Departmental Reports

2018

• A Comparison of Knee Strategies For Hierarchical Spatial Clustering
  Brian J. Ross, February 2018.  [PDF]   [abstract] [close]

  A comparative study of the performance of knee detection approaches for the hierarchical clustering of 2D spatial data is undertaken. Knee detection is usually performed on the dendogram generated during cluster generation. For many problems, the knee is a natural indication of the ideal or optimal number of clusters for the given problem. This research compares the performance of various knee strategies on different spatial datasets. Two hierarchical clustering algorithms, single linkage and group average, are considered. Besides determining knees using conventional cluster distances, we also explore alternative metrics such as average global medoid and centroid distances, and F score metrics. Results show that knee determination is difficult, and that efficacy of knee strategies is very much problem dependent. Furthermore, knee determination is often more effectively applied on alternative distance metrics and F scores. In summary, knee strategies are often a useful heuristic, but not a general solution, towards optimal cluster detection.

2017

• A discrete representation of dicomplemented lattices
  Ivo Düntsch, Léonard Kwuida and Ewa Orlowska, March 2017.  [PDF]   [abstract] [close]

  Dicomplemented lattices were introduced as an abstraction of Wille’s concept algebras which provided negations to a concept lattice. We prove a discrete representation theorem for the class of dicomplemented lattices. The theorem is based on a topology free version of Urquhart’s representation of bounded general lattices.

2016

• Mixed algebras and their logics
  Ivo Düntsch, Ewa Orlowska and Tinko Tinchev, January 2016.  [PDF]   [abstract] [close]

  We investigate complex algebras of the form <2^X , <R>, [[S]]> arising from a frame <X, R, S> where S ⊆ R, and exhibit their abstract algebraic and logical counterparts.

• Online Image Classification Using Graphics Processing Unit-Based Genetic Programming
  Mehran Maghoumi, Brian J. Ross, August 2016.  [PDF]   [abstract] [close]

  A texture classification vision system implemented with Graphics Processing Unit-based genetic programming is described. An online learning environment is implemented, in which genetic programming is automatically invoked when un-classified texture instances are present in an image stream. Once a segment is positively classified, the genetic programming classifier expression is reapplied to frames of the image stream. System performance is enhanced using population-parallel evaluation on a graphics processing unit. Various experiments with textures of varying difficulty were performed. Real-time performance was often seen in cases using 4-segments of texture data, as correct classifiers were evolved within seconds. In all cases, once evolved, classifiers were easily applied to the image stream in real-time. This research shows that high-performance real-time learning environments for image classification are attainable with genetic programming.

2015

• Simplifying contextual structures
  Ivo Düntsch and Günther Gediga, January 2015.  [PDF]   [abstract] [close]

  We present a method to reduce a formal context while retaining much of its information content. Although simple, our ICRA approach offers an effective way to reduce the complexity of concept lattices and / or knowledge spaces by changing only little information in comparison to a competing model which uses fuzzy K-Means clustering.

• Rough set clustering
  Ivo Düntsch and Günther Gediga, January 2015.  [PDF]   [abstract] [close]

  We present a survey of clustering methods based on rough set data analysis.

• A relational logic for spatial contact based on rough set approximation
  Ivo Düntsch and Ewa Orloska, Hui Wang, November 2015.  [PDF]   [abstract] [close]

  In previous work we have presented a class of algebras enhanced with two contact relation used in spatial reasoning on the basis of rough sets. In this paper we present a relational logic for such structures in the spirit of Rasiowa -- Sikorki proof systems.

2014

• Virtual Photography Using Multi-Objective Particle Swarm Optimization
  William Barry and Brian J. Ross, January 2014.  [PDF]   [abstract] [close]

  Particle swarm optimization (PSO) is a stochastic population-based search algorithm that is inspired by the flocking behaviour of birds. Here, a PSO is used to implement swarms of cameras flying through a virtual world in search of an image that satisfies a set of compositional constraints, for example, the rule of thirds and horizon line rules. To effectively process these multiple, and possible conflicting, criteria, a new multi-objective PSO algorithm called the sum of ranks PSO (SR-PSO) is introduced. The SR-PSO is useful for solving high-dimensional search problems, while discouraging degenerate solutions that can arise with other approaches. Less user intervention is required for the SR-PSO, as compared to a conventional PSO. A number of problems using different virtual worlds and user-supplied constraints were studied. In all cases, solution images were obtained that satisfied the majority of given constraints. The SR-PSO was shown to be superior to other algorithms in solving the high-dimensional virtual photography problems studied.

• Passive Solar Building Design Using Genetic Programming
  Mohammad Mahdi Oraei Gholami and Brian J. Ross, January 2014.  [PDF]   [abstract] [close]

  Passive solar building design considers the effect that sunlight has on energy usage. The goal is to reduce the need for artificial cooling and heating devices, thereby saving energy costs. A number of competing design objectives can arise. Window heat gain during winter requires large windows. These same windows, however, reduce energy efficiency during nights and summers. Other model requirements add further complications, which creates a challenging optimization problem. We use genetic programming for passive solar building design. The EnergyPlus system is used to evaluate energy consumption. It considers factors ranging from model construction (shape, windows, materials) to location particulars (latitude/longitude, weather, time of day/year). We use a split grammar to build 3D models, and multi-objective fitness to evaluate the multiple design objectives. Experimental results showed that balancing window heat gain and total energy use is challenging, although our multi-objective strategy could find interesting compromises. Many factors (roof shape, material selection) were consistently optimized by evolution. We also found that geographic aspects of the location play a critical role in the final building design.

• Feature Extraction Languages and Visual Pattern Recognition
  Mehran Maghoumi and Brian J. Ross, January 2014.  [PDF]   [abstract] [close]

  Visual pattern recognition and classification is a challenging computer vision problem. Genetic programming has been applied towards automatic visual pattern recognition. An important factor in evolving effective classifiers is the suitability of the GP language for defining expressions for feature extraction and classification. This research presents a comparative study of a variety of GP languages suitable for classification. Four different languages are examined, which use different selections of image processing operators. One of the languages does block classification, which means that an entire region of pixels is classified simultaneously. The other languages are pixel classifiers, which determine classification for a single pixel. Pixel classifiers are more common in the GP-vision literature. We tested the languages on different instances of Brodatz textures, as well as aerial and camera images. Our results show that the most effective languages are pixel-based ones with spatial operators. However, as is to be expected, the nature of the image will naturally determine the effectiveness of the language used.

• Real-Time Automatic Object Classification and Tracking using Genetic Programming and NVidia® Cuda^TM
  Mehran Maghoumi, August 2014.  [PDF]   [abstract] [close]

  Genetic Programming (GP) is a widely used methodology for solving various computa- tional problems. GP’s problem solving ability is usually hindered by its long execution time for large and complex problems. In this thesis, GP is applied toward real-time com- puter vision. In particular, object classification and tracking using a parallel GP system is discussed. First, a study of suitable GP languages for object classification is presented. To this end two main GP approaches for visual pattern classification were studied. These approaches include the block-classifiers and the pixel-classifiers. According to the experi- ments, the pixel-classifiers were generally more accurate and performed better. Next, using the results of these experiments, a suitable language was selected for the implementation of the real-time tracking system. The real-time system was implemented using NVIDIA CUDA. Synthetic video data was used in the experiments. The goal of the experiments was to evolve a unique classifier for each texture pattern that was present in the video. The experiments revealed that the system was capable of correctly classifying and tracking the textures in the video. Furthermore, the performance of the system was on-par with real-time requirements.

• Discrete dualities for n-potent MTL–algebras and 2-potent BL–algebras
  Ivo Düntsch, Ewa Orłowska, Clint van Alten, September 2014.  [PDF]   [abstract] [close]

  Discrete dualities are developed for n-potent MTL–algebras and for 2-potent BL–algebras. That is, classes of frames, or relational systems, are defined that serve as dual counterparts to these classes of algebras. The frames defined here are extensions of the frames that were developed for MTL–algebras by Orlowska, Radzikowska (2009) and Orlowska, Rewitzky (2010) ; the additional frame conditions required are given here and also the proofs that discrete dualities hold with respect to such frames. The duality also provides an embedding from an n-potent MTL–algebra, or 2-potent BL–algebra, into the complex algebra of its canonical frame, which is a complete algebra in the lattice sense.