The associative pattern classifier: Progress in theoretical understanding

The Associative Pattern Classifier (APC) was designed as an associative memory, focusing particularly on pattern classification. This implies that the training memory is constructed in a single operation and pattern classification also occurs in a single process. It is important to note that the APC translates the input patterns through a translation vector, which represents the average of all input patterns. Until now, there is no theoretical framework to explain the inner workings of the APC. Its relevance is inferred from the fact that several studies have been conducted using it as a foundation. This paper seeks to provide a theoretical comprehension of the APC’s operation to facilitate future enhancements. We found the APC creates a system in static equilibrium through concurrent vectors at the origin (translation vector), resulting in a balanced separation of patterns. However, the APC cannot achieve complete pattern separation because of the presence of a neutral region. The neutral region is defined by all the points that define the separation hyperplanes. The points over the hyperplanes cannot be classified by the APC. Additionally, we discovered that the APC is unable to accurately classify the translation vector, which could be included as part of the input patterns. Our previous research showed that the APC is unsuccessful in achieving the linear separation of the AND function. In this research, we broaden the examination of the AND function to illustrate that achieving linear separation is not feasible because the separation line represents a neutral region. The APC demonstrated exceptional performance when tested with artificial datasets where patterns were distributed over balanced regions, thus operating as an efficient multiclass and non-linear classifier. Nevertheless, the performance of the APC is lower when tested with real-world databases, making the APC inaccurate due to its restricted inner workings.