Binding and Normalization of Binary Sparse Distributed Representations by Context-Dependent Thinning

Distributed representations were often criticized as inappropriate for encoding of data with a complex structure. However Plate's Holographic Reduced Representations and Kanerva's Binary Spatter Codes are recent schemes that allow on-the-fly encoding of nested compositional structures by real-valued or dense binary vectors of fixed dimensionality. In this paper we consider procedures of the Context-Dependent Thinning which were developed for representation of complex hierarchical items in the architecture of Associative-Projective Neural Networks. These procedures provide binding of items represented by sparse binary codevectors (with low probability of 1s). Such an encoding is biologically plausible and allows a high storage capacity of distributed associative memory where the codevectors may be stored. In contrast to known binding procedures, Context-Dependent Thinning preserves the same low density (or sparseness) of the bound codevector for varied number of component codevectors. Besides, a bound codevector is not only similar to another one with similar component codevectors (as in other schemes), but it is also similar to the component codevectors themselves. This allows the similarity of structures to be estimated just by the overlap of their codevectors, without retrieval of the component codevectors. This also allows an easy retrieval of the component codevectors. Examples of algorithmic and neural-network implementations of the thinning procedures are considered. We also present representation examples for various types of nested structured data (propositions using role-filler and predicate-arguments representation schemes, trees, directed acyclic graphs) using sparse codevectors of fixed dimension. Such representations may provide a fruitful alternative to the symbolic representations of traditional AI, as well as to the localist and microfeature-based connectionist representations

Parallelization for image processing algorithms based chain and mid-crack codes

Freeman chain code is a widely-used description for a contour image. Another mid-crack code algorithm was proposed as a more precise method for image representation. We have developed a coding algorithm which is suitable to generate either chain code description or mid-crack code description by switching between two different tables. Since there is a strong urge to use parallel processing in image related problems, a parallel coding algorithm is implemented. This algorithm is developed on a pyramid architecture and a N cube architecture. Using link-list data structure and neighbor identification, the algorithm gains efficiency because no sorting or neighborhood pairing is needed. In this dissertation, the local symmetry deficiency (LSD) computation to calculate the local k-symmetry is embedded in the coding algorithm. Therefore, we can finish the code extraction and the LSD computation in one pass. The embedding process is not limited to the k-symmetry algorithm and has the capability of parallelism. An adaptive quadtree to chain code conversion algorithm is also presented. This algorithm is designed for constructing the chain codes of the resulting quadtree from the boolean operation of two quadtrees by using the chain codes of the original one. The algorithm has the parallelism and is ready to be implemented on a pyramid architecture. Our parallel processing approach can be viewed as a parallelization paradigm - a template to embed image processing algorithms in the chain coding process and to implement them in a parallel approach

Thinning-free Polygonal Approximation of Thick Digital Curves Using Cellular Envelope

Since the inception of successful rasterization of curves and objects in the digital space, several algorithms have been proposed for approximating a given digital curve. All these algorithms, however, resort to thinning as preprocessing before approximating a digital curve with changing thickness. Described in this paper is a novel thinning-free algorithm for polygonal approximation of an arbitrarily thick digital curve, using the concept of "cellular envelope", which is newly introduced in this paper. The cellular envelope, defined as the smallest set of cells containing the given curve, and hence bounded by two tightest (inner and outer) isothetic polygons, is constructed using a combinatorial technique. This envelope, in turn, is analyzed to determine a polygonal approximation of the curve as a sequence of cells using certain attributes of digital straightness. Since a real-world curve=curve-shaped object with varying thickness, unexpected disconnectedness, noisy information, etc., is unsuitable for the existing algorithms on polygonal approximation, the curve is encapsulated by the cellular envelope to enable the polygonal approximation. Owing to the implicit Euclidean-free metrics and combinatorial properties prevailing in the cellular plane, implementation of the proposed algorithm involves primitive integer operations only, leading to fast execution of the algorithm. Experimental results that include output polygons for different values of the approximation parameter corresponding to several real-world digital curves, a couple of measures on the quality of approximation, comparative results related with two other well-referred algorithms, and CPU times, have been presented to demonstrate the elegance and efficacy of the proposed algorithm

Approaches to Sequence Similarity Representation

We discuss several approaches to similarity preserving coding of symbol sequences and possible connections of their distributed versions to metric embeddings. Interpreting sequence representation methods with embeddings can help develop an approach to their analysis and may lead to discovering useful properties