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 = [ 0.35126733 -0.54064295], 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

2024-07-19 13:39:26.042014: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2024-07-19 13:39:26.045098: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2024-07-19 13:39:26.051914: E external/local_xla/xla/stream_executor/cuda/cuda_fft.cc:485] Unable to register cuFFT factory: Attempting to register factory for plugin cuFFT when one has already been registered
2024-07-19 13:39:26.064689: E external/local_xla/xla/stream_executor/cuda/cuda_dnn.cc:8454] Unable to register cuDNN factory: Attempting to register factory for plugin cuDNN when one has already been registered
2024-07-19 13:39:26.068766: E external/local_xla/xla/stream_executor/cuda/cuda_blas.cc:1452] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered
2024-07-19 13:39:26.080047: 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.

2024-07-19 13:39:27.110531: W tensorflow/compiler/tf2tensorrt/utils/py_utils.cc:38] TF-TRT Warning: Could not find TensorRT

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/3.11.9/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)

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 474ms/step - accuracy: 0.2400 - loss: 0.7196


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - accuracy: 0.4607 - loss: 0.6982  

Epoch 2/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.7400 - loss: 0.6474


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - accuracy: 0.7360 - loss: 0.6454 

Epoch 3/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.7800 - loss: 0.6283


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.7907 - loss: 0.6196 

Epoch 4/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.7400 - loss: 0.6028


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.7867 - loss: 0.5919 

Epoch 5/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.7400 - loss: 0.6026


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.7860 - loss: 0.5807 

Epoch 6/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 15ms/step - accuracy: 0.8200 - loss: 0.5472


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8080 - loss: 0.5516 

Epoch 7/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8000 - loss: 0.5380


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8067 - loss: 0.5399 

Epoch 8/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - accuracy: 0.8000 - loss: 0.5382


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.7987 - loss: 0.5311 

Epoch 9/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.4737


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8380 - loss: 0.4959 

Epoch 10/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.4766


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8107 - loss: 0.4931 

Epoch 11/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8000 - loss: 0.4920


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.7980 - loss: 0.4837 

Epoch 12/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 15ms/step - accuracy: 0.8200 - loss: 0.4857


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8120 - loss: 0.4764 

Epoch 13/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7800 - loss: 0.4512


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.7987 - loss: 0.4499 

Epoch 14/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.4341


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8133 - loss: 0.4430 

Epoch 15/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.7800 - loss: 0.4494


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8013 - loss: 0.4369 

Epoch 16/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7800 - loss: 0.4121


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.7973 - loss: 0.4222 

Epoch 17/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7600 - loss: 0.4444


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8027 - loss: 0.4172 

Epoch 18/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 15ms/step - accuracy: 0.8200 - loss: 0.4128


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8160 - loss: 0.4048 

Epoch 19/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.3032


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8540 - loss: 0.3599 

Epoch 20/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.3437


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8347 - loss: 0.3721 

Epoch 21/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3424


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8413 - loss: 0.3550 

Epoch 22/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.3858


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8340 - loss: 0.3687 

Epoch 23/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.3348


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8333 - loss: 0.3522 

Epoch 24/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.3047


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8580 - loss: 0.3467 

Epoch 25/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2999


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8767 - loss: 0.3250 

Epoch 26/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2990


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8893 - loss: 0.3064 

Epoch 27/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.3480


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8533 - loss: 0.3305 

Epoch 28/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7800 - loss: 0.3966


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8287 - loss: 0.3475 

Epoch 29/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8200 - loss: 0.3340


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8473 - loss: 0.3103 

Epoch 30/100

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


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8787 - loss: 0.2828 

Epoch 31/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2914


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8700 - loss: 0.2998 

Epoch 32/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.2620


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8720 - loss: 0.2895 

Epoch 33/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.2565


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8600 - loss: 0.2832 

Epoch 34/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.3064


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8507 - loss: 0.3067 

Epoch 35/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.2666


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8660 - loss: 0.2697 

Epoch 36/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2295


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8733 - loss: 0.2767 

Epoch 37/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.3461


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8707 - loss: 0.3060 

Epoch 38/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.3617


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8767 - loss: 0.2899 

Epoch 39/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2544


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8940 - loss: 0.2810 

Epoch 40/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2829


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8940 - loss: 0.2720 

Epoch 41/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2513


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8840 - loss: 0.2706 

Epoch 42/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2964


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8980 - loss: 0.2746 

Epoch 43/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.2813


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8887 - loss: 0.2787 

Epoch 44/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9400 - loss: 0.2071


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9160 - loss: 0.2373 

Epoch 45/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9400 - loss: 0.2344


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9120 - loss: 0.2548 

Epoch 46/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9400 - loss: 0.1984


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9093 - loss: 0.2387 

Epoch 47/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2441


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9087 - loss: 0.2468 

Epoch 48/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2529


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8993 - loss: 0.2633 

Epoch 49/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2420


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9013 - loss: 0.2528 

Epoch 50/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2599


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

Epoch 51/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2301


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8927 - loss: 0.2573 

Epoch 52/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2607


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9220 - loss: 0.2442 

Epoch 53/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.1554


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9233 - loss: 0.2107 

Epoch 54/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2022


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9200 - loss: 0.2191 

Epoch 55/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2208


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9073 - loss: 0.2273 

Epoch 56/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2902


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9067 - loss: 0.2561 

Epoch 57/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.1974


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9120 - loss: 0.2320 

Epoch 58/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - accuracy: 0.9400 - loss: 0.2042


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9140 - loss: 0.2296 

Epoch 59/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.9000 - loss: 0.2545


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9093 - loss: 0.2387 

Epoch 60/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2416


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9047 - loss: 0.2326 

Epoch 61/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.1943


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9253 - loss: 0.1954 

Epoch 62/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.1960


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9180 - loss: 0.2214 

Epoch 63/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9600 - loss: 0.1940


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9233 - loss: 0.2185 

Epoch 64/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9600 - loss: 0.1781


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9273 - loss: 0.2051 

Epoch 65/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9800 - loss: 0.1320


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9340 - loss: 0.2000 

Epoch 66/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2620


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9020 - loss: 0.2398 

Epoch 67/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2592


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9067 - loss: 0.2482 

Epoch 68/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2795


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9207 - loss: 0.2478 

Epoch 69/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.1421


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9207 - loss: 0.2061 

Epoch 70/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9400 - loss: 0.2296


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9333 - loss: 0.2171 

Epoch 71/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2588


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9227 - loss: 0.2288 

Epoch 72/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2594


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9167 - loss: 0.2280 

Epoch 73/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.8600 - loss: 0.3217


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8960 - loss: 0.2544 

Epoch 74/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.1904


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 2ms/step - accuracy: 0.9360 - loss: 0.1983 

Epoch 75/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 15ms/step - accuracy: 0.9000 - loss: 0.2389


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9173 - loss: 0.2295 

Epoch 76/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2304


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9273 - loss: 0.2080 

Epoch 77/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9600 - loss: 0.1908


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9367 - loss: 0.2007 

Epoch 78/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2308


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9207 - loss: 0.2093 

Epoch 79/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.2661


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9160 - loss: 0.2148 

Epoch 80/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.1689


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9273 - loss: 0.1999 

Epoch 81/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9400 - loss: 0.1918


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9380 - loss: 0.1946 

Epoch 82/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9400 - loss: 0.1460


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9280 - loss: 0.1838 

Epoch 83/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - accuracy: 0.8200 - loss: 0.3861


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9020 - loss: 0.2591 

Epoch 84/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9400 - loss: 0.1969


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9233 - loss: 0.1988 

Epoch 85/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2049


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9253 - loss: 0.1968 

Epoch 86/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.1894


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9240 - loss: 0.1927 

Epoch 87/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2660


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9320 - loss: 0.2063 

Epoch 88/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9800 - loss: 0.1613


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9360 - loss: 0.1890 

Epoch 89/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9600 - loss: 0.1351


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9340 - loss: 0.1845 

Epoch 90/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.1590


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9313 - loss: 0.1944 

Epoch 91/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2894


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9333 - loss: 0.2106 

Epoch 92/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9400 - loss: 0.2122


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9307 - loss: 0.1891 

Epoch 93/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9400 - loss: 0.1641


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9273 - loss: 0.1911 

Epoch 94/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2259


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9293 - loss: 0.2005 

Epoch 95/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9600 - loss: 0.1381


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9440 - loss: 0.1659 

Epoch 96/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.1776


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9300 - loss: 0.1868 

Epoch 97/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9400 - loss: 0.2006


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9387 - loss: 0.1959 

Epoch 98/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.1648


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9320 - loss: 0.1789 

Epoch 99/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.1473


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9407 - loss: 0.1556 

Epoch 100/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9600 - loss: 0.1485


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9440 - loss: 0.1649 

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

score = 0.17566385865211487
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 34ms/step


1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 34ms/step

array([[9.303708e-08]], 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 0x7f1868b8d790>