Vector Symbolic Architectures (VSAs) such as Holographic Reduced Representations (HRRs) are computational associative memories used by cognitive psychologists to model behavioural and neurological aspects of human memory. We present a novel analysis of the mathematics of VSAs and a novel technique for representing data in HRRs. Encoding and decoding in VSAs can be characterized by Latin squares. Successful encoding requires the structure of the data to be orthogonal to the structure of the Latin squares. However, HRRs can successfully encode vectors of locally structured data if vectors are shuffled. Shuffling results are illustrated using images, but are applicable to any non-random data. The ability to use locally structured vectors provides a technique for detailed modelling of stimuli in HRR models.
Images form a significant and useful source of information in published biomedical articles, which is still under-utilized in biomedical document classification and retrieval. Much current work on biomedical image retrieval and classification employs simple, standard image features such as gray scale histograms and edge direction to represent and classify images. We have used such features as well to classify images in our early work [5], where we used image-class-tags to represent and classify articles.
Evaluating mathematical expression recognition involves a complex interaction of input primitives (e.g. pen/finger strokes), recognized symbols, and recognized spatial structure. Existing performance metrics simplify this problem by separating the assessment of spatial structure from the assessment of symbol segmentation and classification. These metrics do not characterize the overall accuracy of a pen-based mathematics recognition, making it difficult to compare math recognition algorithms, and preventing the use of machine learning algorithms requiring a criterion function characterizing overall system performance. To address this problem, we introduce performance metrics that bridge the gap from handwritten strokes to spatial structure. Our metrics are computed using bipartite graphs that represent classification, segmentation and spatial structure at the stroke level. Overall correctness of an expression is measured by counting the number of relabelings of nodes and edges needed to make the bipartite graph for a recognition result match the bipartite graph for ground truth. This metric may also be used with other primitive types (e.g. image pixels).
