Vector Symbolic Architectures combine a high-dimensional vector space with a set of carefully designed operators in order to perform symbolic computations with large numerical vectors. Major goals are the exploitation of their representational power and ability to deal with fuzziness and ambiguity. Over the past years, several VSA implementations have been proposed. The available implementations differ in the underlying vector space and the particular implementations of the VSA operators. This paper provides an overview of eleven available VSA implementations and discusses their commonalities and differences in the underlying vector space and operators. We create a taxonomy of available binding operations and show an important ramification for non self-inverse binding operations using an example from analogical reasoning. A main contribution is the experimental comparison of the available implementations in order to evaluate (1) the capacity of bundles, (2) the approximation quality of non-exact unbinding operations, (3) the influence of combining binding and bundling operations on the query answering performance, and (4) the performance on two example applications: visual place- and language-recognition. We expect this comparison and systematization to be relevant for development of VSAs, and to support the selection of an appropriate VSA for a particular task. The implementations are available.

Place recognition is the task of recognizing the current scene from a database of known places. The currently dominant algorithmic paradigm is to use (deep learning based) holistic feature vectors to describe each place and use fast vector query methods to find matchings. We propose a novel type of image descriptor, Vector Semantic Representations (VSR), that encodes the spatial semantic layout from a semantic segmentation together with appearance properties in a, for example, 4,096 dimensional vector for place recognition. We leverage operations from the established class of Vector Symbolic Architectures to combine symbolic (e.g. class label) and numeric (e.g. feature map response) information in a common vector representation. We evaluate the proposed semantic descriptor on 13 standard mobile robotic place recognition datasets and compare to six descriptors from the literature. VSR is on par with the best compared descriptor (NetVLAD) in terms of mean average precision and superior in terms of recall and worst-case average precision. This makes the approach particularly interesting for candidate selection. For a more detailed investigation, we discuss and evaluate recall integrity as additional criterion. Further, we demonstrate that the semantic descriptor is particularly well suited for combination with existing appearance descriptors indicating that semantics provide complementary information for image matching.

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