0.9150 - loss: 0.1894

Epoch 100/200

4/4 - 0s - 7ms/step - accuracy: 0.9200 - loss: 0.1868

Epoch 101/200

4/4 - 0s - 7ms/step - accuracy: 0.9200 - loss: 0.1865

Epoch 102/200

4/4 - 0s - 7ms/step - accuracy: 0.9100 - loss: 0.1848

Epoch 103/200

4/4 - 0s - 7ms/step - accuracy: 0.9150 - loss: 0.1824

Epoch 104/200

4/4 - 0s - 7ms/step - accuracy: 0.9150 - loss: 0.1842

Epoch 105/200

4/4 - 0s - 7ms/step - accuracy: 0.9250 - loss: 0.1808

Epoch 106/200

4/4 - 0s - 7ms/step - accuracy: 0.9200 - loss: 0.1819

Epoch 107/200

4/4 - 0s - 7ms/step - accuracy: 0.9250 - loss: 0.1781

Epoch 108/200

4/4 - 0s - 7ms/step - accuracy: 0.9300 - loss: 0.1767

Epoch 109/200

4/4 - 0s - 7ms/step - accuracy: 0.9300 - loss: 0.1749

Epoch 110/200

4/4 - 0s - 7ms/step - accuracy: 0.9200 - loss: 0.1741

Epoch 111/200

4/4 - 0s - 7ms/step - accuracy: 0.9200 - loss: 0.1743

Epoch 112/200

4/4 - 0s - 7ms/step - accuracy: 0.9300 - loss: 0.1720

Epoch 113/200

4/4 - 0s - 7ms/step - accuracy: 0.9250 - loss: 0.1718

Epoch 114/200

4/4 - 0s - 7ms/step - accuracy: 0.9250 - loss: 0.1695

Epoch 115/200

4/4 - 0s - 7ms/step - accuracy: 0.9300 - loss: 0.1679

Epoch 116/200

4/4 - 0s - 7ms/step - accuracy: 0.9300 - loss: 0.1661

Epoch 117/200

4/4 - 0s - 7ms/step - accuracy: 0.9300 - loss: 0.1655

Epoch 118/200

4/4 - 0s - 7ms/step - accuracy: 0.9300 - loss: 0.1646

Epoch 119/200

4/4 - 0s - 7ms/step - accuracy: 0.9300 - loss: 0.1626

Epoch 120/200

4/4 - 0s - 7ms/step - accuracy: 0.9250 - loss: 0.1614

Epoch 121/200

4/4 - 0s - 7ms/step - accuracy: 0.9300 - loss: 0.1592

Epoch 122/200

4/4 - 0s - 7ms/step - accuracy: 0.9400 - loss: 0.1593

Epoch 123/200

4/4 - 0s - 7ms/step - accuracy: 0.9400 - loss: 0.1575

Epoch 124/200

4/4 - 0s - 7ms/step - accuracy: 0.9350 - loss: 0.1556

Epoch 125/200

4/4 - 0s - 7ms/step - accuracy: 0.9400 - loss: 0.1548

Epoch 126/200

4/4 - 0s - 7ms/step - accuracy: 0.9350 - loss: 0.1532

Epoch 127/200

4/4 - 0s - 7ms/step - accuracy: 0.9450 - loss: 0.1528

Epoch 128/200

4/4 - 0s - 7ms/step - accuracy: 0.9450 - loss: 0.1505

Epoch 129/200

4/4 - 0s - 7ms/step - accuracy: 0.9450 - loss: 0.1484

Epoch 130/200

4/4 - 0s - 7ms/step - accuracy: 0.9450 - loss: 0.1490

Epoch 131/200

4/4 - 0s - 7ms/step - accuracy: 0.9450 - loss: 0.1481

Epoch 132/200

4/4 - 0s - 7ms/step - accuracy: 0.9400 - loss: 0.1453

Epoch 133/200

4/4 - 0s - 7ms/step - accuracy: 0.9500 - loss: 0.1438

Epoch 134/200

4/4 - 0s - 7ms/step - accuracy: 0.9500 - loss: 0.1423

Epoch 135/200

4/4 - 0s - 7ms/step - accuracy: 0.9500 - loss: 0.1426

Epoch 136/200

4/4 - 0s - 7ms/step - accuracy: 0.9500 - loss: 0.1408

Epoch 137/200

4/4 - 0s - 7ms/step - accuracy: 0.9500 - loss: 0.1387

Epoch 138/200

4/4 - 0s - 7ms/step - accuracy: 0.9500 - loss: 0.1376

Epoch 139/200

4/4 - 0s - 7ms/step - accuracy: 0.9550 - loss: 0.1380

Epoch 140/200

4/4 - 0s - 7ms/step - accuracy: 0.9650 - loss: 0.1345

Epoch 141/200

4/4 - 0s - 7ms/step - accuracy: 0.9600 - loss: 0.1340

Epoch 142/200

4/4 - 0s - 7ms/step - accuracy: 0.9600 - loss: 0.1328

Epoch 143/200

4/4 - 0s - 7ms/step - accuracy: 0.9600 - loss: 0.1320

Epoch 144/200

4/4 - 0s - 7ms/step - accuracy: 0.9650 - loss: 0.1298

Epoch 145/200

4/4 - 0s - 7ms/step - accuracy: 0.9650 - loss: 0.1281

Epoch 146/200

4/4 - 0s - 7ms/step - accuracy: 0.9600 - loss: 0.1265

Epoch 147/200

4/4 - 0s - 7ms/step - accuracy: 0.9650 - loss: 0.1262

Epoch 148/200

4/4 - 0s - 7ms/step - accuracy: 0.9600 - loss: 0.1244

Epoch 149/200

4/4 - 0s - 7ms/step - accuracy: 0.9650 - loss: 0.1230

Epoch 150/200

4/4 - 0s - 7ms/step - accuracy: 0.9650 - loss: 0.1234

Epoch 151/200

4/4 - 0s - 7ms/step - accuracy: 0.9700 - loss: 0.1207

Epoch 152/200

4/4 - 0s - 7ms/step - accuracy: 0.9650 - loss: 0.1185

Epoch 153/200

4/4 - 0s - 7ms/step - accuracy: 0.9700 - loss: 0.1181

Epoch 154/200

4/4 - 0s - 7ms/step - accuracy: 0.9750 - loss: 0.1153

Epoch 155/200

4/4 - 0s - 7ms/step - accuracy: 0.9750 - loss: 0.1174

Epoch 156/200

4/4 - 0s - 7ms/step - accuracy: 0.9750 - loss: 0.1128

Epoch 157/200

4/4 - 0s - 7ms/step - accuracy: 0.9700 - loss: 0.1125

Epoch 158/200

4/4 - 0s - 7ms/step - accuracy: 0.9750 - loss: 0.1116

Epoch 159/200

4/4 - 0s - 7ms/step - accuracy: 0.9750 - loss: 0.1090

Epoch 160/200

4/4 - 0s - 7ms/step - accuracy: 0.9800 - loss: 0.1113

Epoch 161/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.1089

Epoch 162/200

4/4 - 0s - 7ms/step - accuracy: 0.9800 - loss: 0.1066

Epoch 163/200

4/4 - 0s - 7ms/step - accuracy: 0.9750 - loss: 0.1070

Epoch 164/200

4/4 - 0s - 7ms/step - accuracy: 0.9800 - loss: 0.1041

Epoch 165/200

4/4 - 0s - 7ms/step - accuracy: 0.9750 - loss: 0.1047

Epoch 166/200

4/4 - 0s - 7ms/step - accuracy: 0.9800 - loss: 0.1019

Epoch 167/200

4/4 - 0s - 7ms/step - accuracy: 0.9800 - loss: 0.1003

Epoch 168/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.1004

Epoch 169/200

4/4 - 0s - 7ms/step - accuracy: 0.9800 - loss: 0.0990

Epoch 170/200

4/4 - 0s - 7ms/step - accuracy: 0.9700 - loss: 0.0993

Epoch 171/200

4/4 - 0s - 7ms/step - accuracy: 0.9800 - loss: 0.0972

Epoch 172/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0954

Epoch 173/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0941

Epoch 174/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0931

Epoch 175/200

4/4 - 0s - 7ms/step - accuracy: 0.9800 - loss: 0.0926

Epoch 176/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0904

Epoch 177/200

4/4 - 0s - 7ms/step - accuracy: 0.9750 - loss: 0.0915

Epoch 178/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0885

Epoch 179/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0870

Epoch 180/200

4/4 - 0s - 7ms/step - accuracy: 0.9800 - loss: 0.0880

Epoch 181/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0850

Epoch 182/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0864

Epoch 183/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0829

Epoch 184/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0827

Epoch 185/200

4/4 - 0s - 7ms/step - accuracy: 0.9800 - loss: 0.0830

Epoch 186/200

4/4 - 0s - 8ms/step - accuracy: 0.9850 - loss: 0.0805

Epoch 187/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0799

Epoch 188/200

4/4 - 0s - 8ms/step - accuracy: 0.9850 - loss: 0.0784

Epoch 189/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0785

Epoch 190/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0764

Epoch 191/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0764

Epoch 192/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0759

Epoch 193/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0735

Epoch 194/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0741

Epoch 195/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0727

Epoch 196/200

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

Epoch 197/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0699

Epoch 198/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0712

Epoch 199/200

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

Epoch 200/200

4/4 - 0s - 7ms/step - accuracy: 0.9850 - loss: 0.0679

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

score = 0.06635206937789917
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 33ms/step


1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 44ms/step

array([[1.7791773e-11]], 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 0x7fd3bc8b3fd0>
../_images/fa960e9fe9d58782c05f60e8411e00cf134fb899d0ad4e9d13747418a99c38cd.png
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