Rosangela Ballini

Evolving fuzzy granular modeling from nonstationary fuzzy data streams

Evolving granular modeling is an approach that considers online granular data stream processing and structurally adaptive rule-based models. As uncertain data prevail in stream applications, excessive data granularity becomes unnecessary and inefficient. This paper introduces an evolving fuzzy granular framework to learn from and model time-varying fuzzy input–output data streams. The fuzzy-set based evolving modeling framework consists of a one-pass learning algorithm capable to gradually develop the structure of rule-based models. This framework is particularly suitable to handle potentially unbounded fuzzy data streams and render singular and granular approximations of nonstationary functions. The main objective of this paper is to shed light into the role of evolving fuzzy granular computing in providing high-quality approximate solutions from large volumes of real-world online data streams. An application example in weather temperature prediction using actual data is used to evaluate and illustrate the usefulness of the modeling approach. The behavior of nonstationary fuzzy data streams with gradual and abrupt regime shifts is also verified in the realm of the weather temperature prediction.

Learning algorithms for a class of neurofuzzy network and application

A class of neurofuzzy networks and a constructive, competition-based learning procedure is introduced. Given a set of training data, the learning procedure automatically adjusts the input space portion to cover the whole space and finds membership functions parameters for each input variable. The network processes data following fuzzy reasoning principles and, due to its structure, it is dual to a rule-based fuzzy inference system. The neurofuzzy model is used to forecast seasonal streamflow, a key step to plan and operate hydroelectric power plants and to price energy. A database of average monthly inflows of three Brazilian hydroelectric plants located at different river basins was used as source of training and test data. The performance of the neurofuzzy network is compared with period regression, a standard approach used by the electric power industry to forecast streamflows. Comparisons with multilayer perceptron, radial basis network and adaptive neural-fuzzy inference system are also included. The results show that the neurofuzzy network provides better one-step-ahead streamflow forecasting, with forecasting errors significantly lower than the other approaches.

Evolving fuzzy systems for pricing fixed income options

During the recent decades, option pricing became an important topic in computational finance. The main issue is to obtain a model of option prices that reflects price movements observed in the real world. In this paper we address option pricing using an evolving fuzzy system model and Brazilian interest rate options pricing data. Evolving models are particularly appropriate since it gradually develops the model structure and its parameters from a stream of data. Therefore, evolving fuzzy models provide a higher level of system adaptation and learns the system dynamics continuously, an essential attribute in pricing option estimation. In particular, we emphasize the use of the evolving participatory learning method. The model suggested in this paper is compared against the traditional Black closed-form formula, artificial neural networks structures and alternative evolving fuzzy system approaches. Actual daily data used in the experiments cover the period from January 2003 to June 2008. We measure forecast performance of all models based on summary measures of forecast accuracy and statistical tests for competing models. The results show that the evolving fuzzy system model is effective especially for out-of-the-money options.

Enhanced evolving participatory learning fuzzy modeling: an application for asset returns volatility forecasting

Evolving participatory learning (ePL) modeling joins the concepts of participatory learning and evolving fuzzy systems. It uses data streams to continuously adapt the structure and functionality of fuzzy models. This paper suggests an enhanced version of the ePL approach, called ePL+, which includes both an utility measure to shrink rule bases, and a variable cluster radius mechanism to improve the cluster structure. These features are useful in adaptive fuzzy rule-based modeling to recursively construct local fuzzy models with variable zone of influence. Moreover, ePL+ extends ePL to multi-input, multi-output fuzzy system modeling. Computational experiments considering financial returns volatility modeling and forecasting are conducted to compare the performance of the ePL+ approach with state of the art fuzzy modeling methods and with GARCH modeling. The experiments use actual data of S&P 500 and Ibovespa stock market indexes. The results suggest that the ePL+ approach is highly capable to model volatility dynamics, in a robust, flexible, parcimonious, and autonomous way.

Participatory Evolving Fuzzy Modeling

This paper introduces an approach to develop evolving fuzzy rule-based models based on the idea of participatory learning. Participatory learning is a means to learn and revise beliefs based on what is already known or believed. Participatory learning naturally induces unsupervised dynamic fuzzy clustering algorithms and provides an effective alternative construct evolving functional fuzzy models and adaptive fuzzy systems. Evolving participatory learning is used to forecast average weekly inflows for hydroelectric generation purposes and compared with eTS, an evolving modeling technique that uses the notion of potential to dynamically cluster data

Fuzzy granular evolving modeling for time series prediction

Modeling large volumes of flowing data from complex systems motivates rethinking several aspects of the machine learning theory. Data stream mining is concerned with extracting structured knowledge from spatio-temporally correlated data. A profusion of systems and algorithms devoted to this end has been constructed under the conceptual framework of granular computing. This paper outlines a fuzzy set based granular evolving modeling — FBeM — approach for learning from imprecise data. Granulation arises because modeling uncertain data dispenses attention to details. The evolving aspect is fundamental to account endless flows of nonstationary data and structural adaptation of models. Experiments with classic Box-Jenkins and Mackey-Glass benchmarks as well as with actual Global40 bond data suggest that the FBeM approach outperforms alternative approaches.

Recursive possibilistic fuzzy modeling

This paper suggests a recursive possibilistic approach for fuzzy modeling of time-varying processes. The approach is based on an extension of the possibilistic fuzzy c-means clustering and functional fuzzy rule-based modeling. Recursive possibilistic fuzzy modeling (rPFM) employs memberships and typicalities to cluster data. Functional fuzzy models uses affine functions in the fuzzy rule consequents. The parameters of the consequent functions are computed using the recursive least squares. Two classic benchmarks, Mackey-Glass time series and Box & Jenkins furnace data, are studied to illustrate the rPFM modeling and applicability. Data produced by a synthetic model with parameter drift is used to show the usefulness of rPFM to model time-varying processes. Performance of rPFM is compared with well established recursive fuzzy and neural fuzzy modeling and identification. The results show that recursive possibilistic fuzzy modeling produces parsimonious models with comparable or better accuracy than the alternative approaches.

Adaptive fuzzy system to forecast financial time series volatility

This paper introduces an adaptive fuzzy rule-based system applied as a financial time series model for volatility forecasting. The model is based on Takagi--Sugeno fuzzy systems and is built in two phases: In the first, the model uses the subtractive clustering algorithm to determine initial group structures in a reduced data set. In the second phase, the system is modified dynamically by adding and pruning operators and applying a recursive learning algorithm based on the expectation maximization optimization technique. The algorithm automatically determines the number of fuzzy rules necessary at each step, and one-step-ahead predictions are estimated and parameters updated. The model is applied to forecast financial time series volatility, considering daily values of the Sao Paulo stock exchange index, the Petrobras preferred stock prices, and the BRL/USD exchange rate. The model suggested is compared against generalized autoregressive conditional heteroskedasticity models. Experimental results show the adequacy of the adaptive fuzzy approach for volatility forecasting purposes.

Online estimation of stochastic volatility for asset returns

An important application of financial institutions is quantifying the risk involved in investing in an asset. These are various measures of risk like volatility or value-at-risk. To estimate them from data, a model for underlying financial time series has to be specified and parameters have to be estimated. In the following, we propose a framework for estimation of stochastic volatility of asset returns based on adaptive fuzzy rule based system. The model is based on Takagi-Sugeno fuzzy systems, and it is built in two phases. In the first phase, the model uses the Subtractive Clustering algorithm to determine group structures in a reduced data set for initialization purpose. In the second phase, the system is modified dynamically via adding and pruning operators and a recursive learning algorithm determines automatically the number of fuzzy rules necessary at each step, whereas one step ahead predictions are estimated and parameters are updated as well. The model is applied for forecasting financial time series volatility, considering daily values the REAL/USD exchange rate. The model suggested is compared against generalized autoregressive conditional heteroskedaticity models. Experimental results show the adequacy of the adaptative fuzzy approach for volatility forecasting purposes.

Learning in recurrent, hybrid neurofuzzy networks

A. novel recurrent, hybrid neurofuzzy network is proposed in this paper. This model is composed by two distinct parts: a fuzzy inference system and a neural network. The fuzzy system is constructed from fuzzy set models whose units of the fuzzy system are modeled through triangular norms and co-norms, and weights defined within the unit interval. The neural network contain classical nonlinear neurons. The hybrid system has a multilayer, recurrent structure. The learning procedure developed is based on two main paradigms: associative reinforcement learning and gradient search. These learning algorithms are associated to the fuzzy system and neural network, respectively. That is, output layer weights are adjusted via an error gradient method whereas a reward and punishment scheme updates the hidden layer weights. The recurrent neurofuzzy network is used to develop models of a nonlinear processes. Numerical results show that the neurofuzzy network proposed here provides accurate models after short period of learning time.