KerasFuzzy: A Jupyter Notebook repository from nrahulreddy

Main goal of this project is to provide trainable representations of real-word input data to regular neural networks. There are two classes implemented so far: FuzzyLayer and DefuzzyLayer.

FuzzyLayer

This layer is suitable for cases when you working with data that can be clustered into interpretable groups e.g. spatial coordinates, multi-function values and etc.

Membership function for this layer have form:

$\mu_{{j}} \left( x,c,a \right) ={e}^{-\sum _{i=0}^{\dim}1/4\,{\frac { \left( x_{{i}}-c_{{i}} \right) ^{2}}{{a_{{i}}}^{2}}}}$

where x is an input vector of dim length, c is centroid of j-th membership function and a is vector of scaling factors.

DefuzzyLayer

DefuzzyLayer can be trained to transform output of an model to continuos values. In other words this layer can be interpreted as an ruleset and input to this layer - firing levels for rules.

$d \left( x,r \right) =\sum _{i=0}^{{\it input\_dim}}x_{{i}}r_{{i}}$

FuzzyLayer 2

Membership function for layer FuzzyLayer2 have form $\mu(x, A) = e^{ -|| [A . ~x]_{1 \cdots m} ||^2}$ where $m$ is task dimension, $A$ is transformation matrix in form

$$A_{(m+1) \times (m+1)} = \left[ {\begin{array}{cccc} s_{1} & a_{12} & \cdots & a_{1m} & c_{1}\\\ a_{21} & s_{2} & \cdots & a_{2m} & c_{2}\\\ \vdots & \vdots & \ddots & \vdots & c_{3}\\\ a_{m1} & a_{m2} & \cdots & s_{m} & c_{m}\\\ 0 & 0 & \cdots & 0 & 1\\\ \end{array} } \right]$$

with $c_{1\cdots m}$ - centroid, $s_{1\cdots m}$ - scaling factor, $a_{1\cdots m, 1\cdots m}$ - alignment coefficients and $x$ is an extended with $1$ vector $x = [x_1, x_2, \cdots, x_m, 1]$.

Main benefit of FuzzyLayer2 over FuzzyLayer is that fuzzy centroids are aligned in arbitrary direction to cover cluster structures more preciesly.

Basic sample

import keras
from FuzzyLayer import FuzzyLayer
from DefuzzyLayer import DefuzzyLayer
from keras.models import Sequential

...

model = Sequential()
model.add(FuzzyLayer(20, input_dim=2))
model.add(DefuzzyLayer(1))

model.compile(loss='logcosh',
              optimizer='rmsprop',
              metrics=['mae'])

model.fit(x_train, y_train,
          epochs=500,
          verbose=1,
          batch_size=100)

MNIST classification with neuro-fuzzy model

latent_dim = 3

mnist_inputs = keras.Input(shape=(28, 28, 1))
x = layers.Conv2D(64, 3, activation="relu", padding="same")(mnist_inputs)
x = layers.Conv2D(64, 3, activation="relu", padding="same")(x)
x = layers.Conv2D(32, 5, activation="relu", strides=2, padding="same")(x)
shape_before_flattening = K.int_shape(x)
x = layers.Flatten()(x)
z = layers.Dense(latent_dim, name="z")(x)
base_model = keras.Model(mnist_inputs, z)

x = base_model(mnist_inputs)
x = FuzzyLayer2(10, name="fuzzy")(x)
x = DefuzzyLayer(10, name="defuzzy")(x)
x = tf.keras.layers.Softmax()(x)
fuzzy_model = keras.Model(mnist_inputs, x)

Accuracy achieved by training fuzzy_model is about 0.995 and presented model has nice clustered latent layer z structure:

Usage examples

MNIST fuzzy anomaly detection with VAE

MNIST fuzzy anomaly detection with CVAE