Page 130 - Artificial Intelligence in the Age of Neural Networks and Brain Computing

2. Evolving Connectionist Systems (ECOS) 119

Samples (examples) that have a distance to an existing node (cluster center, rule
node) less than a certain threshold are allocated to the same cluster. Samples
that do not fit into existing clusters form new clusters. Cluster centers are contin-
uously adjusted according to new data samples, and new clusters are created
incrementally. ECOS learn from data and automatically create or update a local
fuzzy model/function, e.g.,:

IF <data is in a fuzzy cluster C i > THEN <the model is F i >
where F i can be a fuzzy value, a logistic or linear regression function (Fig. 6.5B), or
ANN model [36,37].
The ECOS methods are realized as software modules as part of the free develop-
ment system NeuCom (www.theneucom.com).
A special development of ECOS is transductive reasoning and personalized
modeling. Instead of building a set of local models (i.e., prototypes) to cover the
whole problem space and then use these models to classify/predict any new input
vector, in transductive modeling for every new input vector a new model is created
based on selected nearest neighbor vectors from the available data. Such ECOS
models are the neurofuzzy inference system (NFI) and the transductive weighted
NFI (TWNFI) [42]. In TWNFI, for every new input vector the neighborhood of
closets data vectors is optimized using both the distance between the new vector
and the neighboring ones and the weighted importance of the input variables, so
that the error of the model is minimized in the neighborhood area [43].
The following are examples of methods, systems, and applications that use all or
some of the principles of ECOS from above:
• Evolving self-organized maps (ESOM) [44];
• Evolving clustering method (ECM) [45];
• Incremental feature learning in ECOS [46];
• Online ECOS optimization [47];
• Assessment of EFuNN accuracy for pattern recognition using data with different
statistical distributions [48];
• Recursive clustering based on a GustafsoneKessel algorithm [49];
• Using a map-based encoding to evolve plastic neural networks [50];
• Evolving TakagieSugeno fuzzy model based on switching to neighboring
models [51];
• A soft computing based approach for modeling of chaotic time-series [52];
• Uninorm-based evolving neural networks and approximation capabilities [53];
• Global, local, and personalized modeling and profile discovery in bioinformatics:
an integrated approach [54];
• FLEXFIS: a robust incremental learning approach for evolving TakagieSugeno
fuzzy models [55];
• Evolving fuzzy classifiers using different model architectures [56];
• RSPOP: rough setebased pseudo outer-product fuzzy rule identification algo-
rithm [57];