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 = [0.21878035 0.76753289], 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 - 5ms/step - accuracy: 0.6850 - loss: 0.6806

Epoch 2/200

4/4 - 0s - 5ms/step - accuracy: 0.8550 - loss: 0.6578

Epoch 3/200

4/4 - 0s - 5ms/step - accuracy: 0.8550 - loss: 0.6414

Epoch 4/200

4/4 - 0s - 5ms/step - accuracy: 0.8500 - loss: 0.6281

Epoch 5/200

4/4 - 0s - 5ms/step - accuracy: 0.8550 - loss: 0.6149

Epoch 6/200

4/4 - 0s - 5ms/step - accuracy: 0.8500 - loss: 0.6020

Epoch 7/200

4/4 - 0s - 5ms/step - accuracy: 0.8550 - loss: 0.5891

Epoch 8/200

4/4 - 0s - 5ms/step - accuracy: 0.8550 - loss: 0.5762

Epoch 9/200

4/4 - 0s - 5ms/step - accuracy: 0.8500 - loss: 0.5629

Epoch 10/200

4/4 - 0s - 5ms/step - accuracy: 0.8450 - loss: 0.5498

Epoch 11/200

4/4 - 0s - 5ms/step - accuracy: 0.8450 - loss: 0.5362

Epoch 12/200

4/4 - 0s - 5ms/step - accuracy: 0.8400 - loss: 0.5226

Epoch 13/200

4/4 - 0s - 5ms/step - accuracy: 0.8400 - loss: 0.5089

Epoch 14/200

4/4 - 0s - 5ms/step - accuracy: 0.8450 - loss: 0.4959

Epoch 15/200

4/4 - 0s - 18ms/step - accuracy: 0.8400 - loss: 0.4831

Epoch 16/200

4/4 - 0s - 4ms/step - accuracy: 0.8400 - loss: 0.4699

Epoch 17/200

4/4 - 0s - 4ms/step - accuracy: 0.8400 - loss: 0.4577

Epoch 18/200

4/4 - 0s - 4ms/step - accuracy: 0.8400 - loss: 0.4452

Epoch 19/200

4/4 - 0s - 4ms/step - accuracy: 0.8400 - loss: 0.4338

Epoch 20/200

4/4 - 0s - 5ms/step - accuracy: 0.8400 - loss: 0.4223

Epoch 21/200

4/4 - 0s - 9ms/step - accuracy: 0.8400 - loss: 0.4114

Epoch 22/200

4/4 - 0s - 4ms/step - accuracy: 0.8400 - loss: 0.4008

Epoch 23/200

4/4 - 0s - 4ms/step - accuracy: 0.8450 - loss: 0.3916

Epoch 24/200

4/4 - 0s - 6ms/step - accuracy: 0.8450 - loss: 0.3814

Epoch 25/200

4/4 - 0s - 5ms/step - accuracy: 0.8450 - loss: 0.3735

Epoch 26/200

4/4 - 0s - 5ms/step - accuracy: 0.8500 - loss: 0.3650

Epoch 27/200

4/4 - 0s - 18ms/step - accuracy: 0.8450 - loss: 0.3574

Epoch 28/200

4/4 - 0s - 4ms/step - accuracy: 0.8500 - loss: 0.3500

Epoch 29/200

4/4 - 0s - 4ms/step - accuracy: 0.8450 - loss: 0.3444

Epoch 30/200

4/4 - 0s - 4ms/step - accuracy: 0.8550 - loss: 0.3379

Epoch 31/200

4/4 - 0s - 5ms/step - accuracy: 0.8550 - loss: 0.3323

Epoch 32/200

4/4 - 0s - 4ms/step - accuracy: 0.8600 - loss: 0.3270

Epoch 33/200

4/4 - 0s - 4ms/step - accuracy: 0.8550 - loss: 0.3229

Epoch 34/200

4/4 - 0s - 4ms/step - accuracy: 0.8550 - loss: 0.3183

Epoch 35/200

4/4 - 0s - 4ms/step - accuracy: 0.8650 - loss: 0.3153

Epoch 36/200

4/4 - 0s - 4ms/step - accuracy: 0.8600 - loss: 0.3113

Epoch 37/200

4/4 - 0s - 4ms/step - accuracy: 0.8650 - loss: 0.3114

Epoch 38/200

4/4 - 0s - 4ms/step - accuracy: 0.8650 - loss: 0.3064

Epoch 39/200

4/4 - 0s - 4ms/step - accuracy: 0.8650 - loss: 0.3036

Epoch 40/200

4/4 - 0s - 4ms/step - accuracy: 0.8650 - loss: 0.3019

Epoch 41/200

4/4 - 0s - 5ms/step - accuracy: 0.8600 - loss: 0.2998

Epoch 42/200

4/4 - 0s - 5ms/step - accuracy: 0.8650 - loss: 0.2978

Epoch 43/200

4/4 - 0s - 5ms/step - accuracy: 0.8650 - loss: 0.2966

Epoch 44/200

4/4 - 0s - 5ms/step - accuracy: 0.8650 - loss: 0.2949

Epoch 45/200

4/4 - 0s - 5ms/step - accuracy: 0.8650 - loss: 0.2920

Epoch 46/200

4/4 - 0s - 5ms/step - accuracy: 0.8650 - loss: 0.2911

Epoch 47/200

4/4 - 0s - 5ms/step - accuracy: 0.8700 - loss: 0.2887

Epoch 48/200

4/4 - 0s - 5ms/step - accuracy: 0.8700 - loss: 0.2889

Epoch 49/200

4/4 - 0s - 5ms/step - accuracy: 0.8700 - loss: 0.2860

Epoch 50/200

4/4 - 0s - 5ms/step - accuracy: 0.8650 - loss: 0.2855

Epoch 51/200

4/4 - 0s - 5ms/step - accuracy: 0.8700 - loss: 0.2836

Epoch 52/200

4/4 - 0s - 5ms/step - accuracy: 0.8700 - loss: 0.2819

Epoch 53/200

4/4 - 0s - 5ms/step - accuracy: 0.8700 - loss: 0.2805

Epoch 54/200

4/4 - 0s - 5ms/step - accuracy: 0.8700 - loss: 0.2808

Epoch 55/200

4/4 - 0s - 24ms/step - accuracy: 0.8700 - loss: 0.2790

Epoch 56/200

4/4 - 0s - 5ms/step - accuracy: 0.8700 - loss: 0.2779

Epoch 57/200

4/4 - 0s - 4ms/step - accuracy: 0.8700 - loss: 0.2763

Epoch 58/200

4/4 - 0s - 4ms/step - accuracy: 0.8700 - loss: 0.2746

Epoch 59/200

4/4 - 0s - 5ms/step - accuracy: 0.8750 - loss: 0.2750

Epoch 60/200

4/4 - 0s - 4ms/step - accuracy: 0.8750 - loss: 0.2725

Epoch 61/200

4/4 - 0s - 4ms/step - accuracy: 0.8750 - loss: 0.2713

Epoch 62/200

4/4 - 0s - 5ms/step - accuracy: 0.8750 - loss: 0.2724

Epoch 63/200

4/4 - 0s - 4ms/step - accuracy: 0.8750 - loss: 0.2705

Epoch 64/200

4/4 - 0s - 4ms/step - accuracy: 0.8750 - loss: 0.2680

Epoch 65/200

4/4 - 0s - 11ms/step - accuracy: 0.8750 - loss: 0.2678

Epoch 66/200

4/4 - 0s - 4ms/step - accuracy: 0.8750 - loss: 0.2665

Epoch 67/200

4/4 - 0s - 4ms/step - accuracy: 0.8750 - loss: 0.2674

Epoch 68/200

4/4 - 0s - 7ms/step - accuracy: 0.8800 - loss: 0.2651

Epoch 69/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2629

Epoch 70/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2627

Epoch 71/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2606

Epoch 72/200

4/4 - 0s - 18ms/step - accuracy: 0.8850 - loss: 0.2601

Epoch 73/200

4/4 - 0s - 5ms/step - accuracy: 0.8800 - loss: 0.2583

Epoch 74/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2584

Epoch 75/200

4/4 - 0s - 4ms/step - accuracy: 0.8850 - loss: 0.2557

Epoch 76/200

4/4 - 0s - 4ms/step - accuracy: 0.8850 - loss: 0.2549

Epoch 77/200

4/4 - 0s - 4ms/step - accuracy: 0.8850 - loss: 0.2549

Epoch 78/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2525

Epoch 79/200

4/4 - 0s - 4ms/step - accuracy: 0.8800 - loss: 0.2529

Epoch 80/200

4/4 - 0s - 4ms/step - accuracy: 0.8850 - loss: 0.2496

Epoch 81/200

4/4 - 0s - 4ms/step - accuracy: 0.8850 - loss: 0.2484

Epoch 82/200

4/4 - 0s - 4ms/step - accuracy: 0.8850 - loss: 0.2478

Epoch 83/200

4/4 - 0s - 4ms/step - accuracy: 0.8850 - loss: 0.2470

Epoch 84/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2454

Epoch 85/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2448

Epoch 86/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2432

Epoch 87/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2413

Epoch 88/200

4/4 - 0s - 5ms/step - accuracy: 0.8900 - loss: 0.2395

Epoch 89/200

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

Epoch 90/200

4/4 - 0s - 4ms/step - accuracy: 0.8850 - loss: 0.2374

Epoch 91/200

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

Epoch 92/200

4/4 - 0s - 5ms/step - accuracy: 0.8850 - loss: 0.2344

Epoch 93/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2326

Epoch 94/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2339

Epoch 95/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2295

Epoch 96/200

4/4 - 0s - 4ms/step - accuracy: 0.8900 - loss: 0.2291

Epoch 97/200

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

Epoch 98/200

4/4 - 0s - 4ms/step - accuracy: 0.8950 - loss: 0.2253

Epoch 99/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2240

Epoch 100/200

4/4 - 0s - 30ms/step - accuracy: 0.8950 - loss: 0.2231

Epoch 101/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2209

Epoch 102/200

4/4 - 0s - 4ms/step - accuracy: 0.9000 - loss: 0.2185

Epoch 103/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2177

Epoch 104/200

4/4 - 0s - 4ms/step - accuracy: 0.9000 - loss: 0.2164

Epoch 105/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2153

Epoch 106/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2132

Epoch 107/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2115

Epoch 108/200

4/4 - 0s - 5ms/step - accuracy: 0.8950 - loss: 0.2099

Epoch 109/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.2078

Epoch 110/200

4/4 - 0s - 12ms/step - accuracy: 0.9000 - loss: 0.2064

Epoch 111/200

4/4 - 0s - 5ms/step - accuracy: 0.9050 - loss: 0.2051

Epoch 112/200

4/4 - 0s - 5ms/step - accuracy: 0.9100 - loss: 0.2034

Epoch 113/200

4/4 - 0s - 7ms/step - accuracy: 0.9050 - loss: 0.2034

Epoch 114/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2002

Epoch 115/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1986

Epoch 116/200

4/4 - 0s - 7ms/step - accuracy: 0.9100 - loss: 0.1969

Epoch 117/200

4/4 - 0s - 16ms/step - accuracy: 0.9150 - loss: 0.1961

Epoch 118/200

4/4 - 0s - 5ms/step - accuracy: 0.9100 - loss: 0.1944

Epoch 119/200

4/4 - 0s - 5ms/step - accuracy: 0.9150 - loss: 0.1921

Epoch 120/200

4/4 - 0s - 4ms/step - accuracy: 0.9200 - loss: 0.1904

Epoch 121/200

4/4 - 0s - 4ms/step - accuracy: 0.9150 - loss: 0.1909

Epoch 122/200

4/4 - 0s - 4ms/step - accuracy: 0.9200 - loss: 0.1891

Epoch 123/200

4/4 - 0s - 4ms/step - accuracy: 0.9200 - loss: 0.1860

Epoch 124/200

4/4 - 0s - 4ms/step - accuracy: 0.9200 - loss: 0.1861

Epoch 125/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1833

Epoch 126/200

4/4 - 0s - 4ms/step - accuracy: 0.9200 - loss: 0.1832

Epoch 127/200

4/4 - 0s - 4ms/step - accuracy: 0.9200 - loss: 0.1812

Epoch 128/200

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

Epoch 129/200

4/4 - 0s - 4ms/step - accuracy: 0.9200 - loss: 0.1775

Epoch 130/200

4/4 - 0s - 4ms/step - accuracy: 0.9250 - loss: 0.1764

Epoch 131/200

4/4 - 0s - 5ms/step - accuracy: 0.9250 - loss: 0.1759

Epoch 132/200

4/4 - 0s - 4ms/step - accuracy: 0.9250 - loss: 0.1732

Epoch 133/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1718

Epoch 134/200

4/4 - 0s - 5ms/step - accuracy: 0.9200 - loss: 0.1701

Epoch 135/200

4/4 - 0s - 5ms/step - accuracy: 0.9300 - loss: 0.1687

Epoch 136/200

4/4 - 0s - 4ms/step - accuracy: 0.9200 - loss: 0.1686

Epoch 137/200

4/4 - 0s - 4ms/step - accuracy: 0.9250 - loss: 0.1664

Epoch 138/200

4/4 - 0s - 5ms/step - accuracy: 0.9250 - loss: 0.1642

Epoch 139/200

4/4 - 0s - 5ms/step - accuracy: 0.9300 - loss: 0.1618

Epoch 140/200

4/4 - 0s - 4ms/step - accuracy: 0.9300 - loss: 0.1626

Epoch 141/200

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

Epoch 142/200

4/4 - 0s - 5ms/step - accuracy: 0.9250 - loss: 0.1588

Epoch 143/200

4/4 - 0s - 5ms/step - accuracy: 0.9350 - loss: 0.1566

Epoch 144/200

4/4 - 0s - 4ms/step - accuracy: 0.9400 - loss: 0.1557

Epoch 145/200

4/4 - 0s - 27ms/step - accuracy: 0.9400 - loss: 0.1541

Epoch 146/200

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

Epoch 147/200

4/4 - 0s - 4ms/step - accuracy: 0.9400 - loss: 0.1521

Epoch 148/200

4/4 - 0s - 4ms/step - accuracy: 0.9450 - loss: 0.1499

Epoch 149/200

4/4 - 0s - 4ms/step - accuracy: 0.9450 - loss: 0.1472

Epoch 150/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1459

Epoch 151/200

4/4 - 0s - 4ms/step - accuracy: 0.9500 - loss: 0.1445

Epoch 152/200

4/4 - 0s - 5ms/step - accuracy: 0.9450 - loss: 0.1430

Epoch 153/200

4/4 - 0s - 4ms/step - accuracy: 0.9500 - loss: 0.1413

Epoch 154/200

4/4 - 0s - 11ms/step - accuracy: 0.9500 - loss: 0.1398

Epoch 155/200

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

Epoch 156/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1364

Epoch 157/200

4/4 - 0s - 7ms/step - accuracy: 0.9450 - loss: 0.1374

Epoch 158/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1336

Epoch 159/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1323

Epoch 160/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1307

Epoch 161/200

4/4 - 0s - 19ms/step - accuracy: 0.9500 - loss: 0.1296

Epoch 162/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1284

Epoch 163/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1270

Epoch 164/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1265

Epoch 165/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1241

Epoch 166/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1230

Epoch 167/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1217

Epoch 168/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1209

Epoch 169/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1181

Epoch 170/200

4/4 - 0s - 5ms/step - accuracy: 0.9500 - loss: 0.1169

Epoch 171/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1168

Epoch 172/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1147

Epoch 173/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1131

Epoch 174/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1124

Epoch 175/200

4/4 - 0s - 5ms/step - accuracy: 0.9600 - loss: 0.1102

Epoch 176/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.1092

Epoch 177/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.1085

Epoch 178/200

4/4 - 0s - 5ms/step - accuracy: 0.9550 - loss: 0.1072

Epoch 179/200

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

Epoch 180/200

4/4 - 0s - 4ms/step - accuracy: 0.9650 - loss: 0.1039

Epoch 181/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.1035

Epoch 182/200

4/4 - 0s - 4ms/step - accuracy: 0.9700 - loss: 0.1016

Epoch 183/200

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

Epoch 184/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.1000

Epoch 185/200

4/4 - 0s - 5ms/step - accuracy: 0.9650 - loss: 0.0990

Epoch 186/200

4/4 - 0s - 4ms/step - accuracy: 0.9650 - loss: 0.0996

Epoch 187/200

4/4 - 0s - 4ms/step - accuracy: 0.9700 - loss: 0.0963

Epoch 188/200

4/4 - 0s - 4ms/step - accuracy: 0.9650 - loss: 0.0953

Epoch 189/200

4/4 - 0s - 4ms/step - accuracy: 0.9700 - loss: 0.0946

Epoch 190/200

4/4 - 0s - 28ms/step - accuracy: 0.9650 - loss: 0.0927

Epoch 191/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.0926

Epoch 192/200

4/4 - 0s - 5ms/step - accuracy: 0.9700 - loss: 0.0910

Epoch 193/200

4/4 - 0s - 5ms/step - accuracy: 0.9750 - loss: 0.0898

Epoch 194/200

4/4 - 0s - 4ms/step - accuracy: 0.9750 - loss: 0.0895

Epoch 195/200

4/4 - 0s - 5ms/step - accuracy: 0.9800 - loss: 0.0892

Epoch 196/200

4/4 - 0s - 4ms/step - accuracy: 0.9700 - loss: 0.0876

Epoch 197/200

4/4 - 0s - 5ms/step - accuracy: 0.9800 - loss: 0.0867

Epoch 198/200

4/4 - 0s - 4ms/step - accuracy: 0.9850 - loss: 0.0859

Epoch 199/200

4/4 - 0s - 12ms/step - accuracy: 0.9750 - loss: 0.0845

Epoch 200/200

4/4 - 0s - 4ms/step - accuracy: 0.9800 - loss: 0.0835

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

score = 0.08168599754571915
accuracy = 0.9850000143051147

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 3ms/step

array([[5.1776894e-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 = 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 0x7fd1da75b610>