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 = [0.61599644 0.83202171], 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)

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: 0.7250 - loss: 0.6401

Epoch 2/200

4/4 - 0s - 6ms/step - accuracy: 0.7850 - loss: 0.6117

Epoch 3/200

4/4 - 0s - 6ms/step - accuracy: 0.7900 - loss: 0.5907

Epoch 4/200

4/4 - 0s - 5ms/step - accuracy: 0.7950 - loss: 0.5703

Epoch 5/200

4/4 - 0s - 5ms/step - accuracy: 0.7950 - loss: 0.5519

Epoch 6/200

4/4 - 0s - 5ms/step - accuracy: 0.8100 - loss: 0.5352

Epoch 7/200

4/4 - 0s - 5ms/step - accuracy: 0.8150 - loss: 0.5192

Epoch 8/200

4/4 - 0s - 6ms/step - accuracy: 0.8200 - loss: 0.5041

Epoch 9/200

4/4 - 0s - 5ms/step - accuracy: 0.8150 - loss: 0.4900

Epoch 10/200

4/4 - 0s - 5ms/step - accuracy: 0.8150 - loss: 0.4761

Epoch 11/200

4/4 - 0s - 5ms/step - accuracy: 0.8150 - loss: 0.4628

Epoch 12/200

4/4 - 0s - 5ms/step - accuracy: 0.8150 - loss: 0.4506

Epoch 13/200

4/4 - 0s - 6ms/step - accuracy: 0.8150 - loss: 0.4389

Epoch 14/200

4/4 - 0s - 5ms/step - accuracy: 0.8250 - loss: 0.4274

Epoch 15/200

4/4 - 0s - 19ms/step - accuracy: 0.8200 - loss: 0.4171

Epoch 16/200

4/4 - 0s - 6ms/step - accuracy: 0.8250 - loss: 0.4073

Epoch 17/200

4/4 - 0s - 6ms/step - accuracy: 0.8300 - loss: 0.3983

Epoch 18/200

4/4 - 0s - 5ms/step - accuracy: 0.8350 - loss: 0.3898

Epoch 19/200

4/4 - 0s - 5ms/step - accuracy: 0.8300 - loss: 0.3826

Epoch 20/200

4/4 - 0s - 5ms/step - accuracy: 0.8350 - loss: 0.3744

Epoch 21/200

4/4 - 0s - 6ms/step - accuracy: 0.8350 - loss: 0.3674

Epoch 22/200

4/4 - 0s - 5ms/step - accuracy: 0.8400 - loss: 0.3609

Epoch 23/200

4/4 - 0s - 5ms/step - accuracy: 0.8400 - loss: 0.3541

Epoch 24/200

4/4 - 0s - 6ms/step - accuracy: 0.8500 - loss: 0.3482

Epoch 25/200

4/4 - 0s - 6ms/step - accuracy: 0.8500 - loss: 0.3436

Epoch 26/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.3377

Epoch 27/200

4/4 - 0s - 21ms/step - accuracy: 0.8650 - loss: 0.3321

Epoch 28/200

4/4 - 0s - 5ms/step - accuracy: 0.8650 - loss: 0.3275

Epoch 29/200

4/4 - 0s - 5ms/step - accuracy: 0.8650 - loss: 0.3237

Epoch 30/200

4/4 - 0s - 5ms/step - accuracy: 0.8700 - loss: 0.3194

Epoch 31/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.3157

Epoch 32/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.3109

Epoch 33/200

4/4 - 0s - 5ms/step - accuracy: 0.8750 - loss: 0.3078

Epoch 34/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.3048

Epoch 35/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.3017

Epoch 36/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2996

Epoch 37/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2970

Epoch 38/200

4/4 - 0s - 5ms/step - accuracy: 0.8750 - loss: 0.2934

Epoch 39/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2919

Epoch 40/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2894

Epoch 41/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2855

Epoch 42/200

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

Epoch 43/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2810

Epoch 44/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2797

Epoch 45/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2803

Epoch 46/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2752

Epoch 47/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2751

Epoch 48/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2728

Epoch 49/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2714

Epoch 50/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2691

Epoch 51/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2676

Epoch 52/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2658

Epoch 53/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2643

Epoch 54/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2628

Epoch 55/200

4/4 - 0s - 26ms/step - accuracy: 0.8950 - loss: 0.2615

Epoch 56/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2600

Epoch 57/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2584

Epoch 58/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2571

Epoch 59/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2561

Epoch 60/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2536

Epoch 61/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2518

Epoch 62/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2531

Epoch 63/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2498

Epoch 64/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2487

Epoch 65/200

4/4 - 0s - 12ms/step - accuracy: 0.9000 - loss: 0.2479

Epoch 66/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2455

Epoch 67/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2449

Epoch 68/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2425

Epoch 69/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2439

Epoch 70/200

4/4 - 0s - 7ms/step - accuracy: 0.8850 - loss: 0.2399

Epoch 71/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2391

Epoch 72/200

4/4 - 0s - 20ms/step - accuracy: 0.8850 - loss: 0.2403

Epoch 73/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2382

Epoch 74/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2362

Epoch 75/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2334

Epoch 76/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2331

Epoch 77/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2334

Epoch 78/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2306

Epoch 79/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2285

Epoch 80/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2279

Epoch 81/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2258

Epoch 82/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2268

Epoch 83/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2256

Epoch 84/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2231

Epoch 85/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2215

Epoch 86/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2203

Epoch 87/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2184

Epoch 88/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2178

Epoch 89/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2167

Epoch 90/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2149

Epoch 91/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2135

Epoch 92/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2127

Epoch 93/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2116

Epoch 94/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2091

Epoch 95/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2095

Epoch 96/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2077

Epoch 97/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2053

Epoch 98/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2125

Epoch 99/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2025

Epoch 100/200

4/4 - 0s - 31ms/step - accuracy: 0.9000 - loss: 0.2017

Epoch 101/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2021

Epoch 102/200

4/4 - 0s - 5ms/step - accuracy: 0.9150 - loss: 0.2028

Epoch 103/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.2011

Epoch 104/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.1997

Epoch 105/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.1975

Epoch 106/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.1949

Epoch 107/200

4/4 - 0s - 5ms/step - accuracy: 0.9000 - loss: 0.1940

Epoch 108/200

4/4 - 0s - 5ms/step - accuracy: 0.9100 - loss: 0.1961

Epoch 109/200

4/4 - 0s - 11ms/step - accuracy: 0.9150 - loss: 0.1919

Epoch 110/200

4/4 - 0s - 5ms/step - accuracy: 0.9150 - loss: 0.1920

Epoch 111/200

4/4 - 0s - 5ms/step - accuracy: 0.9100 - loss: 0.1910

Epoch 112/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1890

Epoch 113/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1885

Epoch 114/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1860

Epoch 115/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1848

Epoch 116/200

4/4 - 0s - 8ms/step - accuracy: 0.9100 - loss: 0.1833

Epoch 117/200

4/4 - 0s - 19ms/step - accuracy: 0.9100 - loss: 0.1834

Epoch 118/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1820

Epoch 119/200

4/4 - 0s - 5ms/step - accuracy: 0.9250 - loss: 0.1813

Epoch 120/200

4/4 - 0s - 5ms/step - accuracy: 0.9300 - loss: 0.1783

Epoch 121/200

4/4 - 0s - 5ms/step - accuracy: 0.9250 - loss: 0.1761

Epoch 122/200

4/4 - 0s - 5ms/step - accuracy: 0.9300 - loss: 0.1771

Epoch 123/200

4/4 - 0s - 5ms/step - accuracy: 0.9150 - loss: 0.1744

Epoch 124/200

4/4 - 0s - 5ms/step - accuracy: 0.9300 - loss: 0.1733

Epoch 125/200

4/4 - 0s - 5ms/step - accuracy: 0.9250 - loss: 0.1725

Epoch 126/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1703

Epoch 127/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1694

Epoch 128/200

4/4 - 0s - 5ms/step - accuracy: 0.9300 - loss: 0.1686

Epoch 129/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1662

Epoch 130/200

4/4 - 0s - 5ms/step - accuracy: 0.9400 - loss: 0.1654

Epoch 131/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1652

Epoch 132/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1627

Epoch 133/200

4/4 - 0s - 5ms/step - accuracy: 0.9400 - loss: 0.1609

Epoch 134/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1595

Epoch 135/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1588

Epoch 136/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1577

Epoch 137/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1558

Epoch 138/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1532

Epoch 139/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1531

Epoch 140/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1504

Epoch 141/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1501

Epoch 142/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1553

Epoch 143/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1484

Epoch 144/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1465

Epoch 145/200

4/4 - 0s - 34ms/step - accuracy: 0.9550 - loss: 0.1437

Epoch 146/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1429

Epoch 147/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1424

Epoch 148/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1416

Epoch 149/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1390

Epoch 150/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1379

Epoch 151/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1360

Epoch 152/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1377

Epoch 153/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1332

Epoch 154/200

4/4 - 0s - 11ms/step - accuracy: 0.9600 - loss: 0.1320

Epoch 155/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1320

Epoch 156/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.1307

Epoch 157/200

4/4 - 0s - 7ms/step - accuracy: 0.9600 - loss: 0.1274

Epoch 158/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1271

Epoch 159/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1278

Epoch 160/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1255

Epoch 161/200

4/4 - 0s - 21ms/step - accuracy: 0.9600 - loss: 0.1227

Epoch 162/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1218

Epoch 163/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1243

Epoch 164/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1191

Epoch 165/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1176

Epoch 166/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.1175

Epoch 167/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1157

Epoch 168/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.1144

Epoch 169/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1150

Epoch 170/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1121

Epoch 171/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.1105

Epoch 172/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.1088

Epoch 173/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.1089

Epoch 174/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.1063

Epoch 175/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.1055

Epoch 176/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.1044

Epoch 177/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.1023

Epoch 178/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.1033

Epoch 179/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.1010

Epoch 180/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.0999

Epoch 181/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.0979

Epoch 182/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0973

Epoch 183/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.0954

Epoch 184/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.0947

Epoch 185/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.0938

Epoch 186/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.0949

Epoch 187/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0904

Epoch 188/200

4/4 - 0s - 6ms/step - accuracy: 0.9700 - loss: 0.0936

Epoch 189/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.0893

Epoch 190/200

4/4 - 0s - 31ms/step - accuracy: 0.9750 - loss: 0.0889

Epoch 191/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0875

Epoch 192/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0858

Epoch 193/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0866

Epoch 194/200

4/4 - 0s - 5ms/step - accuracy: 0.9800 - loss: 0.0858

Epoch 195/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0830

Epoch 196/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0832

Epoch 197/200

4/4 - 0s - 6ms/step - accuracy: 0.9750 - loss: 0.0814

Epoch 198/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0809

Epoch 199/200

4/4 - 0s - 13ms/step - accuracy: 0.9800 - loss: 0.0820

Epoch 200/200

4/4 - 0s - 5ms/step - accuracy: 0.9800 - loss: 0.0809

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

score = 0.077033132314682
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 3ms/step


1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step

array([[1.5180542e-18]], 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 0x7f4fbd4b3750>