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 = [0.21385531 0.31492504], 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

2024-04-24 14:38:56.895802: I external/local_tsl/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2024-04-24 14:38:56.898889: I external/local_tsl/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.
2024-04-24 14:38:56.933355: 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.

2024-04-24 14:38:57.894312: 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 487ms/step - accuracy: 0.6200 - loss: 0.6733


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - accuracy: 0.5780 - loss: 0.6772  

Epoch 2/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8000 - loss: 0.6241


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8320 - loss: 0.6227 

Epoch 3/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.6188


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8800 - loss: 0.5921 

Epoch 4/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8200 - loss: 0.5836


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8480 - loss: 0.5633 

Epoch 5/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.5233


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8640 - loss: 0.5276 

Epoch 6/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.5174


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8580 - loss: 0.5116 

Epoch 7/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9600 - loss: 0.4433


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8800 - loss: 0.4738 

Epoch 8/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7600 - loss: 0.5046


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8260 - loss: 0.4773 

Epoch 9/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.4360


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8587 - loss: 0.4438 

Epoch 10/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.7800 - loss: 0.4510


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8380 - loss: 0.4314 

Epoch 11/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.3620


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8833 - loss: 0.3917 

Epoch 12/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.4083


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8727 - loss: 0.4015 

Epoch 13/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.4120


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8660 - loss: 0.3842 

Epoch 14/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3621


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8747 - loss: 0.3593 

Epoch 15/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9400 - loss: 0.3210


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9040 - loss: 0.3399 

Epoch 16/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8000 - loss: 0.4369


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8613 - loss: 0.3613 

Epoch 17/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.4049


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8913 - loss: 0.3425 

Epoch 18/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2931


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8920 - loss: 0.3104 

Epoch 19/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8000 - loss: 0.3823


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8620 - loss: 0.3286 

Epoch 20/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3087


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8820 - loss: 0.3014 

Epoch 21/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2941


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9073 - loss: 0.2882 

Epoch 22/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.9000 - loss: 0.2945


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8967 - loss: 0.2920 

Epoch 23/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2365


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8967 - loss: 0.2824 

Epoch 24/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 14ms/step - accuracy: 0.8600 - loss: 0.3475


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8840 - loss: 0.3086 

Epoch 25/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2343


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9127 - loss: 0.2586 

Epoch 26/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.2075


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9060 - loss: 0.2664 

Epoch 27/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2718


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8987 - loss: 0.2830 

Epoch 28/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2911


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8927 - loss: 0.2767 

Epoch 29/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.2371


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9040 - loss: 0.2613 

Epoch 30/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9600 - loss: 0.1785


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9160 - loss: 0.2370 

Epoch 31/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2586


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8987 - loss: 0.2536 

Epoch 32/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2879


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8920 - loss: 0.2682 

Epoch 33/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.3297


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8907 - loss: 0.2855 

Epoch 34/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9800 - loss: 0.1365


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9307 - loss: 0.2100 

Epoch 35/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.3038


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8927 - loss: 0.2677 

Epoch 36/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.3094


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9013 - loss: 0.2641 

Epoch 37/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2323


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9073 - loss: 0.2421 

Epoch 38/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.2852


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8933 - loss: 0.2541 

Epoch 39/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3365


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8847 - loss: 0.2823 

Epoch 40/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2701


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9060 - loss: 0.2510 

Epoch 41/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2262


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9053 - loss: 0.2308 

Epoch 42/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.1616


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8993 - loss: 0.2263 

Epoch 43/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2751


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8960 - loss: 0.2540 

Epoch 44/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2234


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9013 - loss: 0.2408 

Epoch 45/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.3072


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8920 - loss: 0.2575 

Epoch 46/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2602


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9013 - loss: 0.2500 

Epoch 47/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.1736


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9127 - loss: 0.2150 

Epoch 48/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2583


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8880 - loss: 0.2591 

Epoch 49/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2139


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9087 - loss: 0.2161 

Epoch 50/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2298


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9120 - loss: 0.2195 

Epoch 51/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.1889


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9067 - loss: 0.2280 

Epoch 52/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2804


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8933 - loss: 0.2482 

Epoch 53/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9400 - loss: 0.1842


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9093 - loss: 0.2204 

Epoch 54/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.2276


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9173 - loss: 0.2312 

Epoch 55/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - accuracy: 0.8800 - loss: 0.2757


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8953 - loss: 0.2461 

Epoch 56/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2200


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9053 - loss: 0.2310 

Epoch 57/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2289


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9133 - loss: 0.2305 

Epoch 58/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.2179


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8827 - loss: 0.2449 

Epoch 59/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8400 - loss: 0.2911


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8867 - loss: 0.2434 

Epoch 60/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - accuracy: 0.8600 - loss: 0.2817


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8940 - loss: 0.2398 

Epoch 61/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.1877


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9107 - loss: 0.2015 

Epoch 62/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.1756


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9087 - loss: 0.2155 

Epoch 63/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2758


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8980 - loss: 0.2396 

Epoch 64/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9400 - loss: 0.1432


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9107 - loss: 0.1961 

Epoch 65/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2047


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9053 - loss: 0.2220 

Epoch 66/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2281


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9027 - loss: 0.2197 

Epoch 67/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.2770


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9100 - loss: 0.2461 

Epoch 68/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.3188


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8940 - loss: 0.2537 

Epoch 69/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.1679


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9160 - loss: 0.2106 

Epoch 70/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.2224


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9013 - loss: 0.2257 

Epoch 71/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9200 - loss: 0.1962


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9087 - loss: 0.2167 

Epoch 72/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.1913


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9140 - loss: 0.2185 

Epoch 73/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2129


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8973 - loss: 0.2240 

Epoch 74/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.2231


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9200 - loss: 0.2102 

Epoch 75/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2360


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9007 - loss: 0.2261 

Epoch 76/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9600 - loss: 0.1093


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9160 - loss: 0.1930 

Epoch 77/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.2313


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9027 - loss: 0.2193 

Epoch 78/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2704


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9027 - loss: 0.2254 

Epoch 79/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9800 - loss: 0.1013


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9253 - loss: 0.1898 

Epoch 80/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - accuracy: 0.8800 - loss: 0.2387


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9040 - loss: 0.2213 

Epoch 81/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8400 - loss: 0.3136


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8947 - loss: 0.2391 

Epoch 82/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9400 - loss: 0.1168


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9313 - loss: 0.1684 

Epoch 83/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.1785


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9067 - loss: 0.1993 

Epoch 84/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.3246


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9000 - loss: 0.2451 

Epoch 85/100

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


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9267 - loss: 0.2006 

Epoch 86/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9600 - loss: 0.1436


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9327 - loss: 0.1743 

Epoch 87/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8600 - loss: 0.2706


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9000 - loss: 0.2153 

Epoch 88/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.1973


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9093 - loss: 0.2070 

Epoch 89/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9800 - loss: 0.0740


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9460 - loss: 0.1487 

Epoch 90/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.1633


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9120 - loss: 0.1945 

Epoch 91/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 16ms/step - accuracy: 0.8800 - loss: 0.2347


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9020 - loss: 0.2166 

Epoch 92/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.9000 - loss: 0.1993


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9120 - loss: 0.1912 

Epoch 93/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.1515


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9227 - loss: 0.1738 

Epoch 94/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.1675


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9113 - loss: 0.1916 

Epoch 95/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8600 - loss: 0.2297


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.8973 - loss: 0.2050 

Epoch 96/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 13ms/step - accuracy: 0.8800 - loss: 0.2381


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9047 - loss: 0.2022 

Epoch 97/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.8800 - loss: 0.1928


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9067 - loss: 0.1841 

Epoch 98/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9000 - loss: 0.2738


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9160 - loss: 0.2097 

Epoch 99/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9400 - loss: 0.1382


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9233 - loss: 0.1732 

Epoch 100/100

1/4 ━━━━━━━━━━━━━━━━━━━━ 0s 12ms/step - accuracy: 0.9200 - loss: 0.1946


4/4 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - accuracy: 0.9233 - loss: 0.1866 

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

score = 0.18437233567237854
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 31ms/step


1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 32ms/step

array([[3.3693334e-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 0x7fbc183dc0d0>