Isaac J. Sledge

Relational Generalizations of Cluster Validity Indices

Numerous computational schemes have arisen over the years that attempt to learn information about objects based upon the similarity or dissimilarity of one object to another. One such scheme, clustering, looks for self-similar groups of objects. To use clustering algorithms, an investigator must often have a priori knowledge of the number of clusters, i.e., c, to search for in the data. Moreover, it is often convenient to have ways to rank the returned results, either for a single value of c, a range of cs different clustering methods, or any combination thereof. However, the task of assessing the quality of the results, so that c may be determined objectively, is currently ill-defined for object-object relationships. To bridge this gap, we generalize three well-known validity indices: the modified Huberts Gamma, Xie-Beni, and the generalized Dunns indices, to relational data. In doing so, we develop a framework to convert many other validity indices to a relational form. Numerical examples on 12 datasets (samples from four normal mixtures, four real-world object datasets, and four real-world “pure relational” datasets) using the relational duals of the hard, fuzzy, and possibilistic c-means cluster algorithms are offered to illustrate and evaluate the new indices.

Growing neural gas for temporal clustering

Conventional clustering techniques provide a static snapshot of each vectorpsilas commitment to every group. With additive datasets, however, existing methods may not be sufficient for adapting to the presence of new clusters or even the merging of existing data-dense regions. To overcome this deficit, we explore the use of growing neural gas for temporal clustering and provide evidence that this new algorithm is capable of detecting cluster structures that incrementally emerge.

Finding the number of clusters in ordered dissimilarities

As humans, we have innate faculties that allow us to efficiently segment groups of objects. Computers, to some degree, can be programmed with similar categorical capabilities, which stem from exploratory data analysis. Out of the various subsets of data reasoning, clustering provides insight into the structure and relationships of input samples situated in a number of distributions. To determine these relationships, many clustering methods rely on one or more human inputs; the most important being the number of distributions, c, to seek. This work investigates a technique for estimating the number of clusters from a general type of data called relational data. Several numerical examples are presented to illustrate the effectiveness of the proposed method.

Mapping natural language to imagery: Placing objects intelligently

Humans are endowed with innate faculties, which allow for reasoning in noisy or uncertain environments, that far surpass the current abilities of computing systems. One such example is the notion of forming a “sketch” of some real-world location or route from a series of linguistic descriptions of regions and surrounding landmarks. While mirroring this functionality might seem like a daunting computational task, it is possible, to a certain degree, to mimic many of the underlying humanistic processes. Out of these, the facet that we consider in this paper is iterative object placement from a set of language extracted spatial relations and dependencies.

Automatic) Cluster Count Extraction from Unlabeled Data Sets

Through the years researchers have crafted algorithms to carry out the process of object partitioning (clustering). All clustering algorithms ultimately rely on human inputs, principally in the form of the number of clusters to seek. This work investigates a new technique for automating cluster assessment and estimating the number of clusters to look for in unlabeled data utilizing the VAT [visual assessment of cluster tendency] algorithm coupled with common image processing techniques. Several numerical examples are presented to illustrate the effectiveness of the proposed method.

A relational dual of the fuzzy possibilistic c-means algorithm

The hard, fuzzy and possibilistic c-means clustering algorithms are widely used for partitioning a set of n objects into c groups. There are cases, however, when more than one type of partition is necessary to correctly describe the belongingness of an object to a group. Previously, Pal, Pal and Bezdek listed some of these cases and proposed a method to simultaneously produce both memberships and typicalities for a set of vectorial object data: the fuzzy possibilistic c-means (FPCM) clustering algorithm. However, FPCM is not directly applicable when the data are represented by object-object relationships. In this paper, we reformulate FPCM so that it can work with A-norm relational data. Extensions and properties of the relational clustering algorithm are also considered.

Relational Duals of Cluster-Validity Functions for the

Clustering aims to identify groups of similar objects. To evaluate the results of cluster algorithms, an investigator uses cluster-validity indices. While the theory of cluster validity is well established for vector object data, little effort has been made to extend it to relationship-based data. As such, this paper proposes a theory of reformulation for object-data validity indices so that they can be used to rank the results produced by the relational -means clustering algorithms. More specifically, we create a class of relational validity indices, which is called dual-relational indices, that are guaranteed under certain, but easily met, constraints to produce the same results and, hence, the same cluster counts, as their object-data counterparts.

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Whats in a name? Over the last several years, Lotfi Zadeh has been using the definition of a cluster as an example of a very common fuzzy term that we humans use without a real definition. This paper represents an attempt to construct a degree of clusterness for a given set of points. We introduce two approaches, one based on the Possibilistic C-Means and the other on a Visual Assessment of Cluster Tendency. We compare the measures on several synthetic data sets and discuss the results.

-Means Family

This letter presents a system to solve the vector-to-imagery building conflation problem. To drive the system, structure outlines in high-resolution images are extracted via a shape-driven level set scheme. Shape and relative position features are then computed for the image-extracted buildings and for vector graphics buildings from a geospatial information system (GIS). These two features are used by a graph-matching procedure that finds correspondences between the image-extracted buildings and those from a GIS. Extensions of our system to vector-to-vector building conflation, generic polygonal object conflation, and image-to-image registration are also possible.

A Cluster By Any Other Name

The duality theory for the relational c-means algorithms, relational Gaussian mixture model, etc. requires that a distance matrix R correspond to a set of vector object data whose squared A-norm distances (or less generally, squared Euclidean distances) match the elements of R. For most datasets, this is an unrealistic constraint. As such, this paper proposes an alternating projection-based transform for converting non-Euclidean distance matrices into Euclidean distance matrices. Two synthetic and six real-world non-Euclidean datasets are used to illustrate that this method preserves cluster structure well.