Efficient spatial clustering algorithm using binary tree

In this paper we present an efficient k-Means clustering algorithm for two dimensional data. The proposed algorithm re-organizes dataset into a form of nested binary tree*. Data items are compared at each node with only two nearest means with respect to each dimension and assigned to the one that has the closer mean. The main intuition of our research is as follows: We build the nested binary tree. Then we scan the data in raster order by in-order traversal of the tree. Lastly we compare data item at each node to the only two nearest means to assign the value to the intendant cluster. In this way we are able to save the computational cost significantly by reducing the number of comparisons with means and also by the least use to Euclidian distance formula. Our results showed that our method can perform clustering operation much faster than the classical ones. © Springer-Verlag Berlin Heidelberg 2005

Using siting algorithms in the design of marine reserve networks

Using benthic habitat data from the Florida Keys (USA), we demonstrate how siting algorithms can help identify potential networks of marine reserves that comprehensively represent target habitat types. We applied a flexible optimization tool-simulated annealing-to represent a fixed proportion of different marine habitat types within a geographic area. We investigated the relative influence of spatial information, planning-unit size, detail of habitat classification, and magnitude of the overall conservation goal on the resulting network scenarios. With this method, we were able to identify many adequate reserve systems that met the conservation goals, e.g., representing at least 20% of each conservation target (i.e., habitat type) while fulfilling the overall aim of minimizing the system area and perimeter. One of the most useful types of information provided by this siting algorithm comes from an irreplaceability analysis, which is a count of the number of, times unique planning units were included in reserve system scenarios. This analysis indicated that many different combinations of sites produced networks that met the conservation goals. While individual 1-km(2) areas were fairly interchangeable, the irreplaceability analysis highlighted larger areas within the planning region that were chosen consistently to meet the goals incorporated into the algorithm. Additionally, we found that reserve systems designed with a high degree of spatial clustering tended to have considerably less perimeter and larger overall areas in reserve-a configuration that may be preferable particularly for sociopolitical reasons. This exercise illustrates the value of using the simulated annealing algorithm to help site marine reserves: the approach makes efficient use of;available resources, can be used interactively by conservation decision makers, and offers biologically suitable alternative networks from which an effective system of marine reserves can be crafted.

Mathematical methods for spatially cohesive reserve design

The problem of designing spatially cohesive nature reserve systems that meet biodiversity objectives is formulated as a nonlinear integer programming problem. The multiobjective function minimises a combination of boundary length, area and failed representation of the biological attributes we are trying to conserve. The task is to reserve a subset of sites that best meet this objective. We use data on the distribution of habitats in the Northern Territory, Australia, to show how simulated annealing and a greedy heuristic algorithm can be used to generate good solutions to such large reserve design problems, and to compare the effectiveness of these methods.

Fine-scale spatial genetic correlation analyses reveal strong female philopatry within a brush-tailed rock-wallaby colony in southeast Queensland

We combine spatial data on home ranges of individuals and microsatellite markers to examine patterns of fine-scale spatial genetic structure and dispersal within a brush-tailed rock-wallaby (Petrogale penicillata) colony at Hurdle Creek Valley, Queensland. Brush-tailed rock-wallabies were once abundant and widespread throughout the rocky terrain of southeastern Australia; however, populations are nearly extinct in the south of their range and in decline elsewhere. We use pairwise relatedness measures and a recent multilocus spatial autocorrelation analysis to test the hypotheses that in this species, within-colony dispersal is male-biased and that female philopatry results in spatial clusters of related females within the colony. We provide clear evidence for strong female philopatry and male-biased dispersal within this rock-wallaby colony. There was a strong, significant negative correlation between pairwise relatedness and geographical distance of individual females along only 800 m of cliff line. Spatial genetic autocorrelation analyses showed significant positive correlation for females in close proximity to each other and revealed a genetic neighbourhood size of only 600 m for females. Our study is the first to report on the fine-scale spatial genetic structure within a rock-wallaby colony and we provide the first robust evidence for strong female philopatry and spatial clustering of related females within this taxon. We discuss the ecological and conservation implications of our findings for rock-wallabies, as well as the importance of fine-scale spatial genetic patterns in studies of dispersal behaviour.

Special issue on advances in data mining and its applications

Data mining is the process to identify valid, implicit, previously unknown, potentially useful and understandable information from large databases. It is an important step in the process of knowledge discovery in databases, (Olaru & Wehenkel, 1999). In a data mining process, input data can be structured, seme-structured, or unstructured. Data can be in text, categorical or numerical values. One of the important characteristics of data mining is its ability to deal data with large volume, distributed, time variant, noisy, and high dimensionality. A large number of data mining algorithms have been developed for different applications. For example, association rules mining can be useful for market basket problems, clustering algorithms can be used to discover trends in unsupervised learning problems, classification algorithms can be applied in decision-making problems, and sequential and time series mining algorithms can be used in predicting events, fault detection, and other supervised learning problems (Vapnik, 1999). Classification is among the most important tasks in the data mining, particularly for data mining applications into engineering fields. Together with regression, classification is mainly for predictive modelling. So far, there have been a number of classification algorithms in practice. According to (Sebastiani, 2002), the main classification algorithms can be categorized as: decision tree and rule based approach such as C4.5 (Quinlan, 1996); probability methods such as Bayesian classifier (Lewis, 1998); on-line methods such as Winnow (Littlestone, 1988) and CVFDT (Hulten 2001), neural networks methods (Rumelhart, Hinton & Wiliams, 1986); example-based methods such as k-nearest neighbors (Duda & Hart, 1973), and SVM (Cortes & Vapnik, 1995). Other important techniques for classification tasks include Associative Classification (Liu et al, 1998) and Ensemble Classification (Tumer, 1996).

Mining-associated Seismicity in Kolar Gold Mines: Some Case Studies using Multi-fractals

The occurrence of rockbursts was quite common during active mining periods in the Champion reef mines of Kolar gold fields, India. Among the major rockbursts, the ‘area-rockbursts’ were unique both in regard to their spatio-temporal distribution and the extent of damage caused to the mine workings. A detailed study of the spatial clustering of 3 major area-rockbursts (ARB) was carried out using a multi-fractal technique involving generalized correlation integral functions. The spatial distribution analysis of all 3 area-rockbursts showed that they are heterogeneous. The degree of heterogeneity (D2 – D∞) in the cases of ARB-I, II and III were found to be 0.52, 0.37 and 0.41 respectively. These differences in fractal structure indicate that the ARBs of the present study were fully controlled by different heterogeneous stress fields associated with different mining and geological conditions. The present study clearly showed the advantages of the application of multi-fractals to seismic data and to characterise, analyse and examine the area-rockbursts and their causative factors in the Kolar gold mines.

Data partitioning for parallel spatial join processing

The cost of spatial join processing can be very high because of the large sizes of spatial objects and the computation-intensive spatial operations. While parallel processing seems a natural solution to this problem, it is not clear how spatial data can be partitioned for this purpose. Various spatial data partitioning methods are examined in this paper. A framework combining the data-partitioning techniques used by most parallel join algorithms in relational databases and the filter-and-refine strategy for spatial operation processing is proposed for parallel spatial join processing. Object duplication caused by multi-assignment in spatial data partitioning can result in extra CPU cost as well as extra communication cost. We find that the key to overcome this problem is to preserve spatial locality in task decomposition. We show in this paper that a near-optimal speedup can be achieved for parallel spatial join processing using our new algorithms.

Integrating attribute and space characteristics in choropleth display and spatial data mining

This paper develops an interactive approach for exploratory spatial data analysis. Measures of attribute similarity and spatial proximity are combined in a clustering model to support the identification of patterns in spatial information. Relationships between the developed clustering approach, spatial data mining and choropleth display are discussed. Analysis of property crime rates in Brisbane, Australia is presented. A surprising finding in this research is that there are substantial inconsistencies in standard choropleth display options found in two widely used commercial geographical information systems, both in terms of definition and performance. The comparative results demonstrate the usefulness and appeal of the developed approach in a geographical information system environment for exploratory spatial data analysis.

Disaggregation of polygons of surficial geology and soil maps using spatial modelling and legacy data

Examples from the Murray-Darling basin in Australia are used to illustrate different methods of disaggregation of reconnaissance-scale maps. One approach for disaggregation revolves around the de-convolution of the soil-landscape paradigm elaborated during a soil survey. The descriptions of soil ma units and block diagrams in a soil survey report detail soil-landscape relationships or soil toposequences that can be used to disaggregate map units into component landscape elements. Toposequences can be visualised on a computer by combining soil maps with digital elevation data. Expert knowledge or statistics can be used to implement the disaggregation. Use of a restructuring element and k-means clustering are illustrated. Another approach to disaggregation uses training areas to develop rules to extrapolate detailed mapping into other, larger areas where detailed mapping is unavailable. A two-level decision tree example is presented. At one level, the decision tree method is used to capture mapping rules from the training area; at another level, it is used to define the domain over which those rules can be extrapolated. (C) 2001 Elsevier Science B.V. All rights reserved.

Multiresolution spatial databases: Making web-based spatial applications faster

Spatial data has now been used extensively in the Web environment, providing online customized maps and supporting map-based applications. The full potential of Web-based spatial applications, however, has yet to be achieved due to performance issues related to the large sizes and high complexity of spatial data. In this paper, we introduce a multiresolution approach to spatial data management and query processing such that the database server can choose spatial data at the right resolution level for different Web applications. One highly desirable property of the proposed approach is that the server-side processing cost and network traffic can be reduced when the level of resolution required by applications are low. Another advantage is that our approach pushes complex multiresolution structures and algorithms into the spatial database engine. That is, the developer of spatial Web applications needs not to be concerned with such complexity. This paper explains the basic idea, technical feasibility and applications of multiresolution spatial databases.

Spatial distribution of benthic microalgae on coral reefs determined by remote sensing

Understanding the ecological role of benthic microalgae, a highly productive component of coral reef ecosystems, requires information on their spatial distribution. The spatial extent of benthic microalgae on Heron Reef (southern Great Barrier Reef, Australia) was mapped using data from the Landsat 5 Thematic Mapper sensor. integrated with field measurements of sediment chlorophyll concentration and reflectance. Field-measured sediment chlorophyll concentrations. 2 ranging from 23-1.153 mg chl a m(2), were classified into low, medium, and high concentration classes (1-170, 171-290, and > 291 mg chl a m(-2)) using a K-means clustering algorithm. The mapping process assumed that areas in the Thematic Mapper image exhibiting similar reflectance levels in red and blue bands would correspond to areas of similar chlorophyll a levels. Regions of homogenous reflectance values corresponding to low, medium, and high chlorophyll levels were identified over the reef sediment zone by applying a standard image classification algorithm to the Thematic Mapper image. The resulting distribution map revealed large-scale ( > 1 km 2) patterns in chlorophyll a levels throughout the sediment zone of Heron Reef. Reef-wide estimates of chlorophyll a distribution indicate that benthic Microalgae may constitute up to 20% of the total benthic chlorophyll a at Heron Reef. and thus contribute significantly to total primary productivity on the reef.

Model-based clustering in gene expression microarrays: An application to breast cancer data

In microarray studies, the application of clustering techniques is often used to derive meaningful insights into the data. In the past, hierarchical methods have been the primary clustering tool employed to perform this task. The hierarchical algorithms have been mainly applied heuristically to these cluster analysis problems. Further, a major limitation of these methods is their inability to determine the number of clusters. Thus there is a need for a model-based approach to these. clustering problems. To this end, McLachlan et al. [7] developed a mixture model-based algorithm (EMMIX-GENE) for the clustering of tissue samples. To further investigate the EMMIX-GENE procedure as a model-based -approach, we present a case study involving the application of EMMIX-GENE to the breast cancer data as studied recently in van 't Veer et al. [10]. Our analysis considers the problem of clustering the tissue samples on the basis of the genes which is a non-standard problem because the number of genes greatly exceed the number of tissue samples. We demonstrate how EMMIX-GENE can be useful in reducing the initial set of genes down to a more computationally manageable size. The results from this analysis also emphasise the difficulty associated with the task of separating two tissue groups on the basis of a particular subset of genes. These results also shed light on why supervised methods have such a high misallocation error rate for the breast cancer data.

An internet GIS and spatial model to benchmark local government socio-economic performance

This paper develops an Internet geographical information system (GIS) and spatial model application that provides socio-economic information and exploratory spatial data analysis for local government authorities (LGAs) in Queensland, Australia. The application aims to improve the means by which large quantities of data may be analysed, manipulated and displayed in order to highlight trends and patterns as well as provide performance benchmarking that is readily understandable and easily accessible for decision-makers. Measures of attribute similarity and spatial proximity are combined in a clustering model with a spatial autocorrelation index for exploratory spatial data analysis to support the identification of spatial patterns of change. Analysis of socio-economic changes in Queensland is presented. The results demonstrate the usefulness and potential appeal of the Internet GIS applications as a tool to inform the process of regional analysis, planning and policy.