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 = [-0.37970462  0.98819232], 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/d44feab08cad25831e29efcd1fe9a5ec357ecd6fcd9584d3600aa95e5113a294.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

2025-09-02 17:39:39.800149: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:31] Could not find cuda drivers on your machine, GPU will not be used.
2025-09-02 17:39:39.845542: 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.

2025-09-02 17:39:41.600522: 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"))

2025-09-02 17:39:41.897871: 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: 0.6250 - loss: 0.6766

Epoch 2/200

4/4 - 0s - 6ms/step - accuracy: 0.7400 - loss: 0.6399

Epoch 3/200

4/4 - 0s - 6ms/step - accuracy: 0.7700 - loss: 0.6145

Epoch 4/200

4/4 - 0s - 6ms/step - accuracy: 0.7800 - loss: 0.5931

Epoch 5/200

4/4 - 0s - 6ms/step - accuracy: 0.7850 - loss: 0.5730

Epoch 6/200

4/4 - 0s - 6ms/step - accuracy: 0.7900 - loss: 0.5545

Epoch 7/200

4/4 - 0s - 6ms/step - accuracy: 0.8050 - loss: 0.5365

Epoch 8/200

4/4 - 0s - 6ms/step - accuracy: 0.8050 - loss: 0.5186

Epoch 9/200

4/4 - 0s - 6ms/step - accuracy: 0.8150 - loss: 0.5021

Epoch 10/200

4/4 - 0s - 6ms/step - accuracy: 0.8200 - loss: 0.4857

Epoch 11/200

4/4 - 0s - 6ms/step - accuracy: 0.8300 - loss: 0.4696

Epoch 12/200

4/4 - 0s - 6ms/step - accuracy: 0.8300 - loss: 0.4544

Epoch 13/200

4/4 - 0s - 6ms/step - accuracy: 0.8400 - loss: 0.4406

Epoch 14/200

4/4 - 0s - 6ms/step - accuracy: 0.8450 - loss: 0.4285

Epoch 15/200

4/4 - 0s - 6ms/step - accuracy: 0.8450 - loss: 0.4166

Epoch 16/200

4/4 - 0s - 6ms/step - accuracy: 0.8450 - loss: 0.4054

Epoch 17/200

4/4 - 0s - 6ms/step - accuracy: 0.8450 - loss: 0.3960

Epoch 18/200

4/4 - 0s - 6ms/step - accuracy: 0.8500 - loss: 0.3858

Epoch 19/200

4/4 - 0s - 6ms/step - accuracy: 0.8500 - loss: 0.3774

Epoch 20/200

4/4 - 0s - 6ms/step - accuracy: 0.8500 - loss: 0.3692

Epoch 21/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3611

Epoch 22/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.3538

Epoch 23/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3468

Epoch 24/200

4/4 - 0s - 7ms/step - accuracy: 0.8600 - loss: 0.3405

Epoch 25/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3350

Epoch 26/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3296

Epoch 27/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3254

Epoch 28/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3220

Epoch 29/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3172

Epoch 30/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3140

Epoch 31/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.3102

Epoch 32/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3075

Epoch 33/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.3049

Epoch 34/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.3014

Epoch 35/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2984

Epoch 36/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2958

Epoch 37/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2933

Epoch 38/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2912

Epoch 39/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2897

Epoch 40/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2869

Epoch 41/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2856

Epoch 42/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2854

Epoch 43/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2811

Epoch 44/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2805

Epoch 45/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2782

Epoch 46/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2778

Epoch 47/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2754

Epoch 48/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2733

Epoch 49/200

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

Epoch 50/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2706

Epoch 51/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2698

Epoch 52/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2675

Epoch 53/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2668

Epoch 54/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2651

Epoch 55/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2640

Epoch 56/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2625

Epoch 57/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2603

Epoch 58/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2589

Epoch 59/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2585

Epoch 60/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2560

Epoch 61/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2570

Epoch 62/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2557

Epoch 63/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2553

Epoch 64/200

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

Epoch 65/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2504

Epoch 66/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2495

Epoch 67/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2483

Epoch 68/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2486

Epoch 69/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2461

Epoch 70/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2450

Epoch 71/200

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

Epoch 72/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2434

Epoch 73/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2423

Epoch 74/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2406

Epoch 75/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2393

Epoch 76/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2395

Epoch 77/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2373

Epoch 78/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2371

Epoch 79/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2383

Epoch 80/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2355

Epoch 81/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2326

Epoch 82/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2321

Epoch 83/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2307

Epoch 84/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2303

Epoch 85/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2300

Epoch 86/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2267

Epoch 87/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2255

Epoch 88/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2251

Epoch 89/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2240

Epoch 90/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2215

Epoch 91/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2219

Epoch 92/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2209

Epoch 93/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2193

Epoch 94/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2173

Epoch 95/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2154

Epoch 96/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2134

Epoch 97/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2125

Epoch 98/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2113

Epoch 99/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2095

Epoch 100/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2075

Epoch 101/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2081

Epoch 102/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2061

Epoch 103/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2039

Epoch 104/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2015

Epoch 105/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2008

Epoch 106/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.1988

Epoch 107/200

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

Epoch 108/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1966

Epoch 109/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.1953

Epoch 110/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.1943

Epoch 111/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.1924

Epoch 112/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1926

Epoch 113/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1892

Epoch 114/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1879

Epoch 115/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.1858

Epoch 116/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.1853

Epoch 117/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1836

Epoch 118/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1833

Epoch 119/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.1809

Epoch 120/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1799

Epoch 121/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1768

Epoch 122/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1790

Epoch 123/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1737

Epoch 124/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1731

Epoch 125/200

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

Epoch 126/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1696

Epoch 127/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1695

Epoch 128/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1675

Epoch 129/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1662

Epoch 130/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1640

Epoch 131/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1627

Epoch 132/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1609

Epoch 133/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1603

Epoch 134/200

4/4 - 0s - 7ms/step - accuracy: 0.9400 - loss: 0.1584

Epoch 135/200

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

Epoch 136/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1577

Epoch 137/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1561

Epoch 138/200

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

Epoch 139/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1524

Epoch 140/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1502

Epoch 141/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1490

Epoch 142/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1497

Epoch 143/200

4/4 - 0s - 7ms/step - accuracy: 0.9500 - loss: 0.1466

Epoch 144/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1460

Epoch 145/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1437

Epoch 146/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1422

Epoch 147/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1439

Epoch 148/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1398

Epoch 149/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1389

Epoch 150/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1380

Epoch 151/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1363

Epoch 152/200

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

Epoch 153/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1334

Epoch 154/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1345

Epoch 155/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1326

Epoch 156/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1303

Epoch 157/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1288

Epoch 158/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1277

Epoch 159/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1266

Epoch 160/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1251

Epoch 161/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1254

Epoch 162/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1225

Epoch 163/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1214

Epoch 164/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1198

Epoch 165/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1178

Epoch 166/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1190

Epoch 167/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1153

Epoch 168/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1139

Epoch 169/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1129

Epoch 170/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1124

Epoch 171/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1110

Epoch 172/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1085

Epoch 173/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1078

Epoch 174/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1067

Epoch 175/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1066

Epoch 176/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1049

Epoch 177/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1059

Epoch 178/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1014

Epoch 179/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1001

Epoch 180/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.0992

Epoch 181/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.0979

Epoch 182/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.0981

Epoch 183/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.0980

Epoch 184/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.0950

Epoch 185/200

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

Epoch 186/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.0933

Epoch 187/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.0929

Epoch 188/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.0906

Epoch 189/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0893

Epoch 190/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0877

Epoch 191/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0864

Epoch 192/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.0865

Epoch 193/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0845

Epoch 194/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.0853

Epoch 195/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0835

Epoch 196/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0839

Epoch 197/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0803

Epoch 198/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0800

Epoch 199/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0780

Epoch 200/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0787

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

score = 0.07585819810628891
accuracy = 0.9750000238418579

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([[3.7041666e-14]], 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 0x7fdcd06f2a10>
../_images/6c7fd70db46911b12acfe7d34574a658d7c04af169e43f6cce73331813bf8d21.png
Contents