Four versions of a k-nearest neighbor algorithm with locally adaptive k are introduced and compared to the basic k-nearest neighbor algorithm (kNN). Locally adaptive kNN algorithms choose the value of k that should be used to classify a query by consulting the results of cross-validation computations in the local neighborhood of the query. Local kNN methods are shown to perform similar to kNN in experiments with twelve commonly used data sets. Encouraging results in three constructed tasks show that local methods can significantly outperform kNN in specific applications. Local methods can be recommended for online learning and for applications where different regions of the input space are covered by patterns solving different sub-tasks.

We propose a method for improving the performance of any network designed to predict the next value of a time series. Vve advocate analyzing the deviations of the network's predictions from the data in the training set. This can be carried out by a secondary network trained on the time series of these residuals. The combined system of the two networks is viewed as the new predictor. We demonstrate the simplicity and success of this method, by applying it to the sunspots data. The small corrections of the secondary network can be regarded as resulting from a Taylor expansion of a complex network which includes the combined system.

Memory-based learning methods operate by storing all (or most) of the training data and deferring analysis of that data until "run time" (i.e., when a query is presented and a decision or prediction must be made). When a query is received, these methods generally answer the query by retrieving and analyzing a small subset of the training data-namely, data in the immediate neighborhood of the query point. In short, memory-based methods are "lazy" (they wait until the query) and "local" (they use only a local neighborhood). The purpose of this workshop was to review the state-of-the-art in memory-based methods and to understand their relationship to "eager" and "global" learning algorithms such as batch backpropagation. There are two essential components to any memory-based algorithm: the method for defining the "local neighborhood" and the learning method that is applied to the training examples in the local neighborhood.

Researchers often try to understand-post hoc-representations that emerge in the hidden layers of a neural net following training. Interpretation is difficult because these representations are typically highly distributed and continuous. By "continuous," we mean that if one constructed a scatterplot over the hidden unit activity space of patterns obtained in response to various inputs, examination at any scale would reveal the patterns to be broadly distributed over the space.

Recently, Ott, Grebogi and Yorke (OGY) [6] found an effective method to control chaotic systems to unstable fixed points by using only small control forces; however, OGY's method is based on and limited to a linear theory and requires considerable knowledge of the dynamics of the system to be controlled. In this paper we use two radial basis function networks: one as a model of an unknown plant and the other as the controller. The controller is trained with a recurrent learning algorithm to minimize a novel objective function such that the controller can locate an unstable fixed point and drive the system into the fixed point with no a priori knowledge of the system dynamics. Our results indicate that the neural controller offers many advantages over OGY's technique.

An approach is presented to learning high dimensional functions in the case where the learning algorithm can affect the generation of new data. A local modeling algorithm, locally weighted regression, is used to represent the learned function. Architectural parameters of the approach, such as distance metrics, are also localized and become a function of the query point instead of being global. Statistical tests are given for when a local model is good enough and sampling should be moved to a new area. Our methods explicitly deal with the case where prediction accuracy requirements exist during exploration: By gradually shifting a "center of exploration" and controlling the speed of the shift with local prediction accuracy, a goal-directed exploration of state space takes place along the fringes of the current data support until the task goal is achieved.

We describe a number of learning rules that can be used to train unsupervised parallel feature extraction systems. The learning rules are derived using gradient ascent of a quality function. We consider a number of quality functions that are rational functions of higher order moments of the extracted feature values. We show that one system learns the principle components of the correlation matrix. Principal component analysis systems are usually not optimal feature extractors for classification.

Such decisions include which function approximator to use, how to trade smoothness for goodness of fit and which features are relevant.

Dimension reduction provides compact representations for storage, transmission, and classification. Dimension reduction algorithms operate by identifying and eliminating statistical redundancies in the data. The optimal linear technique for dimension reduction is principal component analysis (PCA).

The distance measure and learning problem are formally described as nested objective functions. We derive an efficient algorithm by using optimization techniques that allow us to divide up the objective function into parts which may be minimized in distinct phases. The algorithm has accurately recreated 10 prototypes from a randomly generated sample database of 100 images consisting of 20 points each in 120 experiments. Finally, by incorporating permutation invariance in our distance measure, we have a technique that we may be able to apply to the clustering of graphs. Our goal is to develop measures which will enable the learning of objects with shape or structure. Acknowledgements This work has been supported by AFOSR grant F49620-92-J-0465 and ONR/DARPA grant N00014-92-J-4048.