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 = [-0.4074968   0.45431147], 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 Dense, Dropout, Activation
from tensorflow.keras.optimizers import RMSprop

2025-04-20 21:56:53.770806: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2025-04-20 21:56:53.774153: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2025-04-20 21:56:53.782957: 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 00:00:1745186213.797305    3397 cuda_dnn.cc:8579] Unable to register cuDNN factory: Attempting to register factory for plugin cuDNN when one has already been registered
E0000 00:00:1745186213.801627    3397 cuda_blas.cc:1407] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered
W0000 00:00:1745186213.813931    3397 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
W0000 00:00:1745186213.813948    3397 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
W0000 00:00:1745186213.813950    3397 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
W0000 00:00:1745186213.813952    3397 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
2025-04-20 21:56:53.818909: 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/3.11.12/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)
2025-04-20 21:56:55.698840: 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 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 630ms/step - accuracy: 0.3400 - loss: 0.7226


4/4 ━━━━━━━━━━━━━━━━━━━━ 1s 6ms/step - accuracy: 0.4627 - loss: 0.7059  

Epoch 2/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.7400 - loss: 0.6624


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.7560 - loss: 0.6571 

Epoch 3/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.6210


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8573 - loss: 0.6230 

Epoch 4/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.8200 - loss: 0.6129


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8380 - loss: 0.6026 

Epoch 5/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.5692


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8840 - loss: 0.5739 

Epoch 6/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.5630


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8647 - loss: 0.5546 

Epoch 7/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8000 - loss: 0.5562


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8407 - loss: 0.5365 

Epoch 8/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.5221


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8527 - loss: 0.5182 

Epoch 9/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.7600 - loss: 0.5375


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8247 - loss: 0.5068 

Epoch 10/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9600 - loss: 0.4503


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8887 - loss: 0.4651 

Epoch 11/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.4645


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8420 - loss: 0.4696 

Epoch 12/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.4413


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8687 - loss: 0.4438 

Epoch 13/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.4360


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8553 - loss: 0.4304 

Epoch 14/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8000 - loss: 0.4466


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8287 - loss: 0.4350 

Epoch 15/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.3861


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8533 - loss: 0.4086 

Epoch 16/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.4108


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8567 - loss: 0.4011 

Epoch 17/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.3485


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8587 - loss: 0.3857 

Epoch 18/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.3795


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8633 - loss: 0.3749 

Epoch 19/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8000 - loss: 0.4115


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8413 - loss: 0.3741 

Epoch 20/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.3100


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8607 - loss: 0.3481 

Epoch 21/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3951


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8467 - loss: 0.3729 

Epoch 22/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8200 - loss: 0.4095


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8493 - loss: 0.3664 

Epoch 23/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.7800 - loss: 0.4421


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8333 - loss: 0.3738 

Epoch 24/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2908


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8700 - loss: 0.3109 

Epoch 25/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.7200 - loss: 0.4961


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8193 - loss: 0.3787 

Epoch 26/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3474


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8567 - loss: 0.3297 

Epoch 27/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2642


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8707 - loss: 0.3073 

Epoch 28/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3684


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8593 - loss: 0.3362 

Epoch 29/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3448


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8600 - loss: 0.3242 

Epoch 30/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2582


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8680 - loss: 0.2905 

Epoch 31/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2781


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8767 - loss: 0.2924 

Epoch 32/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8200 - loss: 0.3800


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8487 - loss: 0.3297 

Epoch 33/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3161


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8733 - loss: 0.2964 

Epoch 34/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3274


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8533 - loss: 0.3189 

Epoch 35/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.3093


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8680 - loss: 0.3059 

Epoch 36/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2660


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8887 - loss: 0.2831 

Epoch 37/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8200 - loss: 0.3452


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8467 - loss: 0.3211 

Epoch 38/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8200 - loss: 0.3301


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8540 - loss: 0.3123 

Epoch 39/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8000 - loss: 0.3289


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8473 - loss: 0.3016 

Epoch 40/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.8800 - loss: 0.2595


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8693 - loss: 0.2839 

Epoch 41/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.2152


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8933 - loss: 0.2622 

Epoch 42/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3074


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8733 - loss: 0.3018 

Epoch 43/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2037


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8827 - loss: 0.2822 

Epoch 44/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.7800 - loss: 0.4109


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8507 - loss: 0.3231 

Epoch 45/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2973


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8887 - loss: 0.2910 

Epoch 46/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2647


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8767 - loss: 0.2940 

Epoch 47/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8000 - loss: 0.3720


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8527 - loss: 0.3111 

Epoch 48/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3523


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8700 - loss: 0.2997 

Epoch 49/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3135


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8760 - loss: 0.2930 

Epoch 50/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8000 - loss: 0.3925


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8560 - loss: 0.3159 

Epoch 51/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3496


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8720 - loss: 0.2974 

Epoch 52/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3174


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8713 - loss: 0.2805 

Epoch 53/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2314


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8780 - loss: 0.2678 

Epoch 54/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.1890


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9027 - loss: 0.2461 

Epoch 55/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8200 - loss: 0.3423


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8640 - loss: 0.2872 

Epoch 56/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8000 - loss: 0.3982


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8607 - loss: 0.3067 

Epoch 57/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2860


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8833 - loss: 0.2668 

Epoch 58/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3309


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8813 - loss: 0.2806 

Epoch 59/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2348


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8787 - loss: 0.2695 

Epoch 60/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3041


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8713 - loss: 0.2716 

Epoch 61/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2623


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8840 - loss: 0.2615 

Epoch 62/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.9200 - loss: 0.1970


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8940 - loss: 0.2421 

Epoch 63/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2486


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8840 - loss: 0.2682 

Epoch 64/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2542


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8907 - loss: 0.2617 

Epoch 65/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2662


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8973 - loss: 0.2502 

Epoch 66/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.9000 - loss: 0.2514


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8880 - loss: 0.2590 

Epoch 67/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2778


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8833 - loss: 0.2601 

Epoch 68/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2321


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8880 - loss: 0.2367 

Epoch 69/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2030


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8880 - loss: 0.2378 

Epoch 70/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2166


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8813 - loss: 0.2435 

Epoch 71/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3159


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8720 - loss: 0.2759 

Epoch 72/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.1689


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8973 - loss: 0.2255 

Epoch 73/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.1994


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8920 - loss: 0.2245 

Epoch 74/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.2027


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9080 - loss: 0.2230 

Epoch 75/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8200 - loss: 0.3611


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8647 - loss: 0.2761 

Epoch 76/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.1608


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9007 - loss: 0.2192 

Epoch 77/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.9200 - loss: 0.2143


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8973 - loss: 0.2300 

Epoch 78/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.1962


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8900 - loss: 0.2308 

Epoch 79/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2033


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8847 - loss: 0.2376 

Epoch 80/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.8600 - loss: 0.2770


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8733 - loss: 0.2520 

Epoch 81/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2306


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8800 - loss: 0.2366 

Epoch 82/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3021


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8720 - loss: 0.2593 

Epoch 83/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.2315


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8807 - loss: 0.2299 

Epoch 84/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8200 - loss: 0.2864


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8740 - loss: 0.2439 

Epoch 85/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.2382


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8773 - loss: 0.2300 

Epoch 86/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2052


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9067 - loss: 0.2033 

Epoch 87/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2090


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8880 - loss: 0.2217 

Epoch 88/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.1603


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8800 - loss: 0.2262 

Epoch 89/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2331


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8933 - loss: 0.2232 

Epoch 90/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.1650


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9013 - loss: 0.2001 

Epoch 91/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.1966


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8847 - loss: 0.2199 

Epoch 92/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.2286


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8773 - loss: 0.2146 

Epoch 93/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2204


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8893 - loss: 0.2139 

Epoch 94/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.1826


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8933 - loss: 0.2090 

Epoch 95/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2504


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8987 - loss: 0.2162 

Epoch 96/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.2478


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8933 - loss: 0.2194 

Epoch 97/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.1683


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9047 - loss: 0.1946 

Epoch 98/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2502


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9047 - loss: 0.2175 

Epoch 99/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.2105


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9173 - loss: 0.2032 

Epoch 100/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2517


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9080 - loss: 0.2205 

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

score = 0.19891922175884247
accuracy = 0.9200000166893005

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 42ms/step

array([[1.4592869e-05]], 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 0x7fca0dbd6510>