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 = [1.81301572 0.18800229], 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: 0.7000 - loss: 0.6287

Epoch 2/200

4/4 - 0s - 5ms/step - accuracy: 0.7400 - loss: 0.5998

Epoch 3/200

4/4 - 0s - 5ms/step - accuracy: 0.7600 - loss: 0.5805

Epoch 4/200

4/4 - 0s - 5ms/step - accuracy: 0.7700 - loss: 0.5632

Epoch 5/200

4/4 - 0s - 5ms/step - accuracy: 0.7750 - loss: 0.5474

Epoch 6/200

4/4 - 0s - 5ms/step - accuracy: 0.7850 - loss: 0.5324

Epoch 7/200

4/4 - 0s - 5ms/step - accuracy: 0.8000 - loss: 0.5179

Epoch 8/200

4/4 - 0s - 5ms/step - accuracy: 0.8050 - loss: 0.5027

Epoch 9/200

4/4 - 0s - 5ms/step - accuracy: 0.8100 - loss: 0.4868

Epoch 10/200

4/4 - 0s - 5ms/step - accuracy: 0.8150 - loss: 0.4723

Epoch 11/200

4/4 - 0s - 5ms/step - accuracy: 0.8250 - loss: 0.4580

Epoch 12/200

4/4 - 0s - 5ms/step - accuracy: 0.8300 - loss: 0.4449

Epoch 13/200

4/4 - 0s - 26ms/step - accuracy: 0.8350 - loss: 0.4308

Epoch 14/200

4/4 - 0s - 4ms/step - accuracy: 0.8400 - loss: 0.4189

Epoch 15/200

4/4 - 0s - 5ms/step - accuracy: 0.8400 - loss: 0.4058

Epoch 16/200

4/4 - 0s - 5ms/step - accuracy: 0.8400 - loss: 0.3960

Epoch 17/200

4/4 - 0s - 4ms/step - accuracy: 0.8450 - loss: 0.3844

Epoch 18/200

4/4 - 0s - 4ms/step - accuracy: 0.8450 - loss: 0.3743

Epoch 19/200

4/4 - 0s - 5ms/step - accuracy: 0.8500 - loss: 0.3646

Epoch 20/200

4/4 - 0s - 9ms/step - accuracy: 0.8550 - loss: 0.3547

Epoch 21/200

4/4 - 0s - 4ms/step - accuracy: 0.8600 - loss: 0.3460

Epoch 22/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.3377

Epoch 23/200

4/4 - 0s - 5ms/step - accuracy: 0.8700 - loss: 0.3295

Epoch 24/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.3231

Epoch 25/200

4/4 - 0s - 21ms/step - accuracy: 0.8700 - loss: 0.3166

Epoch 26/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.3098

Epoch 27/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.3042

Epoch 28/200

4/4 - 0s - 4ms/step - accuracy: 0.8750 - loss: 0.2996

Epoch 29/200

4/4 - 0s - 4ms/step - accuracy: 0.8800 - loss: 0.2960

Epoch 30/200

4/4 - 0s - 4ms/step - accuracy: 0.8800 - loss: 0.2901

Epoch 31/200

4/4 - 0s - 4ms/step - accuracy: 0.8850 - loss: 0.2872

Epoch 32/200

4/4 - 0s - 4ms/step - accuracy: 0.8850 - loss: 0.2832

Epoch 33/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2803

Epoch 34/200

4/4 - 0s - 4ms/step - accuracy: 0.8900 - loss: 0.2785

Epoch 35/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2748

Epoch 36/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2720

Epoch 37/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2696

Epoch 38/200

4/4 - 0s - 4ms/step - accuracy: 0.8950 - loss: 0.2682

Epoch 39/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2661

Epoch 40/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2637

Epoch 41/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2616

Epoch 42/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2607

Epoch 43/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2584

Epoch 44/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2562

Epoch 45/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2562

Epoch 46/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2541

Epoch 47/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2531

Epoch 48/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2498

Epoch 49/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2488

Epoch 50/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2472

Epoch 51/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2458

Epoch 52/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2459

Epoch 53/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.2429

Epoch 54/200

4/4 - 0s - 42ms/step - accuracy: 0.8950 - loss: 0.2428

Epoch 55/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2409

Epoch 56/200

4/4 - 0s - 4ms/step - accuracy: 0.9000 - loss: 0.2408

Epoch 57/200

4/4 - 0s - 4ms/step - accuracy: 0.9000 - loss: 0.2380

Epoch 58/200

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

Epoch 59/200

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

Epoch 60/200

4/4 - 0s - 4ms/step - accuracy: 0.9000 - loss: 0.2339

Epoch 61/200

4/4 - 0s - 4ms/step - accuracy: 0.9000 - loss: 0.2325

Epoch 62/200

4/4 - 0s - 4ms/step - accuracy: 0.9100 - loss: 0.2329

Epoch 63/200

4/4 - 0s - 4ms/step - accuracy: 0.9000 - loss: 0.2296

Epoch 64/200

4/4 - 0s - 11ms/step - accuracy: 0.9100 - loss: 0.2305

Epoch 65/200

4/4 - 0s - 4ms/step - accuracy: 0.9000 - loss: 0.2281

Epoch 66/200

4/4 - 0s - 4ms/step - accuracy: 0.9000 - loss: 0.2273

Epoch 67/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2286

Epoch 68/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.2233

Epoch 69/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2223

Epoch 70/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2213

Epoch 71/200

4/4 - 0s - 23ms/step - accuracy: 0.9050 - loss: 0.2213

Epoch 72/200

4/4 - 0s - 4ms/step - accuracy: 0.9050 - loss: 0.2196

Epoch 73/200

4/4 - 0s - 4ms/step - accuracy: 0.9050 - loss: 0.2174

Epoch 74/200

4/4 - 0s - 4ms/step - accuracy: 0.9050 - loss: 0.2164

Epoch 75/200

4/4 - 0s - 4ms/step - accuracy: 0.9050 - loss: 0.2155

Epoch 76/200

4/4 - 0s - 4ms/step - accuracy: 0.9050 - loss: 0.2140

Epoch 77/200

4/4 - 0s - 4ms/step - accuracy: 0.9050 - loss: 0.2138

Epoch 78/200

4/4 - 0s - 4ms/step - accuracy: 0.9050 - loss: 0.2119

Epoch 79/200

4/4 - 0s - 4ms/step - accuracy: 0.9050 - loss: 0.2102

Epoch 80/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.2110

Epoch 81/200

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

Epoch 82/200

4/4 - 0s - 4ms/step - accuracy: 0.9050 - loss: 0.2077

Epoch 83/200

4/4 - 0s - 4ms/step - accuracy: 0.9050 - loss: 0.2054

Epoch 84/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.2050

Epoch 85/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.2018

Epoch 86/200

4/4 - 0s - 4ms/step - accuracy: 0.9050 - loss: 0.2026

Epoch 87/200

4/4 - 0s - 4ms/step - accuracy: 0.9050 - loss: 0.2009

Epoch 88/200

4/4 - 0s - 4ms/step - accuracy: 0.9100 - loss: 0.2015

Epoch 89/200

4/4 - 0s - 4ms/step - accuracy: 0.9100 - loss: 0.1971

Epoch 90/200

4/4 - 0s - 4ms/step - accuracy: 0.9100 - loss: 0.1983

Epoch 91/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1961

Epoch 92/200

4/4 - 0s - 4ms/step - accuracy: 0.9150 - loss: 0.1948

Epoch 93/200

4/4 - 0s - 4ms/step - accuracy: 0.9150 - loss: 0.1931

Epoch 94/200

4/4 - 0s - 4ms/step - accuracy: 0.9150 - loss: 0.1916

Epoch 95/200

4/4 - 0s - 4ms/step - accuracy: 0.9150 - loss: 0.1910

Epoch 96/200

4/4 - 0s - 5ms/step - accuracy: 0.9150 - loss: 0.1913

Epoch 97/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1883

Epoch 98/200

4/4 - 0s - 5ms/step - accuracy: 0.9150 - loss: 0.1867

Epoch 99/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1878

Epoch 100/200

4/4 - 0s - 46ms/step - accuracy: 0.9200 - loss: 0.1848

Epoch 101/200

4/4 - 0s - 5ms/step - accuracy: 0.9150 - loss: 0.1832

Epoch 102/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1841

Epoch 103/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1810

Epoch 104/200

4/4 - 0s - 5ms/step - accuracy: 0.9250 - loss: 0.1806

Epoch 105/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1797

Epoch 106/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1783

Epoch 107/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1780

Epoch 108/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1749

Epoch 109/200

4/4 - 0s - 5ms/step - accuracy: 0.9250 - loss: 0.1736

Epoch 110/200

4/4 - 0s - 12ms/step - accuracy: 0.9250 - loss: 0.1723

Epoch 111/200

4/4 - 0s - 5ms/step - accuracy: 0.9250 - loss: 0.1722

Epoch 112/200

4/4 - 0s - 5ms/step - accuracy: 0.9300 - loss: 0.1702

Epoch 113/200

4/4 - 0s - 7ms/step - accuracy: 0.9300 - loss: 0.1685

Epoch 114/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1694

Epoch 115/200

4/4 - 0s - 7ms/step - accuracy: 0.9300 - loss: 0.1678

Epoch 116/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1653

Epoch 117/200

4/4 - 0s - 22ms/step - accuracy: 0.9300 - loss: 0.1633

Epoch 118/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1644

Epoch 119/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1613

Epoch 120/200

4/4 - 0s - 4ms/step - accuracy: 0.9200 - loss: 0.1617

Epoch 121/200

4/4 - 0s - 4ms/step - accuracy: 0.9300 - loss: 0.1589

Epoch 122/200

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

Epoch 123/200

4/4 - 0s - 4ms/step - accuracy: 0.9350 - loss: 0.1566

Epoch 124/200

4/4 - 0s - 4ms/step - accuracy: 0.9350 - loss: 0.1564

Epoch 125/200

4/4 - 0s - 5ms/step - accuracy: 0.9400 - loss: 0.1550

Epoch 126/200

4/4 - 0s - 5ms/step - accuracy: 0.9400 - loss: 0.1527

Epoch 127/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1530

Epoch 128/200

4/4 - 0s - 4ms/step - accuracy: 0.9300 - loss: 0.1528

Epoch 129/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1509

Epoch 130/200

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

Epoch 131/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1478

Epoch 132/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1476

Epoch 133/200

4/4 - 0s - 5ms/step - accuracy: 0.9400 - loss: 0.1454

Epoch 134/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1464

Epoch 135/200

4/4 - 0s - 5ms/step - accuracy: 0.9400 - loss: 0.1430

Epoch 136/200

4/4 - 0s - 5ms/step - accuracy: 0.9400 - loss: 0.1445

Epoch 137/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1410

Epoch 138/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1399

Epoch 139/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1396

Epoch 140/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1379

Epoch 141/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1385

Epoch 142/200

4/4 - 0s - 4ms/step - accuracy: 0.9500 - loss: 0.1367

Epoch 143/200

4/4 - 0s - 4ms/step - accuracy: 0.9450 - loss: 0.1346

Epoch 144/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1350

Epoch 145/200

4/4 - 0s - 5ms/step - accuracy: 0.9400 - loss: 0.1352

Epoch 146/200

4/4 - 0s - 50ms/step - accuracy: 0.9500 - loss: 0.1315

Epoch 147/200

4/4 - 0s - 4ms/step - accuracy: 0.9450 - loss: 0.1320

Epoch 148/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1318

Epoch 149/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1304

Epoch 150/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1290

Epoch 151/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1277

Epoch 152/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1270

Epoch 153/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1253

Epoch 154/200

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

Epoch 155/200

4/4 - 0s - 12ms/step - accuracy: 0.9450 - loss: 0.1252

Epoch 156/200

4/4 - 0s - 4ms/step - accuracy: 0.9550 - loss: 0.1234

Epoch 157/200

4/4 - 0s - 4ms/step - accuracy: 0.9500 - loss: 0.1226

Epoch 158/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1218

Epoch 159/200

4/4 - 0s - 7ms/step - accuracy: 0.9450 - loss: 0.1247

Epoch 160/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1194

Epoch 161/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1202

Epoch 162/200

4/4 - 0s - 7ms/step - accuracy: 0.9550 - loss: 0.1186

Epoch 163/200

4/4 - 0s - 19ms/step - accuracy: 0.9550 - loss: 0.1176

Epoch 164/200

4/4 - 0s - 4ms/step - accuracy: 0.9550 - loss: 0.1170

Epoch 165/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1161

Epoch 166/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1148

Epoch 167/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1159

Epoch 168/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1135

Epoch 169/200

4/4 - 0s - 4ms/step - accuracy: 0.9550 - loss: 0.1144

Epoch 170/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1117

Epoch 171/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1140

Epoch 172/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1097

Epoch 173/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1115

Epoch 174/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1109

Epoch 175/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1092

Epoch 176/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1079

Epoch 177/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1064

Epoch 178/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1066

Epoch 179/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1072

Epoch 180/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1066

Epoch 181/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1043

Epoch 182/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1043

Epoch 183/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1027

Epoch 184/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1046

Epoch 185/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1016

Epoch 186/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1008

Epoch 187/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1020

Epoch 188/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1040

Epoch 189/200

4/4 - 0s - 4ms/step - accuracy: 0.9600 - loss: 0.0995

Epoch 190/200

4/4 - 0s - 4ms/step - accuracy: 0.9600 - loss: 0.0986

Epoch 191/200

4/4 - 0s - 53ms/step - accuracy: 0.9600 - loss: 0.0989

Epoch 192/200

4/4 - 0s - 4ms/step - accuracy: 0.9600 - loss: 0.0977

Epoch 193/200

4/4 - 0s - 4ms/step - accuracy: 0.9600 - loss: 0.0978

Epoch 194/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.0964

Epoch 195/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.0978

Epoch 196/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.0964

Epoch 197/200

4/4 - 0s - 4ms/step - accuracy: 0.9600 - loss: 0.0951

Epoch 198/200

4/4 - 0s - 4ms/step - accuracy: 0.9600 - loss: 0.0967

Epoch 199/200

4/4 - 0s - 4ms/step - accuracy: 0.9600 - loss: 0.0952

Epoch 200/200

4/4 - 0s - 4ms/step - accuracy: 0.9600 - loss: 0.0946

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

score = 0.09179027378559113
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([[1.338889e-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 = 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)

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 0x7f3e64db6d50>