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

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=0.2)

    # 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)

x, v = generate_data()

Let’s look at a point and it’s value

print(f"x = {x[0]}, value = {v[0]}")

x = [ 1.38213337 -0.38387933], 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.

First we setup and train our network

from keras.models import Sequential
from keras.layers import Dense, Dropout, Activation, Input
from keras.optimizers import RMSprop

model = Sequential()
model.add(Input(shape=(2,)))
model.add(Dense(50, activation="relu"))
model.add(Dense(20, activation="relu"))
model.add(Dense(1, activation="sigmoid"))

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)

We seem to need a lot of epochs here to get a good result

epochs = 200
results = model.fit(x, v, batch_size=50, epochs=epochs, verbose=2)

Epoch 1/200

4/4 - 0s - 5ms/step - accuracy: 0.4000 - loss: 0.7086

Epoch 2/200

4/4 - 0s - 5ms/step - accuracy: 0.5800 - loss: 0.6690

Epoch 3/200

4/4 - 0s - 5ms/step - accuracy: 0.7750 - loss: 0.6429

Epoch 4/200

4/4 - 0s - 5ms/step - accuracy: 0.7750 - loss: 0.6202

Epoch 5/200

4/4 - 0s - 5ms/step - accuracy: 0.7800 - loss: 0.6003

Epoch 6/200

4/4 - 0s - 6ms/step - accuracy: 0.7800 - loss: 0.5831

Epoch 7/200

4/4 - 0s - 6ms/step - accuracy: 0.7850 - loss: 0.5668

Epoch 8/200

4/4 - 0s - 5ms/step - accuracy: 0.7850 - loss: 0.5511

Epoch 9/200

4/4 - 0s - 5ms/step - accuracy: 0.7900 - loss: 0.5361

Epoch 10/200

4/4 - 0s - 5ms/step - accuracy: 0.7950 - loss: 0.5220

Epoch 11/200

4/4 - 0s - 5ms/step - accuracy: 0.7900 - loss: 0.5082

Epoch 12/200

4/4 - 0s - 5ms/step - accuracy: 0.7950 - loss: 0.4950

Epoch 13/200

4/4 - 0s - 5ms/step - accuracy: 0.8000 - loss: 0.4820

Epoch 14/200

4/4 - 0s - 5ms/step - accuracy: 0.8000 - loss: 0.4689

Epoch 15/200

4/4 - 0s - 5ms/step - accuracy: 0.8000 - loss: 0.4570

Epoch 16/200

4/4 - 0s - 5ms/step - accuracy: 0.8150 - loss: 0.4446

Epoch 17/200

4/4 - 0s - 5ms/step - accuracy: 0.8200 - loss: 0.4324

Epoch 18/200

4/4 - 0s - 5ms/step - accuracy: 0.8200 - loss: 0.4211

Epoch 19/200

4/4 - 0s - 5ms/step - accuracy: 0.8300 - loss: 0.4097

Epoch 20/200

4/4 - 0s - 5ms/step - accuracy: 0.8350 - loss: 0.3991

Epoch 21/200

4/4 - 0s - 5ms/step - accuracy: 0.8400 - loss: 0.3893

Epoch 22/200

4/4 - 0s - 5ms/step - accuracy: 0.8450 - loss: 0.3802

Epoch 23/200

4/4 - 0s - 5ms/step - accuracy: 0.8600 - loss: 0.3718

Epoch 24/200

4/4 - 0s - 5ms/step - accuracy: 0.8550 - loss: 0.3644

Epoch 25/200

4/4 - 0s - 5ms/step - accuracy: 0.8550 - loss: 0.3569

Epoch 26/200

4/4 - 0s - 5ms/step - accuracy: 0.8650 - loss: 0.3503

Epoch 27/200

4/4 - 0s - 5ms/step - accuracy: 0.8550 - loss: 0.3450

Epoch 28/200

4/4 - 0s - 5ms/step - accuracy: 0.8600 - loss: 0.3384

Epoch 29/200

4/4 - 0s - 5ms/step - accuracy: 0.8600 - loss: 0.3336

Epoch 30/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.3291

Epoch 31/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.3255

Epoch 32/200

4/4 - 0s - 5ms/step - accuracy: 0.8700 - loss: 0.3212

Epoch 33/200

4/4 - 0s - 5ms/step - accuracy: 0.8700 - loss: 0.3177

Epoch 34/200

4/4 - 0s - 5ms/step - accuracy: 0.8700 - loss: 0.3152

Epoch 35/200

4/4 - 0s - 5ms/step - accuracy: 0.8700 - loss: 0.3120

Epoch 36/200

4/4 - 0s - 5ms/step - accuracy: 0.8700 - loss: 0.3091

Epoch 37/200

4/4 - 0s - 5ms/step - accuracy: 0.8700 - loss: 0.3082

Epoch 38/200

4/4 - 0s - 5ms/step - accuracy: 0.8700 - loss: 0.3046

Epoch 39/200

4/4 - 0s - 5ms/step - accuracy: 0.8750 - loss: 0.3041

Epoch 40/200

4/4 - 0s - 5ms/step - accuracy: 0.8650 - loss: 0.3023

Epoch 41/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.3003

Epoch 42/200

4/4 - 0s - 5ms/step - accuracy: 0.8750 - loss: 0.2993

Epoch 43/200

4/4 - 0s - 5ms/step - accuracy: 0.8750 - loss: 0.2988

Epoch 44/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2964

Epoch 45/200

4/4 - 0s - 5ms/step - accuracy: 0.8700 - loss: 0.2951

Epoch 46/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2945

Epoch 47/200

4/4 - 0s - 5ms/step - accuracy: 0.8750 - loss: 0.2926

Epoch 48/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2915

Epoch 49/200

4/4 - 0s - 5ms/step - accuracy: 0.8750 - loss: 0.2905

Epoch 50/200

4/4 - 0s - 5ms/step - accuracy: 0.8750 - loss: 0.2907

Epoch 51/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2896

Epoch 52/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2873

Epoch 53/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2885

Epoch 54/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2860

Epoch 55/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2866

Epoch 56/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2847

Epoch 57/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2837

Epoch 58/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2834

Epoch 59/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2834

Epoch 60/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2818

Epoch 61/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2807

Epoch 62/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2814

Epoch 63/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2785

Epoch 64/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2774

Epoch 65/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2766

Epoch 66/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2756

Epoch 67/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2749

Epoch 68/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2745

Epoch 69/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2739

Epoch 70/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2727

Epoch 71/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2711

Epoch 72/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2714

Epoch 73/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2716

Epoch 74/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2693

Epoch 75/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2687

Epoch 76/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2686

Epoch 77/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2687

Epoch 78/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2671

Epoch 79/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2656

Epoch 80/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2649

Epoch 81/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2633

Epoch 82/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2636

Epoch 83/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2624

Epoch 84/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2618

Epoch 85/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2603

Epoch 86/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2594

Epoch 87/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2585

Epoch 88/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2580

Epoch 89/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2594

Epoch 90/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2569

Epoch 91/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2569

Epoch 92/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2539

Epoch 93/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2531

Epoch 94/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2523

Epoch 95/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2531

Epoch 96/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2510

Epoch 97/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2503

Epoch 98/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2485

Epoch 99/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2484

Epoch 100/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2467

Epoch 101/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2457

Epoch 102/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.2446

Epoch 103/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2438

Epoch 104/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2435

Epoch 105/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2417

Epoch 106/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.2421

Epoch 107/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2392

Epoch 108/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2377

Epoch 109/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2374

Epoch 110/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.2358

Epoch 111/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2345

Epoch 112/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.2329

Epoch 113/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2321

Epoch 114/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.2293

Epoch 115/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.2292

Epoch 116/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2277

Epoch 117/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.2263

Epoch 118/200

4/4 - 0s - 5ms/step - accuracy: 0.9100 - loss: 0.2247

Epoch 119/200

4/4 - 0s - 5ms/step - accuracy: 0.9150 - loss: 0.2237

Epoch 120/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.2229

Epoch 121/200

4/4 - 0s - 5ms/step - accuracy: 0.9100 - loss: 0.2215

Epoch 122/200

4/4 - 0s - 5ms/step - accuracy: 0.9100 - loss: 0.2215

Epoch 123/200

4/4 - 0s - 5ms/step - accuracy: 0.9100 - loss: 0.2199

Epoch 124/200

4/4 - 0s - 5ms/step - accuracy: 0.9150 - loss: 0.2171

Epoch 125/200

4/4 - 0s - 5ms/step - accuracy: 0.9150 - loss: 0.2169

Epoch 126/200

4/4 - 0s - 5ms/step - accuracy: 0.9100 - loss: 0.2147

Epoch 127/200

4/4 - 0s - 5ms/step - accuracy: 0.9150 - loss: 0.2153

Epoch 128/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.2136

Epoch 129/200

4/4 - 0s - 5ms/step - accuracy: 0.9150 - loss: 0.2114

Epoch 130/200

4/4 - 0s - 5ms/step - accuracy: 0.9150 - loss: 0.2110

Epoch 131/200

4/4 - 0s - 5ms/step - accuracy: 0.9100 - loss: 0.2109

Epoch 132/200

4/4 - 0s - 5ms/step - accuracy: 0.9150 - loss: 0.2079

Epoch 133/200

4/4 - 0s - 5ms/step - accuracy: 0.9150 - loss: 0.2075

Epoch 134/200

4/4 - 0s - 5ms/step - accuracy: 0.9150 - loss: 0.2053

Epoch 135/200

4/4 - 0s - 5ms/step - accuracy: 0.9150 - loss: 0.2055

Epoch 136/200

4/4 - 0s - 5ms/step - accuracy: 0.9150 - loss: 0.2030

Epoch 137/200

4/4 - 0s - 5ms/step - accuracy: 0.9150 - loss: 0.2029

Epoch 138/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.2006

Epoch 139/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1994

Epoch 140/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1983

Epoch 141/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1993

Epoch 142/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1961

Epoch 143/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1952

Epoch 144/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1939

Epoch 145/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1928

Epoch 146/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1919

Epoch 147/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1920

Epoch 148/200

4/4 - 0s - 5ms/step - accuracy: 0.9250 - loss: 0.1888

Epoch 149/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1882

Epoch 150/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1867

Epoch 151/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1856

Epoch 152/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1871

Epoch 153/200

4/4 - 0s - 5ms/step - accuracy: 0.9250 - loss: 0.1824

Epoch 154/200

4/4 - 0s - 5ms/step - accuracy: 0.9250 - loss: 0.1812

Epoch 155/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1813

Epoch 156/200

4/4 - 0s - 5ms/step - accuracy: 0.9250 - loss: 0.1789

Epoch 157/200

4/4 - 0s - 5ms/step - accuracy: 0.9250 - loss: 0.1789

Epoch 158/200

4/4 - 0s - 5ms/step - accuracy: 0.9250 - loss: 0.1762

Epoch 159/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1762

Epoch 160/200

4/4 - 0s - 5ms/step - accuracy: 0.9300 - loss: 0.1748

Epoch 161/200

4/4 - 0s - 5ms/step - accuracy: 0.9250 - loss: 0.1746

Epoch 162/200

4/4 - 0s - 5ms/step - accuracy: 0.9250 - loss: 0.1717

Epoch 163/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1700

Epoch 164/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1696

Epoch 165/200

4/4 - 0s - 5ms/step - accuracy: 0.9400 - loss: 0.1679

Epoch 166/200

4/4 - 0s - 5ms/step - accuracy: 0.9300 - loss: 0.1671

Epoch 167/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1656

Epoch 168/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1654

Epoch 169/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1638

Epoch 170/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1624

Epoch 171/200

4/4 - 0s - 5ms/step - accuracy: 0.9400 - loss: 0.1607

Epoch 172/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1599

Epoch 173/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1580

Epoch 174/200

4/4 - 0s - 5ms/step - accuracy: 0.9400 - loss: 0.1589

Epoch 175/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1566

Epoch 176/200

4/4 - 0s - 5ms/step - accuracy: 0.9400 - loss: 0.1545

Epoch 177/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1556

Epoch 178/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1528

Epoch 179/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1528

Epoch 180/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1506

Epoch 181/200

4/4 - 0s - 5ms/step - accuracy: 0.9400 - loss: 0.1517

Epoch 182/200

4/4 - 0s - 5ms/step - accuracy: 0.9400 - loss: 0.1501

Epoch 183/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1488

Epoch 184/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1479

Epoch 185/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1452

Epoch 186/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1456

Epoch 187/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1450

Epoch 188/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1432

Epoch 189/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1412

Epoch 190/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1414

Epoch 191/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1407

Epoch 192/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1404

Epoch 193/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1382

Epoch 194/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1375

Epoch 195/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1351

Epoch 196/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1371

Epoch 197/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1340

Epoch 198/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1343

Epoch 199/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1331

Epoch 200/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1308

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

score = 0.12911249697208405
accuracy = 0.9599999785423279

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 3ms/step


1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step

array([[1.3078371e-09]], 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 = 128
N = 128

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)

/tmp/ipykernel_3175/3968438749.py:2: DeprecationWarning: Setting the shape on a NumPy array has been deprecated in NumPy 2.5.
As an alternative, you can create a new view using np.reshape (with copy=False if needed).
  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 0x7f8af9592490>