Clustering

Clustering seeks to group data into clusters based on their properties and then allow us to predict which cluster a new member belongs.

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.

import numpy as np
import matplotlib.pyplot as plt
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 = [0.84620768 0.42818795], 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.

First we setup and train our network

from keras.models import Sequential
from keras.layers import Dense, Dropout, Activation
from tensorflow.keras.optimizers import RMSprop

2025-01-21 15:49:11.347350: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2025-01-21 15:49:11.350575: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2025-01-21 15:49:11.357131: E external/local_xla/xla/stream_executor/cuda/cuda_fft.cc:477] 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 00:00:1737474551.370252    3332 cuda_dnn.cc:8310] Unable to register cuDNN factory: Attempting to register factory for plugin cuDNN when one has already been registered
E0000 00:00:1737474551.374422    3332 cuda_blas.cc:1418] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered
2025-01-21 15:49:11.390797: 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(Dense(50, input_dim=2, activation="relu"))
model.add(Dense(20, activation="relu"))
model.add(Dense(1, activation="sigmoid"))

/opt/hostedtoolcache/Python/3.11.11/x64/lib/python3.11/site-packages/keras/src/layers/core/dense.py:87: UserWarning: Do not pass an `input_shape`/`input_dim` argument to a layer. When using Sequential models, prefer using an `Input(shape)` object as the first layer in the model instead.
  super().__init__(activity_regularizer=activity_regularizer, **kwargs)
2025-01-21 15:49:13.045088: E external/local_xla/xla/stream_executor/cuda/cuda_driver.cc:152] 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 plot_model

plot_model(model, show_shapes=True, dpi=100)

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 599ms/step - accuracy: 0.7800 - loss: 0.6726


4/4 ━━━━━━━━━━━━━━━━━━━━ 1s 6ms/step - accuracy: 0.7973 - loss: 0.6609  

Epoch 2/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.6204


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8160 - loss: 0.6181 

Epoch 3/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.6027


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8027 - loss: 0.5957 

Epoch 4/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.5784


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8120 - loss: 0.5716 

Epoch 5/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7600 - loss: 0.5754


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.7947 - loss: 0.5576 

Epoch 6/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8000 - loss: 0.5444


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.7960 - loss: 0.5366 

Epoch 7/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7400 - loss: 0.5405


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.7800 - loss: 0.5238 

Epoch 8/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.5007


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8100 - loss: 0.4995 

Epoch 9/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.7600 - loss: 0.5089


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.7920 - loss: 0.4928 

Epoch 10/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.5074


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8140 - loss: 0.4823 

Epoch 11/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7400 - loss: 0.5182


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.7880 - loss: 0.4764 

Epoch 12/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7000 - loss: 0.5135


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.7820 - loss: 0.4705 

Epoch 13/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.3976


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8367 - loss: 0.4238 

Epoch 14/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.3725


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8360 - loss: 0.4076 

Epoch 15/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.4188


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8267 - loss: 0.4204 

Epoch 16/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8000 - loss: 0.4021


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8200 - loss: 0.4006 

Epoch 17/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.3335


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8427 - loss: 0.3875 

Epoch 18/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8000 - loss: 0.3994


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8260 - loss: 0.3905 

Epoch 19/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3792


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8407 - loss: 0.3776 

Epoch 20/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.3248


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8420 - loss: 0.3660 

Epoch 21/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 15ms/step - accuracy: 0.8600 - loss: 0.3640


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8473 - loss: 0.3642 

Epoch 22/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.3499


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8227 - loss: 0.3712 

Epoch 23/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8200 - loss: 0.4245


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8193 - loss: 0.3944 

Epoch 24/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.3334


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8327 - loss: 0.3517 

Epoch 25/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3363


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8380 - loss: 0.3503 

Epoch 26/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.7400 - loss: 0.4536


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8033 - loss: 0.3779 

Epoch 27/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.3762


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8420 - loss: 0.3480 

Epoch 28/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8200 - loss: 0.3658


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8307 - loss: 0.3493 

Epoch 29/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.3404


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8413 - loss: 0.3339 

Epoch 30/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.7800 - loss: 0.3893


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8327 - loss: 0.3462 

Epoch 31/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.7600 - loss: 0.4224


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8227 - loss: 0.3530 

Epoch 32/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7800 - loss: 0.4212


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8173 - loss: 0.3703 

Epoch 33/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2956


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8593 - loss: 0.3211 

Epoch 34/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3187


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8367 - loss: 0.3330 

Epoch 35/100

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


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8500 - loss: 0.3181 

Epoch 36/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 15ms/step - accuracy: 0.7800 - loss: 0.3968


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8320 - loss: 0.3415 

Epoch 37/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8000 - loss: 0.3884


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8393 - loss: 0.3373 

Epoch 38/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7800 - loss: 0.4043


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8300 - loss: 0.3410 

Epoch 39/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.3507


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8533 - loss: 0.3217 

Epoch 40/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2370


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8727 - loss: 0.2951 

Epoch 41/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.2964


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8647 - loss: 0.2873 

Epoch 42/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.1972


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8747 - loss: 0.2701 

Epoch 43/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8200 - loss: 0.3514


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8420 - loss: 0.3208 

Epoch 44/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.2881


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8693 - loss: 0.2819 

Epoch 45/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.2354


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8680 - loss: 0.2672 

Epoch 46/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.3594


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8507 - loss: 0.3126 

Epoch 47/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2373


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8907 - loss: 0.2644 

Epoch 48/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2553


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8840 - loss: 0.2727 

Epoch 49/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.2664


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8693 - loss: 0.2809 

Epoch 50/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.2487


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8660 - loss: 0.2683 

Epoch 51/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2677


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8840 - loss: 0.2762 

Epoch 52/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.2305


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8793 - loss: 0.2612 

Epoch 53/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.1808


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8893 - loss: 0.2511 

Epoch 54/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3092


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8800 - loss: 0.2749 

Epoch 55/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3032


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8773 - loss: 0.2794 

Epoch 56/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - accuracy: 0.9400 - loss: 0.1909


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8927 - loss: 0.2571 

Epoch 57/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3301


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8847 - loss: 0.2704 

Epoch 58/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.8400 - loss: 0.2881


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8740 - loss: 0.2696 

Epoch 59/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3143


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8820 - loss: 0.2738 

Epoch 60/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.2840


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8807 - loss: 0.2651 

Epoch 61/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.2582


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8800 - loss: 0.2473 

Epoch 62/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.3246


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8533 - loss: 0.2950 

Epoch 63/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.2538


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8827 - loss: 0.2524 

Epoch 64/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.2657


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8940 - loss: 0.2399 

Epoch 65/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8000 - loss: 0.3610


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8587 - loss: 0.2858 

Epoch 66/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.2765


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8733 - loss: 0.2538 

Epoch 67/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.2910


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8920 - loss: 0.2451 

Epoch 68/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.3312


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8740 - loss: 0.2689 

Epoch 69/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2299


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8940 - loss: 0.2355 

Epoch 70/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9600 - loss: 0.1923


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9180 - loss: 0.2168 

Epoch 71/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2013


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8987 - loss: 0.2234 

Epoch 72/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.2411


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8893 - loss: 0.2404 

Epoch 73/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2432


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8993 - loss: 0.2341 

Epoch 74/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2276


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8973 - loss: 0.2304 

Epoch 75/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9400 - loss: 0.1721


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9153 - loss: 0.1939 

Epoch 76/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2196


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9100 - loss: 0.2219 

Epoch 77/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2161


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9053 - loss: 0.2083 

Epoch 78/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2166


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9200 - loss: 0.2059 

Epoch 79/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2306


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9120 - loss: 0.2175 

Epoch 80/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2422


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9140 - loss: 0.2115 

Epoch 81/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.2516


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9053 - loss: 0.2202 

Epoch 82/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9600 - loss: 0.1896


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9420 - loss: 0.1877 

Epoch 83/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9400 - loss: 0.1985


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9360 - loss: 0.1901 

Epoch 84/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9600 - loss: 0.1492


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9433 - loss: 0.1712 

Epoch 85/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2348


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9247 - loss: 0.2052 

Epoch 86/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9800 - loss: 0.1476


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9353 - loss: 0.1946 

Epoch 87/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.1980


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9127 - loss: 0.2029 

Epoch 88/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9600 - loss: 0.1275


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9367 - loss: 0.1699 

Epoch 89/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.1898


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9280 - loss: 0.1896 

Epoch 90/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 20ms/step - accuracy: 0.9600 - loss: 0.1462


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 6ms/step - accuracy: 0.9433 - loss: 0.1674 

Epoch 91/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 20ms/step - accuracy: 0.9400 - loss: 0.1790


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9293 - loss: 0.1926 

Epoch 92/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2391


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9267 - loss: 0.1899 

Epoch 93/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2247


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9140 - loss: 0.2045 

Epoch 94/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.1748


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9340 - loss: 0.1711 

Epoch 95/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.1674


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9280 - loss: 0.1785 

Epoch 96/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.1449


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9293 - loss: 0.1703 

Epoch 97/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2397


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9320 - loss: 0.1931 

Epoch 98/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.1801


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9253 - loss: 0.1679 

Epoch 99/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9400 - loss: 0.1344


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9413 - loss: 0.1516 

Epoch 100/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9400 - loss: 0.1812


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9420 - loss: 0.1693 

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

score = 0.15979984402656555

accuracy = 0.9399999976158142

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 31ms/step


1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 41ms/step

array([[6.9725087e-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 0x7f5c27f133d0>