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 = [ 0.79665708 -0.51838563], 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

model = Sequential()
model.add(Input((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)

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 - 6ms/step - accuracy: 0.5950 - loss: 0.6729

Epoch 2/200

4/4 - 0s - 6ms/step - accuracy: 0.7700 - loss: 0.6294

Epoch 3/200

4/4 - 0s - 6ms/step - accuracy: 0.8000 - loss: 0.5995

Epoch 4/200

4/4 - 0s - 6ms/step - accuracy: 0.8000 - loss: 0.5739

Epoch 5/200

4/4 - 0s - 6ms/step - accuracy: 0.8050 - loss: 0.5504

Epoch 6/200

4/4 - 0s - 6ms/step - accuracy: 0.8100 - loss: 0.5289

Epoch 7/200

4/4 - 0s - 6ms/step - accuracy: 0.8100 - loss: 0.5095

Epoch 8/200

4/4 - 0s - 5ms/step - accuracy: 0.8100 - loss: 0.4904

Epoch 9/200

4/4 - 0s - 6ms/step - accuracy: 0.8100 - loss: 0.4739

Epoch 10/200

4/4 - 0s - 6ms/step - accuracy: 0.8200 - loss: 0.4578

Epoch 11/200

4/4 - 0s - 5ms/step - accuracy: 0.8250 - loss: 0.4422

Epoch 12/200

4/4 - 0s - 6ms/step - accuracy: 0.8400 - loss: 0.4281

Epoch 13/200

4/4 - 0s - 25ms/step - accuracy: 0.8450 - loss: 0.4150

Epoch 14/200

4/4 - 0s - 6ms/step - accuracy: 0.8500 - loss: 0.4029

Epoch 15/200

4/4 - 0s - 5ms/step - accuracy: 0.8500 - loss: 0.3912

Epoch 16/200

4/4 - 0s - 5ms/step - accuracy: 0.8550 - loss: 0.3805

Epoch 17/200

4/4 - 0s - 5ms/step - accuracy: 0.8550 - loss: 0.3702

Epoch 18/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.3610

Epoch 19/200

4/4 - 0s - 5ms/step - accuracy: 0.8550 - loss: 0.3518

Epoch 20/200

4/4 - 0s - 9ms/step - accuracy: 0.8650 - loss: 0.3435

Epoch 21/200

4/4 - 0s - 5ms/step - accuracy: 0.8650 - loss: 0.3348

Epoch 22/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.3275

Epoch 23/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.3210

Epoch 24/200

4/4 - 0s - 8ms/step - accuracy: 0.8700 - loss: 0.3145

Epoch 25/200

4/4 - 0s - 24ms/step - accuracy: 0.8700 - loss: 0.3079

Epoch 26/200

4/4 - 0s - 7ms/step - accuracy: 0.8700 - loss: 0.3044

Epoch 27/200

4/4 - 0s - 5ms/step - accuracy: 0.8650 - loss: 0.2984

Epoch 28/200

4/4 - 0s - 5ms/step - accuracy: 0.8700 - loss: 0.2950

Epoch 29/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2911

Epoch 30/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2877

Epoch 31/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2844

Epoch 32/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2804

Epoch 33/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2782

Epoch 34/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2750

Epoch 35/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2729

Epoch 36/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2705

Epoch 37/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2678

Epoch 38/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2664

Epoch 39/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2637

Epoch 40/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2625

Epoch 41/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2599

Epoch 42/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2592

Epoch 43/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2567

Epoch 44/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2555

Epoch 45/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2547

Epoch 46/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2514

Epoch 47/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2523

Epoch 48/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2481

Epoch 49/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2470

Epoch 50/200

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

Epoch 51/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2443

Epoch 52/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2447

Epoch 53/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2408

Epoch 54/200

4/4 - 0s - 34ms/step - accuracy: 0.8900 - loss: 0.2396

Epoch 55/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2381

Epoch 56/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2367

Epoch 57/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2337

Epoch 58/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2330

Epoch 59/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2311

Epoch 60/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2286

Epoch 61/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2278

Epoch 62/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2249

Epoch 63/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2229

Epoch 64/200

4/4 - 0s - 11ms/step - accuracy: 0.8800 - loss: 0.2211

Epoch 65/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2188

Epoch 66/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2169

Epoch 67/200

4/4 - 0s - 7ms/step - accuracy: 0.8850 - loss: 0.2179

Epoch 68/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2146

Epoch 69/200

4/4 - 0s - 7ms/step - accuracy: 0.8850 - loss: 0.2106

Epoch 70/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2093

Epoch 71/200

4/4 - 0s - 22ms/step - accuracy: 0.9100 - loss: 0.2080

Epoch 72/200

4/4 - 0s - 5ms/step - accuracy: 0.9100 - loss: 0.2045

Epoch 73/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.2049

Epoch 74/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.2027

Epoch 75/200

4/4 - 0s - 7ms/step - accuracy: 0.9200 - loss: 0.1988

Epoch 76/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1969

Epoch 77/200

4/4 - 0s - 5ms/step - accuracy: 0.9250 - loss: 0.1953

Epoch 78/200

4/4 - 0s - 5ms/step - accuracy: 0.9250 - loss: 0.1935

Epoch 79/200

4/4 - 0s - 5ms/step - accuracy: 0.9300 - loss: 0.1920

Epoch 80/200

4/4 - 0s - 5ms/step - accuracy: 0.9300 - loss: 0.1902

Epoch 81/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1881

Epoch 82/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1876

Epoch 83/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1845

Epoch 84/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1830

Epoch 85/200

4/4 - 0s - 5ms/step - accuracy: 0.9400 - loss: 0.1809

Epoch 86/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1788

Epoch 87/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1770

Epoch 88/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1759

Epoch 89/200

4/4 - 0s - 5ms/step - accuracy: 0.9400 - loss: 0.1748

Epoch 90/200

4/4 - 0s - 5ms/step - accuracy: 0.9400 - loss: 0.1712

Epoch 91/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1696

Epoch 92/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1693

Epoch 93/200

4/4 - 0s - 5ms/step - accuracy: 0.9400 - loss: 0.1664

Epoch 94/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1656

Epoch 95/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1663

Epoch 96/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1614

Epoch 97/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1599

Epoch 98/200

4/4 - 0s - 5ms/step - accuracy: 0.9400 - loss: 0.1582

Epoch 99/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1561

Epoch 100/200

4/4 - 0s - 49ms/step - accuracy: 0.9500 - loss: 0.1551

Epoch 101/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1542

Epoch 102/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1515

Epoch 103/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1518

Epoch 104/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1490

Epoch 105/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1459

Epoch 106/200

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

Epoch 107/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1433

Epoch 108/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1427

Epoch 109/200

4/4 - 0s - 11ms/step - accuracy: 0.9600 - loss: 0.1398

Epoch 110/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1392

Epoch 111/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1401

Epoch 112/200

4/4 - 0s - 7ms/step - accuracy: 0.9550 - loss: 0.1355

Epoch 113/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1339

Epoch 114/200

4/4 - 0s - 7ms/step - accuracy: 0.9600 - loss: 0.1319

Epoch 115/200

4/4 - 0s - 7ms/step - accuracy: 0.9550 - loss: 0.1321

Epoch 116/200

4/4 - 0s - 8ms/step - accuracy: 0.9600 - loss: 0.1321

Epoch 117/200

4/4 - 0s - 20ms/step - accuracy: 0.9600 - loss: 0.1273

Epoch 118/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1259

Epoch 119/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1272

Epoch 120/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1245

Epoch 121/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1230

Epoch 122/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1211

Epoch 123/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1193

Epoch 124/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1192

Epoch 125/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1161

Epoch 126/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1155

Epoch 127/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1138

Epoch 128/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1134

Epoch 129/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1108

Epoch 130/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1106

Epoch 131/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1078

Epoch 132/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1069

Epoch 133/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1053

Epoch 134/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1035

Epoch 135/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1025

Epoch 136/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.1013

Epoch 137/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.0997

Epoch 138/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.0976

Epoch 139/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.0961

Epoch 140/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.0954

Epoch 141/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.0935

Epoch 142/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.0920

Epoch 143/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.0915

Epoch 144/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.0894

Epoch 145/200

4/4 - 0s - 53ms/step - accuracy: 0.9600 - loss: 0.0876

Epoch 146/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.0877

Epoch 147/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.0856

Epoch 148/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.0847

Epoch 149/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.0833

Epoch 150/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.0824

Epoch 151/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.0811

Epoch 152/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.0801

Epoch 153/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.0793

Epoch 154/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.0781

Epoch 155/200

4/4 - 0s - 12ms/step - accuracy: 0.9650 - loss: 0.0768

Epoch 156/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.0753

Epoch 157/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.0739

Epoch 158/200

4/4 - 0s - 7ms/step - accuracy: 0.9650 - loss: 0.0740

Epoch 159/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0714

Epoch 160/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0704

Epoch 161/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.0697

Epoch 162/200

4/4 - 0s - 22ms/step - accuracy: 0.9700 - loss: 0.0679

Epoch 163/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.0683

Epoch 164/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.0672

Epoch 165/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.0667

Epoch 166/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.0661

Epoch 167/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.0644

Epoch 168/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0637

Epoch 169/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.0629

Epoch 170/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.0643

Epoch 171/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.0621

Epoch 172/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.0604

Epoch 173/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.0604

Epoch 174/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.0614

Epoch 175/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.0586

Epoch 176/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0583

Epoch 177/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.0570

Epoch 178/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0572

Epoch 179/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0567

Epoch 180/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0553

Epoch 181/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0559

Epoch 182/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0542

Epoch 183/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0538

Epoch 184/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0521

Epoch 185/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0525

Epoch 186/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0527

Epoch 187/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0517

Epoch 188/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0513

Epoch 189/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0505

Epoch 190/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0495

Epoch 191/200

4/4 - 0s - 53ms/step - accuracy: 0.9750 - loss: 0.0492

Epoch 192/200

4/4 - 0s - 6ms/step - accuracy: 0.9800 - loss: 0.0504

Epoch 193/200

4/4 - 0s - 5ms/step - accuracy: 0.9800 - loss: 0.0478

Epoch 194/200

4/4 - 0s - 5ms/step - accuracy: 0.9800 - loss: 0.0468

Epoch 195/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0472

Epoch 196/200

4/4 - 0s - 5ms/step - accuracy: 0.9800 - loss: 0.0465

Epoch 197/200

4/4 - 0s - 5ms/step - accuracy: 0.9800 - loss: 0.0469

Epoch 198/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0457

Epoch 199/200

4/4 - 0s - 5ms/step - accuracy: 0.9800 - loss: 0.0453

Epoch 200/200

4/4 - 0s - 5ms/step - accuracy: 0.9800 - loss: 0.0457

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

score = 0.04306682199239731
accuracy = 0.9800000190734863

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 3ms/step


1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step

array([[5.614998e-22]], 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 0x7f1b89c9ccd0>