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

from sklearn import datasets

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.

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)

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 = [ 0.78861367 -0.68574509], 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 Input, Dense, Dropout, Activation
from keras.optimizers import RMSprop

2025-04-18 16:21:08.964137: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2025-04-18 16:21:08.967481: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2025-04-18 16:21:08.976171: 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 00:00:1744993268.990284    4855 cuda_dnn.cc:8579] Unable to register cuDNN factory: Attempting to register factory for plugin cuDNN when one has already been registered
E0000 00:00:1744993268.994447    4855 cuda_blas.cc:1407] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered
W0000 00:00:1744993269.006578    4855 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
W0000 00:00:1744993269.006593    4855 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
W0000 00:00:1744993269.006595    4855 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
W0000 00:00:1744993269.006596    4855 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
2025-04-18 16:21:09.011025: 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"))

2025-04-18 16:21:10.817025: 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'])

from IPython.display import SVG
from keras.utils import model_to_dot

SVG(model_to_dot(model, show_shapes=True, dpi=65).create(prog='dot', format='svg'))

Important

We seem to need a lot of epochs here to get a good result

epochs = 100
results = model.fit(x, v, batch_size=50, epochs=epochs)

Epoch 1/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 1s 457ms/step - accuracy: 0.5000 - loss: 0.7107


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - accuracy: 0.5333 - loss: 0.6997  

Epoch 2/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.7800 - loss: 0.6649


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8093 - loss: 0.6617 

Epoch 3/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.6439


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8367 - loss: 0.6419 

Epoch 4/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.7400 - loss: 0.6295


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.7987 - loss: 0.6238 

Epoch 5/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.6021


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8360 - loss: 0.6048 

Epoch 6/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.5922


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8233 - loss: 0.5908 

Epoch 7/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.5656


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8413 - loss: 0.5696 

Epoch 8/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8000 - loss: 0.5787


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8133 - loss: 0.5660 

Epoch 9/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7400 - loss: 0.5612


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8160 - loss: 0.5405 

Epoch 10/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.5365


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8193 - loss: 0.5290 

Epoch 11/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.4985


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8340 - loss: 0.5064 

Epoch 12/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7600 - loss: 0.5235


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8140 - loss: 0.5003 

Epoch 13/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8200 - loss: 0.4717


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8187 - loss: 0.4793 

Epoch 14/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.4798


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8200 - loss: 0.4722 

Epoch 15/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.4243


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8460 - loss: 0.4377 

Epoch 16/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.4351


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8340 - loss: 0.4325 

Epoch 17/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.3574


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8673 - loss: 0.3918 

Epoch 18/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.3561


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8393 - loss: 0.3999 

Epoch 19/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7800 - loss: 0.4456


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8267 - loss: 0.4080 

Epoch 20/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3905


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8333 - loss: 0.3973 

Epoch 21/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.3812


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8613 - loss: 0.3774 

Epoch 22/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.3305


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8373 - loss: 0.3743 

Epoch 23/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3460


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8460 - loss: 0.3557 

Epoch 24/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.7400 - loss: 0.4382


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8233 - loss: 0.3726 

Epoch 25/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8200 - loss: 0.4156


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8347 - loss: 0.3784 

Epoch 26/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.7800 - loss: 0.4491


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8167 - loss: 0.3826 

Epoch 27/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 23ms/step - accuracy: 0.8400 - loss: 0.3365


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8507 - loss: 0.3387 

Epoch 28/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3944


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8507 - loss: 0.3573 

Epoch 29/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.4083


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8493 - loss: 0.3552 

Epoch 30/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3210


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8533 - loss: 0.3266 

Epoch 31/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2369


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8813 - loss: 0.3026 

Epoch 32/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3214


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8600 - loss: 0.3202 

Epoch 33/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2516


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8593 - loss: 0.3065 

Epoch 34/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3267


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8567 - loss: 0.3196 

Epoch 35/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3043


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8680 - loss: 0.3081 

Epoch 36/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.3807


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8440 - loss: 0.3333 

Epoch 37/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3197


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8600 - loss: 0.3055 

Epoch 38/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.8800 - loss: 0.2841


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8720 - loss: 0.3025 

Epoch 39/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.9200 - loss: 0.2411


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8947 - loss: 0.2743 

Epoch 40/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3547


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8627 - loss: 0.3188 

Epoch 41/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2374


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8887 - loss: 0.2783 

Epoch 42/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3038


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8600 - loss: 0.3102 

Epoch 43/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.2999


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8760 - loss: 0.2816 

Epoch 44/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3099


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8553 - loss: 0.3005 

Epoch 45/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.7800 - loss: 0.4355


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8500 - loss: 0.3222 

Epoch 46/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8200 - loss: 0.3597


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8527 - loss: 0.3160 

Epoch 47/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2517


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8913 - loss: 0.2614 

Epoch 48/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2541


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8713 - loss: 0.2941 

Epoch 49/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.3353


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8667 - loss: 0.3005 

Epoch 50/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3521


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8620 - loss: 0.3034 

Epoch 51/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3131


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8807 - loss: 0.2789 

Epoch 52/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8000 - loss: 0.4100


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8493 - loss: 0.3268 

Epoch 53/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3200


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8747 - loss: 0.2885 

Epoch 54/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2777


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8813 - loss: 0.2720 

Epoch 55/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2283


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8807 - loss: 0.2708 

Epoch 56/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2226


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8767 - loss: 0.2675 

Epoch 57/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.2937


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8613 - loss: 0.2925 

Epoch 58/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.2738


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8860 - loss: 0.2766 

Epoch 59/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.1955


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8767 - loss: 0.2546 

Epoch 60/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2489


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8967 - loss: 0.2549 

Epoch 61/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 24ms/step - accuracy: 0.8600 - loss: 0.2675


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8827 - loss: 0.2568 

Epoch 62/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.3350


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8860 - loss: 0.2919 

Epoch 63/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2641


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8860 - loss: 0.2697 

Epoch 64/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2946


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8907 - loss: 0.2800 

Epoch 65/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.2888


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8820 - loss: 0.2722 

Epoch 66/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2198


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8913 - loss: 0.2652 

Epoch 67/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.3783


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8760 - loss: 0.2943 

Epoch 68/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2398


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8847 - loss: 0.2634 

Epoch 69/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.3040


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8887 - loss: 0.2767 

Epoch 70/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2556


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9013 - loss: 0.2517 

Epoch 71/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.2053


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9173 - loss: 0.2377 

Epoch 72/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.1997


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8940 - loss: 0.2554 

Epoch 73/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.9000 - loss: 0.2537


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8960 - loss: 0.2585 

Epoch 74/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2461


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8867 - loss: 0.2642 

Epoch 75/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9800 - loss: 0.1045


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9193 - loss: 0.2165 

Epoch 76/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2819


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8940 - loss: 0.2693 

Epoch 77/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3167


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8840 - loss: 0.2787 

Epoch 78/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3452


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8787 - loss: 0.2775 

Epoch 79/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2275


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9013 - loss: 0.2500 

Epoch 80/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.2756


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9007 - loss: 0.2553 

Epoch 81/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.8800 - loss: 0.2537


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8947 - loss: 0.2501 

Epoch 82/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9600 - loss: 0.2224


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9173 - loss: 0.2454 

Epoch 83/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.9800 - loss: 0.1453


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9220 - loss: 0.2249 

Epoch 84/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2485


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9020 - loss: 0.2514 

Epoch 85/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2029


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9067 - loss: 0.2397 

Epoch 86/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.1602


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9107 - loss: 0.2288 

Epoch 87/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3876


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8860 - loss: 0.2881 

Epoch 88/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2532


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9007 - loss: 0.2461 

Epoch 89/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.8600 - loss: 0.3646


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8800 - loss: 0.3024 

Epoch 90/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.1856


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9147 - loss: 0.2281 

Epoch 91/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.3405


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8807 - loss: 0.2763 

Epoch 92/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2188


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9053 - loss: 0.2417 

Epoch 93/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2706


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8987 - loss: 0.2505 

Epoch 94/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2905


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8860 - loss: 0.2680 

Epoch 95/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 26ms/step - accuracy: 0.9600 - loss: 0.1455


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9173 - loss: 0.2193 

Epoch 96/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.2095


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9233 - loss: 0.2164 

Epoch 97/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.1773


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9193 - loss: 0.2139 

Epoch 98/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3286


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8913 - loss: 0.2641 

Epoch 99/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.2666


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8900 - loss: 0.2480 

Epoch 100/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2004


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8967 - loss: 0.2376 

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

score = 0.2389511615037918

accuracy = 0.8999999761581421

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 32ms/step


1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 43ms/step

array([[8.1855285e-07]], 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 0x7ff9dcfd5890>