Sensitivity Analysis for Decision Boundaries

A novel approach is presented to visualize and analyze decision boundaries for feedforward neural networks. First order sensitivity analysis of the neural network output function with respect to input perturbations is used to visualize the position of decision boundaries over input space. Similarly, sensitivity analysis of each hidden unit activation function reveals which boundary is implemented by which hidden unit. The paper shows how these sensitivity analysis models can be used to better understand the data being modelled, and to visually identify irrelevant input and hidden units.     

C-Net: A Method for Generating Non-deterministic and Dynamic Multivariate Decision Trees

Despite the fact that artificial neural networks (ANNs) are universal function approximators, their black box nature (that is, their lack of direct interpretability or expressive power) limits their utility. In contrast, univariate decision trees (UDTs) have expressive power, although usually they are not as accurate as ANNs. We propose an improvement, C-Net, for both the expressiveness of ANNs and the accuracy of UDTs by consolidating both technologies for generating multivariate decision trees (MDTs). In addition, we introduce a new concept, recurrent decision trees, where C-Net uses recurrent neural networks to generate an MDT with a recurrent feature. That is, a memory is associated with each node in the tree with a recursive condition which replaces the conventional linear one. Furthermore, we show empirically that, in our test cases, our proposed method achieves a balance of comprehensibility and accuracy intermediate between ANNs and UDTs. MDTs are found to be intermediate since they are more expressive than ANNs and more accurate than UDTs. Moreover, in all cases MDTs are more compact (i.e., smaller tree size) than UDTs. Received 27 January 2000 / Revised 30 May 2000 / Accepted in revised form 30 October 2000     

Inductive Learning Methods for Knowledge-Based Decision Support: A Comparative Analysis

This paper describes the inductive learning methods for generating decision rules in decision support systems. Three similarity-based learning systems are studied based on: (1) the AQ-Star method, (2) the Tree-Induction method, and (3) the Probabilistic Learning method. Loan evaluation examples and empirical data are used as a basis for comparing these inductive learning methods on their algorithmic characteristics and decision support performance.