Convex hulls in concept induction

Classification learning is dominated by systems which induce large numbers of small axis-orthogonal decision surfaces. This strongly biases such systems towards particular hypothesis types but there is reason believe that many domains have underlying concepts which do not involve axis orthogonal surfaces. Further, the multiplicity of small decision regions mitigates against any holistic appreciation of the theories produced by these systems, notwithstanding the fact that many of the small regions are individually comprehensible. This thesis investigates modeling concepts as large geometric structures in n-dimensional space. Convex hulls are a superset of the set of axis orthogonal hyperrectangles into which axis orthogonal systems partition the instance space. In consequence, there is reason to believe that convex hulls might provide a more flexible and general learning bias than axis orthogonal regions. The formation of convex hulls around a group of points of the same class is shown to be a usable generalisation and is more general than generalisations produced by axis-orthogonal based classifiers, without constructive induction, like decision trees, decision lists and rules. The use of a small number of large hulls as a concept representation is shown to provide classification performance which can be better than that of classifiers which use a large number of small fragmentary regions for each concept. A convex hull based classifier, CH1, has been implemented and tested. CH1 can handle categorical and continuous data. Algorithms for two basic generalisation operations on hulls, inflation and facet deletion, are presented. The two operations are shown to improve the accuracy of the classifier and provide moderate classification accuracy over a representative selection of typical, largely or wholly continuous valued machine learning tasks. The classifier exhibits superior performance to well-known axis-orthogonal-based classifiers when presented with domains where the underlying decision surfaces are not axis parallel. The strengths and weaknesses of the system are identified. One particular advantage is the ability of the system to model domains with approximately the same number of structures as there are underlying concepts. This leads to the possibility of extraction of higher level mathematical descriptions of the induced concepts, using the techniques of computational geometry, which is not possible from a multiplicity of small regions.

Density based fuzzy c-means clustering of non-convex patterns

We propose a new technique to perform unsupervised data classification (clustering) based on density induced metric and non-smooth optimization. Our goal is to automatically recognize multidimensional clusters of non-convex shape. We present a modification of the fuzzy c-means algorithm, which uses the data induced metric, defined with the help of Delaunay triangulation. We detail computation of the distances in such a metric using graph algorithms. To find optimal positions of cluster prototypes we employ the discrete gradient method of non-smooth optimization. The new clustering method is capable to identify non-convex overlapped d-dimensional clusters.

Fuzzy clustering of non-convex patterns using global optimization

This paper discusses various extensions of the classical within-group sum of squared errors functional, routinely used as the clustering criterion. Fuzzy c-means algorithm is extended to the case when clusters have irregular shapes, by representing the clusters with more than one prototype. The resulting minimization problem is non-convex and non-smooth. A recently developed cutting angle method of global optimization is applied to this difficult problem

The rough sets feature selection for trees recognition in color aerial images using genetic algorithms

Selecting a set of features which is optimal for a given task is the problem which plays an important role in a wide variety of contexts including pattern recognition, images understanding and machine learning. The concept of reduction of the decision table based on the rough set is very useful for feature selection. In this paper, a genetic algorithm based approach is presented to search the relative reduct decision table of the rough set. This approach has the ability to accommodate multiple criteria such as accuracy and cost of classification into the feature selection process and finds the effective feature subset for texture classification . On the basis of the effective feature subset selected, this paper presents a method to extract the objects which are higher than their surroundings, such as trees or forest, in the color aerial images. The experiments results show that the feature subset selected and the method of the object extraction presented in this paper are practical and effective.

Convex hulls as an hypothesis language bias

Classification learning is dominated by systems which induce large numbers of small axis-orthogonal decision surfaces which biases such systems towards particular hypothesis types. However, there is reason to believe that many domains have underlying concepts which do not involve axis orthogonal surfaces. Further, the multiplicity of small decision regions mitigates against any holistic appreciation of the theories produced by these systems, notwithstanding the fact that many of the small regions are individually comprehensible. We propose the use of less strongly biased hypothesis languages which might be expected to model' concepts using a number of structures close to the number of actual structures in the domain. An instantiation of such a language, a convex hull based classifier, CHI, has been implemented to investigate modeling concepts as a small number of large geometric structures in n-dimensional space. A comparison of the number of regions induced is made against other well-known systems on a representative selection of largely or wholly continuous valued machine learning tasks. The convex hull system is shown to produce a number of induced regions about an order of magnitude less than well-known systems and very close to the number of actual concepts. This representation, as convex hulls, allows the possibility of extraction of higher level mathematical descriptions of the induced concepts, using the techniques of computational geometry.

Problem and solution trees : a practical approach for identifying potential interventions to improve population nutrition

Population nutrition problems have a diversity of contributory factors and, ideally, multi-sectoral solutions should be developed by the relevant stakeholders, based on a common understanding of these factors. The problem and solution tree approach is a participatory process of working through the layers of determinants and then developing potential interventions for a specific issue, using the available data and expertise. We tailored this approach for non-communicable disease-related nutrition problems in Pacific Islands and applied it in several countries. The process led to the identification of a considerable range of determinants of unhealthy diets and potential interventions to improve the situation. This practical approach also offered the additional benefit of developing stakeholder awareness in the issues. Problem trees are a relatively simple tool to implement, easy to adapt to differing needs, can generate a wealth of information and can be more widely used.

Other communities : Box mistletoe (Amyema miquelii) parasitism is not detrimental to the health of grey box (Eucalyptus microcarpa) trees at a regional scale

Mistletoes are hemiparasites that occur worldwide in many types of forest, woodland and shrubland ecosystems (Watson 2001). Some species are regarded as pests due to their detrimental effects on host species (Hawksworth 1983; Reid & Yan 2000). Heavy infestations can affect the growth, productivity and form of host trees, and may cause host death (Reid et al. 1994; Shaw et al.2004, 2008). In south-eastern Australia, mistletoes often are visibly obvious in trees along roadsides, in paddocks and on the margins of open forests; and concerns have been expressed about their potentially detrimental effects on host trees.Despite this, little quantitative information is available on the effects of mistletoes on tree health and mortality (Reid et al. 1994). Are detrimental effects widespread or localized? A first step is to assess whether trees parasitized by mistletoe are less healthy than those without such parasites. Here, we investigate the relationship between parasitism by Box Mistletoe (Amyema miquelii (Lehm. ex Miq.) Tiegh.), a common species in south-eastern Australia, and the health of trees of a widespread host species, Grey Box (Eucalyptus microcarpa (Maiden) Maiden), across a large geographic region.