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Multivariate Regression and Classification Using an Adaptive Neuro-Fuzzy Inference System (Takagi-Sugeno) and Particle Swarm Optimization

Features

  • The code has been written in C++ using the Eigen library (ver. 3.4.0) and tested using g++ 11.2.0 in MinGW-W64 9.0.0-r1.
  • Multi-input/multi-output (multivariate) adaptive neuro-fuzzy inference system (ANFIS) implementation for regression and classification.
  • Quadratic cost function for continuous problems and cross-entropy cost function for classification problems.
  • Classes in classification problems can be determined automatically.
  • Sigmoid and cross-entropy function are computed using a numerically stable implementation.
  • Generalized Bell curves depending on three parameters (mean, standard deviation, and exponent) are used as premise membership functions.
  • Hyperplanes depending on the number of features are used as consequent functions.
  • A population-based particle swarm optimizer (PSO) is used to solve the minimization problem.
  • Limits/constraints on the parameter values (similar to regularization in neural networks) can be easily done through the PSO boundary arrays.
  • The ANFIS class is not constrained to the PSO solver but it can be easily adapted to any other optimizer not gradient-based.
  • File utils.cpp consists of several helper functions.
  • Included are also helper functions to build the SA boundary arrays and to build classes in classifications problems.
  • Usage: test.exe example.

Main Parameters

example Name of the example to run (plant, stock, wine, pulsar.)

classification Defines the type of problem, with true specifying a classification problem.

split_factor Split value between training and test data.

data_file File name with the dataset (comma separated format).

n_mf Array with the number of premise functions of each feature. Its lenght must be the same as the number of features.

nPop, epochs Number of agents (population) and number of iterations.

mu_delta Allowed variation (plus/minus) of the mean in the premise functions. It is given as fraction of the corresponding feature data range.

s_par Center value and allowed variation (plus/minus) of the standard deviation in the premise functions. The center value is scaled based on the corresponding feature data range.

c_par Range of allowed values of the exponent in the premise functions.

A_par Range of allowed values of the coefficients in the consequent functions.

tol Tolerance used to group classes in classification problems.

agents Array of agents used by the SA solver. Each agent is one ANFIS instance.

See file pso.cpp for the meaning of the other quantities defined in structure p.

Examples

There are four examples in test.cpp: plant, stock, wine, pulsar.

plant (single-label regression problem):

stock (multi-label regression problem):

wine (multi-class classification problem):

  • The dataset has 2 features (inputs), 6 classes (outputs), and 1599 samples.

  • The ANFIS has a layout of [3, 2] and 123 variables.

  • Predicted/actual accuracy values: 59.8% (training), 54.4% (test).

  • Original dataset: https://archive.ics.uci.edu/ml/datasets/Wine+Quality.

pulsar (two-class classification problem):

  • The dataset has 3 features (inputs), 2 classes (outputs), and 17898 samples.

  • The ANFIS has a layout of [3, 4, 2] and 219 variables.

  • Predicted/actual accuracy values: 97.9% (training), 97.7% (test).

  • Original dataset: https://archive.ics.uci.edu/ml/datasets/HTRU2.

References