title: Integrating regression formulas and kernel functions into locally adaptive knowledge-based neural networks: a case study on renal function evaluation.
abstract: OBJECTIVE
  In many medical areas, there exist different regression formulas to predict/evaluate a medical outcome on the same problem, each of them being efficient only in a particular sub-space of the problem space. The paper aims at the development of a generic, incremental learning model that includes all available regression formulas for a particular prediction problem to define local areas of the problem space with their best performing formula along with useful explanation rules. Another objective of the paper is to develop a specific model for renal function evaluation using nine existing formulas.
  
  
  METHODS
  We have used a connectionist neuro-fuzzy approach and have developed a knowledge-based neural network model (KBNN) which incorporates and adapts incrementally several existing regression formulas and kernel functions. The model incorporates different non-linear regression functions as neurons in its hidden layer and adapts these functions through incremental learning from data in particular local areas of the space. More specifically, each hidden neural node has a pair of functions associated with it--one regression formula, that represents existing knowledge and one Gaussian kernel function, that defines the sub-space of the whole problem space, in which the formula is locally adapted to new data. All these functions are aggregated and changed through incremental learning. The proposed KBNN model is illustrated using a medical dataset of observed patient glomerular filtration rate (GFR) measurements for renal function evaluation. In this case study, the regression function for each cluster is selected by the model from nine formulas commonly used by medical practitioners to predict GFR. 441 GFR data vectors from 141 patients taken from 12 sites in Australia and New Zealand have been used as a case study experimental data set.
  
  
  RESULTS
  The proposed GFR prediction model, based on the proposed generic KBNN model, outperforms at least by 10% accuracy any of the individual regression formulas or a standard neural network model. Furthermore, we have derived locally adapted regression formulas to perform best on local clusters of data along with useful explanatory rules.
  
  
  CONCLUSIONS
  The proposed KBNN model manifests better accuracy then existing regression formulas or neural network models for renal function evaluation and extracts modified formulas that perform well in local areas of the problem space.
authors.affiliation: Knowledge Engineering & Discovery Research Institute, Auckland University of Technology, Private Bag 92006, Auckland 1020, New Zealand.
authors.forename: Qun
authors.initials: Q
authors.lastname: Song
authors.forename: Nikola
authors.initials: N
authors.lastname: Kasabov
authors.forename: Tianmin
authors.initials: T
authors.lastname: Ma
authors.forename: Mark Roger
authors.initials: MR
authors.lastname: Marshall
mesh_terms: D000465:Algorithms; D003404:Creatinine / Q000097:blood; D005260:Female; D005919:Glomerular Filtration Rate; D006801:Humans; D008297:Male; D008875:Middle Aged; D016571:Neural Networks, Computer; D012044:Regression Analysis
chemical_list: D003404:Creatinine