Can mathematical fields revolutionize pattern recognition? This paper explores the concept of using mathematical fields as limit functions for stochastic discrimination, a type of classification method. The research demonstrates that for a specific type of elementary function, stochastic discrimination has an analytic limit function, allowing classifications to be performed directly without sampling procedures. The limit function is interpreted in terms of fields originating from training examples, depending on the global configuration of training points. Two modifications of the limit function are proposed. First, for nonlinear problems, fields can be quantized, leading to classification functions with perfect generalization for high-dimensional parity problems. Second, fields can be provided with adaptable amplitudes, improving the performance of stochastic discrimination. Due to the nature of the fields, generalization improves even if the amplitude of every training example is adaptable. These findings have implications for machine learning and pattern recognition. The use of fields as limit functions offers a new approach to classification, potentially leading to more efficient and accurate algorithms. The proposed modifications enhance the adaptability and performance of stochastic discrimination, making it suitable for a wider range of problems. Further research could explore the application of this method to other machine learning tasks and real-world datasets.
This article was published in Neural Computation, a journal focusing on computational neuroscience and machine learning. The paper aligns with the journal's scope by presenting a novel approach to classification using concepts from mathematical fields. This theoretical contribution is relevant to the development of new algorithms and techniques in neural computation.