Clustering

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 = [-0.54985286  0.81307278], 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)
../_images/cc11745ce58355eba38990728029f303f56fdd81621635df872b1f373fa5b2e2.png

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

2025-05-13 13:31:00.089528: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2025-05-13 13:31:00.092653: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2025-05-13 13:31:00.101181: E external/local_xla/xla/stream_executor/cuda/cuda_fft.cc:467] Unable to register cuFFT factory: Attempting to register factory for plugin cuFFT when one has already been registered
WARNING: All log messages before absl::InitializeLog() is called are written to STDERR
E0000 00:00:1747143060.115458    4916 cuda_dnn.cc:8579] Unable to register cuDNN factory: Attempting to register factory for plugin cuDNN when one has already been registered
E0000 00:00:1747143060.119675    4916 cuda_blas.cc:1407] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered
W0000 00:00:1747143060.131197    4916 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
W0000 00:00:1747143060.131211    4916 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
W0000 00:00:1747143060.131212    4916 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
W0000 00:00:1747143060.131214    4916 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
2025-05-13 13:31:00.135568: I tensorflow/core/platform/cpu_feature_guard.cc:210] This TensorFlow binary is optimized to use available CPU instructions in performance-critical operations.
To enable the following instructions: AVX2 FMA, in other operations, rebuild TensorFlow with the appropriate compiler flags.

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

2025-05-13 13:31:01.922498: E external/local_xla/xla/stream_executor/cuda/cuda_platform.cc:51] failed call to cuInit: INTERNAL: CUDA error: Failed call to cuInit: UNKNOWN ERROR (303)

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 - 118ms/step - accuracy: 0.1800 - loss: 0.7270

Epoch 2/200

4/4 - 0s - 6ms/step - accuracy: 0.7400 - loss: 0.6704

Epoch 3/200

4/4 - 0s - 6ms/step - accuracy: 0.8150 - loss: 0.6342

Epoch 4/200

4/4 - 0s - 6ms/step - accuracy: 0.8200 - loss: 0.6089

Epoch 5/200

4/4 - 0s - 6ms/step - accuracy: 0.8300 - loss: 0.5863

Epoch 6/200

4/4 - 0s - 6ms/step - accuracy: 0.8300 - loss: 0.5651

Epoch 7/200

4/4 - 0s - 8ms/step - accuracy: 0.8400 - loss: 0.5451

Epoch 8/200

4/4 - 0s - 6ms/step - accuracy: 0.8400 - loss: 0.5273

Epoch 9/200

4/4 - 0s - 6ms/step - accuracy: 0.8400 - loss: 0.5120

Epoch 10/200

4/4 - 0s - 6ms/step - accuracy: 0.8400 - loss: 0.4965

Epoch 11/200

4/4 - 0s - 7ms/step - accuracy: 0.8400 - loss: 0.4820

Epoch 12/200

4/4 - 0s - 6ms/step - accuracy: 0.8400 - loss: 0.4689

Epoch 13/200

4/4 - 0s - 6ms/step - accuracy: 0.8400 - loss: 0.4560

Epoch 14/200

4/4 - 0s - 6ms/step - accuracy: 0.8400 - loss: 0.4445

Epoch 15/200

4/4 - 0s - 6ms/step - accuracy: 0.8400 - loss: 0.4322

Epoch 16/200

4/4 - 0s - 6ms/step - accuracy: 0.8450 - loss: 0.4215

Epoch 17/200

4/4 - 0s - 6ms/step - accuracy: 0.8450 - loss: 0.4107

Epoch 18/200

4/4 - 0s - 6ms/step - accuracy: 0.8400 - loss: 0.4004

Epoch 19/200

4/4 - 0s - 6ms/step - accuracy: 0.8450 - loss: 0.3913

Epoch 20/200

4/4 - 0s - 6ms/step - accuracy: 0.8450 - loss: 0.3840

Epoch 21/200

4/4 - 0s - 6ms/step - accuracy: 0.8450 - loss: 0.3750

Epoch 22/200

4/4 - 0s - 6ms/step - accuracy: 0.8450 - loss: 0.3670

Epoch 23/200

4/4 - 0s - 6ms/step - accuracy: 0.8450 - loss: 0.3616

Epoch 24/200

4/4 - 0s - 6ms/step - accuracy: 0.8450 - loss: 0.3546

Epoch 25/200

4/4 - 0s - 6ms/step - accuracy: 0.8500 - loss: 0.3475

Epoch 26/200

4/4 - 0s - 6ms/step - accuracy: 0.8500 - loss: 0.3415

Epoch 27/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.3358

Epoch 28/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.3305

Epoch 29/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3254

Epoch 30/200

4/4 - 0s - 6ms/step - accuracy: 0.8550 - loss: 0.3195

Epoch 31/200

4/4 - 0s - 6ms/step - accuracy: 0.8600 - loss: 0.3147

Epoch 32/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.3111

Epoch 33/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.3065

Epoch 34/200

4/4 - 0s - 6ms/step - accuracy: 0.8650 - loss: 0.3025

Epoch 35/200

4/4 - 0s - 6ms/step - accuracy: 0.8700 - loss: 0.2997

Epoch 36/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2955

Epoch 37/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2934

Epoch 38/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2894

Epoch 39/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2871

Epoch 40/200

4/4 - 0s - 6ms/step - accuracy: 0.8800 - loss: 0.2841

Epoch 41/200

4/4 - 0s - 6ms/step - accuracy: 0.8750 - loss: 0.2828

Epoch 42/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2795

Epoch 43/200

4/4 - 0s - 6ms/step - accuracy: 0.8850 - loss: 0.2779

Epoch 44/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2750

Epoch 45/200

4/4 - 0s - 8ms/step - accuracy: 0.8900 - loss: 0.2744

Epoch 46/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2723

Epoch 47/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2702

Epoch 48/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2687

Epoch 49/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2665

Epoch 50/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2670

Epoch 51/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2645

Epoch 52/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2626

Epoch 53/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2637

Epoch 54/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2608

Epoch 55/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2624

Epoch 56/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2599

Epoch 57/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2576

Epoch 58/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2560

Epoch 59/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2570

Epoch 60/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2540

Epoch 61/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2545

Epoch 62/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2515

Epoch 63/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2505

Epoch 64/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2507

Epoch 65/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2505

Epoch 66/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2493

Epoch 67/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2480

Epoch 68/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2465

Epoch 69/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2453

Epoch 70/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2449

Epoch 71/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2428

Epoch 72/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2428

Epoch 73/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2418

Epoch 74/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2399

Epoch 75/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2394

Epoch 76/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2410

Epoch 77/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2400

Epoch 78/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2364

Epoch 79/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2358

Epoch 80/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2368

Epoch 81/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2362

Epoch 82/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2337

Epoch 83/200

4/4 - 0s - 8ms/step - accuracy: 0.8900 - loss: 0.2320

Epoch 84/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2318

Epoch 85/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2310

Epoch 86/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2301

Epoch 87/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2307

Epoch 88/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2289

Epoch 89/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2292

Epoch 90/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2263

Epoch 91/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2258

Epoch 92/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2253

Epoch 93/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2239

Epoch 94/200

4/4 - 0s - 6ms/step - accuracy: 0.8950 - loss: 0.2255

Epoch 95/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2229

Epoch 96/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2222

Epoch 97/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2204

Epoch 98/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2204

Epoch 99/200

4/4 - 0s - 6ms/step - accuracy: 0.9000 - loss: 0.2188

Epoch 100/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2190

Epoch 101/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2173

Epoch 102/200

4/4 - 0s - 6ms/step - accuracy: 0.8900 - loss: 0.2176

Epoch 103/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2148

Epoch 104/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.2149

Epoch 105/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2131

Epoch 106/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2119

Epoch 107/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2116

Epoch 108/200

4/4 - 0s - 6ms/step - accuracy: 0.9050 - loss: 0.2114

Epoch 109/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.2105

Epoch 110/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.2074

Epoch 111/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.2074

Epoch 112/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.2061

Epoch 113/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.2060

Epoch 114/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.2031

Epoch 115/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.2025

Epoch 116/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.2015

Epoch 117/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.2048

Epoch 118/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.2003

Epoch 119/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1986

Epoch 120/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.1982

Epoch 121/200

4/4 - 0s - 9ms/step - accuracy: 0.9200 - loss: 0.1979

Epoch 122/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1990

Epoch 123/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.1946

Epoch 124/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.1961

Epoch 125/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1943

Epoch 126/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1926

Epoch 127/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1916

Epoch 128/200

4/4 - 0s - 6ms/step - accuracy: 0.9100 - loss: 0.1909

Epoch 129/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1906

Epoch 130/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1875

Epoch 131/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1866

Epoch 132/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1865

Epoch 133/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1846

Epoch 134/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1861

Epoch 135/200

4/4 - 0s - 6ms/step - accuracy: 0.9150 - loss: 0.1832

Epoch 136/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1826

Epoch 137/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1810

Epoch 138/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1794

Epoch 139/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1784

Epoch 140/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1783

Epoch 141/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1816

Epoch 142/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1765

Epoch 143/200

4/4 - 0s - 6ms/step - accuracy: 0.9200 - loss: 0.1754

Epoch 144/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1737

Epoch 145/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1744

Epoch 146/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1736

Epoch 147/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1712

Epoch 148/200

4/4 - 0s - 6ms/step - accuracy: 0.9300 - loss: 0.1737

Epoch 149/200

4/4 - 0s - 6ms/step - accuracy: 0.9250 - loss: 0.1691

Epoch 150/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1678

Epoch 151/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1671

Epoch 152/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1663

Epoch 153/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1647

Epoch 154/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1646

Epoch 155/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1625

Epoch 156/200

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

Epoch 157/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1626

Epoch 158/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1603

Epoch 159/200

4/4 - 0s - 8ms/step - accuracy: 0.9450 - loss: 0.1596

Epoch 160/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1583

Epoch 161/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1605

Epoch 162/200

4/4 - 0s - 6ms/step - accuracy: 0.9350 - loss: 0.1567

Epoch 163/200

4/4 - 0s - 6ms/step - accuracy: 0.9400 - loss: 0.1557

Epoch 164/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1528

Epoch 165/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1545

Epoch 166/200

4/4 - 0s - 6ms/step - accuracy: 0.9450 - loss: 0.1534

Epoch 167/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1498

Epoch 168/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1498

Epoch 169/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1474

Epoch 170/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1470

Epoch 171/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1465

Epoch 172/200

4/4 - 0s - 6ms/step - accuracy: 0.9500 - loss: 0.1488

Epoch 173/200

4/4 - 0s - 7ms/step - accuracy: 0.9500 - loss: 0.1464

Epoch 174/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1425

Epoch 175/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1412

Epoch 176/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1448

Epoch 177/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1396

Epoch 178/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1388

Epoch 179/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1384

Epoch 180/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1370

Epoch 181/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1355

Epoch 182/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1367

Epoch 183/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1333

Epoch 184/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1316

Epoch 185/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1324

Epoch 186/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1305

Epoch 187/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1293

Epoch 188/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1278

Epoch 189/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1270

Epoch 190/200

4/4 - 0s - 6ms/step - accuracy: 0.9550 - loss: 0.1282

Epoch 191/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1264

Epoch 192/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1236

Epoch 193/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.1226

Epoch 194/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1210

Epoch 195/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.1197

Epoch 196/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.1200

Epoch 197/200

4/4 - 0s - 8ms/step - accuracy: 0.9600 - loss: 0.1185

Epoch 198/200

4/4 - 0s - 6ms/step - accuracy: 0.9600 - loss: 0.1162

Epoch 199/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.1150

Epoch 200/200

4/4 - 0s - 6ms/step - accuracy: 0.9650 - loss: 0.1141

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

score = 0.11215672641992569
accuracy = 0.9649999737739563

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 30ms/step


1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 40ms/step

array([[5.589949e-15]], 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 0x7fc0d05e4190>
../_images/e2a1472ea99be775b51b7c0a60ca6d20a5c5ce95f2b34188c9dceee6d88d5d92.png
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