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 = [-0.19114745  1.0553034 ], 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

2025-02-18 13:19:43.867815: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2025-02-18 13:19:43.871025: I external/local_xla/xla/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2025-02-18 13:19:43.877568: 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 00:00:1739884783.891087    3393 cuda_dnn.cc:8310] Unable to register cuDNN factory: Attempting to register factory for plugin cuDNN when one has already been registered
E0000 00:00:1739884783.895284    3393 cuda_blas.cc:1418] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered
2025-02-18 13:19:43.911364: 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)
2025-02-18 13:19:45.547668: 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 639ms/step - accuracy: 0.4200 - loss: 0.7097


4/4 ━━━━━━━━━━━━━━━━━━━━ 1s 6ms/step - accuracy: 0.5093 - loss: 0.6938  

Epoch 2/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.7800 - loss: 0.6584


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8227 - loss: 0.6502 

Epoch 3/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8200 - loss: 0.6316


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8033 - loss: 0.6258 

Epoch 4/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8000 - loss: 0.5993


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8107 - loss: 0.6012 

Epoch 5/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.5766


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8360 - loss: 0.5773 

Epoch 6/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.5426


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8527 - loss: 0.5538 

Epoch 7/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.9000 - loss: 0.5244


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8513 - loss: 0.5398 

Epoch 8/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8200 - loss: 0.5396


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8340 - loss: 0.5301 

Epoch 9/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8000 - loss: 0.5198


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8267 - loss: 0.5144 

Epoch 10/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.8400 - loss: 0.4845


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8420 - loss: 0.4921 

Epoch 11/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.4424


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8767 - loss: 0.4608 

Epoch 12/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.7800 - loss: 0.4923


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8160 - loss: 0.4769 

Epoch 13/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.3933


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8747 - loss: 0.4330 

Epoch 14/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.4376


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8440 - loss: 0.4358 

Epoch 15/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.4375


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8540 - loss: 0.4258 

Epoch 16/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.8200 - loss: 0.4161


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8540 - loss: 0.4036 

Epoch 17/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.4097


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8607 - loss: 0.4075 

Epoch 18/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 22ms/step - accuracy: 0.9400 - loss: 0.3484


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8887 - loss: 0.3768 

Epoch 19/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.3488


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8620 - loss: 0.3776 

Epoch 20/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.3437


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8740 - loss: 0.3638 

Epoch 21/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.3177


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8873 - loss: 0.3487 

Epoch 22/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2874


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8807 - loss: 0.3463 

Epoch 23/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3904


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8613 - loss: 0.3640 

Epoch 24/100

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


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8633 - loss: 0.3489 

Epoch 25/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8000 - loss: 0.4066


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8620 - loss: 0.3469 

Epoch 26/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.8600 - loss: 0.4023


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8653 - loss: 0.3502 

Epoch 27/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.7800 - loss: 0.4256


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8347 - loss: 0.3657 

Epoch 28/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.2335


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8953 - loss: 0.3023 

Epoch 29/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2448


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9007 - loss: 0.2809 

Epoch 30/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2909


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8840 - loss: 0.3075 

Epoch 31/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2988


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9000 - loss: 0.2923 

Epoch 32/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2889


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8927 - loss: 0.2971 

Epoch 33/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.3479


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9000 - loss: 0.3011 

Epoch 34/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2947


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8907 - loss: 0.3061 

Epoch 35/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2322


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8927 - loss: 0.2796 

Epoch 36/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.8800 - loss: 0.3602


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8953 - loss: 0.3072 

Epoch 37/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.2167


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9033 - loss: 0.2732 

Epoch 38/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.1798


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8953 - loss: 0.2709 

Epoch 39/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.8800 - loss: 0.2883


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8887 - loss: 0.2837 

Epoch 40/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3468


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8920 - loss: 0.2883 

Epoch 41/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3508


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8767 - loss: 0.3222 

Epoch 42/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 15ms/step - accuracy: 0.9400 - loss: 0.1979


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9053 - loss: 0.2599 

Epoch 43/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.3590


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8800 - loss: 0.3164 

Epoch 44/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.3105


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8853 - loss: 0.3090 

Epoch 45/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.9400 - loss: 0.2643


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9033 - loss: 0.2900 

Epoch 46/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8200 - loss: 0.3549


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8747 - loss: 0.3044 

Epoch 47/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.9000 - loss: 0.2224


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8947 - loss: 0.2753 

Epoch 48/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2372


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8900 - loss: 0.2632 

Epoch 49/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2951


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9060 - loss: 0.2773 

Epoch 50/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.1934


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9107 - loss: 0.2425 

Epoch 51/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.4069


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8787 - loss: 0.3155 

Epoch 52/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - accuracy: 0.9600 - loss: 0.1919


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9213 - loss: 0.2422 

Epoch 53/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.9600 - loss: 0.1570


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9253 - loss: 0.2206 

Epoch 54/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2497


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8987 - loss: 0.2755 

Epoch 55/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.9200 - loss: 0.2542


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9013 - loss: 0.2740 

Epoch 56/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.2032


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9100 - loss: 0.2574 

Epoch 57/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2899


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8873 - loss: 0.2793 

Epoch 58/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.3499


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9000 - loss: 0.2894 

Epoch 59/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8200 - loss: 0.3521


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8760 - loss: 0.2928 

Epoch 60/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.2451


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9093 - loss: 0.2608 

Epoch 61/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9600 - loss: 0.1887


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9173 - loss: 0.2446 

Epoch 62/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.3169


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8953 - loss: 0.2696 

Epoch 63/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.3606


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8927 - loss: 0.2955 

Epoch 64/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2657


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9033 - loss: 0.2483 

Epoch 65/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3822


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8773 - loss: 0.3082 

Epoch 66/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.8800 - loss: 0.3476


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8960 - loss: 0.2847 

Epoch 67/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.9000 - loss: 0.2647


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8940 - loss: 0.2605 

Epoch 68/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.9200 - loss: 0.2150


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9080 - loss: 0.2341 

Epoch 69/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.9200 - loss: 0.2098


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9027 - loss: 0.2482 

Epoch 70/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.9200 - loss: 0.2153


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8960 - loss: 0.2565 

Epoch 71/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.9000 - loss: 0.2435


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8960 - loss: 0.2538 

Epoch 72/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.8800 - loss: 0.3073


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8860 - loss: 0.2831 

Epoch 73/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3113


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8820 - loss: 0.2741 

Epoch 74/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.3313


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9007 - loss: 0.2719 

Epoch 75/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.9000 - loss: 0.2511


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9087 - loss: 0.2359 

Epoch 76/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2783


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8927 - loss: 0.2680 

Epoch 77/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9600 - loss: 0.1627


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9247 - loss: 0.2249 

Epoch 78/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2205


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9047 - loss: 0.2507 

Epoch 79/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9600 - loss: 0.1566


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9273 - loss: 0.2135 

Epoch 80/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.8800 - loss: 0.3042


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9040 - loss: 0.2616 

Epoch 81/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3803


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8827 - loss: 0.2840 

Epoch 82/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2046


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9040 - loss: 0.2427 

Epoch 83/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2668


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9053 - loss: 0.2653 

Epoch 84/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3464


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 8ms/step - accuracy: 0.8927 - loss: 0.2841 

Epoch 85/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.1589


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9160 - loss: 0.2185 

Epoch 86/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.9000 - loss: 0.2996


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8967 - loss: 0.2758 

Epoch 87/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2554


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9013 - loss: 0.2469 

Epoch 88/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.8800 - loss: 0.2475


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8940 - loss: 0.2534 

Epoch 89/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3613


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8847 - loss: 0.2852 

Epoch 90/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3279


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.8927 - loss: 0.2784 

Epoch 91/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2437


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9100 - loss: 0.2456 

Epoch 92/100

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


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9073 - loss: 0.2452 

Epoch 93/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2034


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9100 - loss: 0.2369 

Epoch 94/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9600 - loss: 0.1699


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9233 - loss: 0.2237 

Epoch 95/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.1942


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9107 - loss: 0.2192 

Epoch 96/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2670


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9040 - loss: 0.2651 

Epoch 97/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2470


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9020 - loss: 0.2321 

Epoch 98/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2356


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9193 - loss: 0.2315 

Epoch 99/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2910


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9053 - loss: 0.2491 

Epoch 100/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2176


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 5ms/step - accuracy: 0.9067 - loss: 0.2420 

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

score = 0.23782259225845337
accuracy = 0.9150000214576721

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 33ms/step


1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 44ms/step

array([[6.096349e-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 0x7fb7105e3390>