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 = [0.19184908 0.00117974], 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

2025-03-24 20:53:13.555167: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2025-03-24 20:53:13.558389: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2025-03-24 20:53:13.566792: 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 00:00:1742849593.580562    3350 cuda_dnn.cc:8579] Unable to register cuDNN factory: Attempting to register factory for plugin cuDNN when one has already been registered
E0000 00:00:1742849593.584698    3350 cuda_blas.cc:1407] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered
W0000 00:00:1742849593.596631    3350 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
W0000 00:00:1742849593.596641    3350 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
W0000 00:00:1742849593.596642    3350 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
W0000 00:00:1742849593.596644    3350 computation_placer.cc:177] computation placer already registered. Please check linkage and avoid linking the same target more than once.
2025-03-24 20:53:13.600494: 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)
2025-03-24 20:53:15.335430: 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 424ms/step - accuracy: 0.3000 - loss: 0.7174


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.3913 - loss: 0.6959  

Epoch 2/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.5200 - loss: 0.6534


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.6547 - loss: 0.6410 

Epoch 3/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7800 - loss: 0.5873


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.7767 - loss: 0.5977 

Epoch 4/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.5804


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8087 - loss: 0.5844 

Epoch 5/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.5735


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8187 - loss: 0.5580 

Epoch 6/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.5372


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8280 - loss: 0.5296 

Epoch 7/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8000 - loss: 0.5339


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8233 - loss: 0.5231 

Epoch 8/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.4662


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8400 - loss: 0.4959 

Epoch 9/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.4977


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8267 - loss: 0.4892 

Epoch 10/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.4813


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8673 - loss: 0.4678 

Epoch 11/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.4579


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8407 - loss: 0.4625 

Epoch 12/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.4285


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8453 - loss: 0.4400 

Epoch 13/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.4180


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8380 - loss: 0.4253 

Epoch 14/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.4121


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8560 - loss: 0.4074 

Epoch 15/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.3928


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8520 - loss: 0.4128 

Epoch 16/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.4135


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8447 - loss: 0.3954 

Epoch 17/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.4159


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8607 - loss: 0.3927 

Epoch 18/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.3662


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8567 - loss: 0.3754 

Epoch 19/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7600 - loss: 0.4791


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8253 - loss: 0.4079 

Epoch 20/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.4161


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8400 - loss: 0.3856 

Epoch 21/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.4156


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8520 - loss: 0.3735 

Epoch 22/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.4025


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8447 - loss: 0.3722 

Epoch 23/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.3542


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8400 - loss: 0.3681 

Epoch 24/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.2726


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8620 - loss: 0.3307 

Epoch 25/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.4144


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8567 - loss: 0.3534 

Epoch 26/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.3075


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8460 - loss: 0.3426 

Epoch 27/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7800 - loss: 0.4328


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8387 - loss: 0.3641 

Epoch 28/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.3601


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8587 - loss: 0.3375 

Epoch 29/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.3839


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8553 - loss: 0.3390 

Epoch 30/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7800 - loss: 0.4116


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8340 - loss: 0.3550 

Epoch 31/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.3276


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8420 - loss: 0.3529 

Epoch 32/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.3547


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8600 - loss: 0.3281 

Epoch 33/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.3402


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8480 - loss: 0.3362 

Epoch 34/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.3111


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8500 - loss: 0.3254 

Epoch 35/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7800 - loss: 0.3854


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8247 - loss: 0.3598 

Epoch 36/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.3014


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8633 - loss: 0.3133 

Epoch 37/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.3254


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8440 - loss: 0.3391 

Epoch 38/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.2998


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8573 - loss: 0.3030 

Epoch 39/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.3385


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8553 - loss: 0.3324 

Epoch 40/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.3468


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8587 - loss: 0.3251 

Epoch 41/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.3552


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8500 - loss: 0.3371 

Epoch 42/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9400 - loss: 0.1915


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8767 - loss: 0.2894 

Epoch 43/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.2460


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8453 - loss: 0.3156 

Epoch 44/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9400 - loss: 0.1582


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8893 - loss: 0.2526 

Epoch 45/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.3199


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8493 - loss: 0.3261 

Epoch 46/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.3305


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8407 - loss: 0.3231 

Epoch 47/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2067


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8820 - loss: 0.2686 

Epoch 48/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.3548


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8553 - loss: 0.3147 

Epoch 49/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2631


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8673 - loss: 0.2995 

Epoch 50/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7800 - loss: 0.3554


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8220 - loss: 0.3487 

Epoch 51/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7800 - loss: 0.3962


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8387 - loss: 0.3240 

Epoch 52/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8000 - loss: 0.3505


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8313 - loss: 0.3307 

Epoch 53/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.2794


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8660 - loss: 0.2973 

Epoch 54/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2319


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8767 - loss: 0.2708 

Epoch 55/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.3370


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8427 - loss: 0.3208 

Epoch 56/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.1989


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8653 - loss: 0.2855 

Epoch 57/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.2794


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8573 - loss: 0.2884 

Epoch 58/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7800 - loss: 0.3651


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8380 - loss: 0.3130 

Epoch 59/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.3458


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8440 - loss: 0.3304 

Epoch 60/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2293


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8893 - loss: 0.2637 

Epoch 61/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2702


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8627 - loss: 0.3043 

Epoch 62/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.2415


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8627 - loss: 0.2753 

Epoch 63/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.3085


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8667 - loss: 0.2817 

Epoch 64/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7600 - loss: 0.4251


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8400 - loss: 0.3206 

Epoch 65/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8000 - loss: 0.3562


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8507 - loss: 0.3012 

Epoch 66/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.3070


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

Epoch 67/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.2515


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8680 - loss: 0.2767 

Epoch 68/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.3503


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8560 - loss: 0.3067 

Epoch 69/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2228


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8807 - loss: 0.2641 

Epoch 70/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.3773


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8553 - loss: 0.3063 

Epoch 71/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.2401


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

Epoch 72/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.2669


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8760 - loss: 0.2693 

Epoch 73/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7800 - loss: 0.4400


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8347 - loss: 0.3301 

Epoch 74/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.3553


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8513 - loss: 0.3003 

Epoch 75/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.2937


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8500 - loss: 0.2823 

Epoch 76/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.2960


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8760 - loss: 0.2803 

Epoch 77/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.3676


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8613 - loss: 0.3081 

Epoch 78/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2373


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.9033 - loss: 0.2442 

Epoch 79/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9800 - loss: 0.1671


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.9093 - loss: 0.2372 

Epoch 80/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.1974


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8920 - loss: 0.2421 

Epoch 81/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.2881


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8780 - loss: 0.2729 

Epoch 82/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.2472


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8700 - loss: 0.2652 

Epoch 83/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.3100


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8827 - loss: 0.2798 

Epoch 84/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.1602


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8753 - loss: 0.2395 

Epoch 85/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.2909


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8733 - loss: 0.2778 

Epoch 86/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2338


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8860 - loss: 0.2557 

Epoch 87/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2400


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8913 - loss: 0.2538 

Epoch 88/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.2887


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8820 - loss: 0.2587 

Epoch 89/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2557


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8987 - loss: 0.2446 

Epoch 90/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.3177


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8900 - loss: 0.2713 

Epoch 91/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9600 - loss: 0.1487


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9107 - loss: 0.2257 

Epoch 92/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.2281


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8820 - loss: 0.2551 

Epoch 93/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2046


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9100 - loss: 0.2240 

Epoch 94/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.3238


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8927 - loss: 0.2599 

Epoch 95/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.2608


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 4ms/step - accuracy: 0.8920 - loss: 0.2463 

Epoch 96/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9400 - loss: 0.2109


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9093 - loss: 0.2304 

Epoch 97/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2382


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9147 - loss: 0.2314 

Epoch 98/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.1824


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9047 - loss: 0.2262 

Epoch 99/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9400 - loss: 0.1931


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9200 - loss: 0.2288 

Epoch 100/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2371


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9033 - loss: 0.2593 

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

score = 0.23693643510341644
accuracy = 0.9100000262260437

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([[2.2736137e-06]], 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 0x7f1d1d76a350>