Skewness-Based Partitioning in SpatialHadoop

In recent years, several extensions of the Hadoop system have been proposed for dealing with spatial data. SpatialHadoop belongs to this group of projects and includes some MapReduce implementations of spatial operators, like range queries and spatial join. the MapReduce paradigm is based on the fundamental principle that a task can be parallelized by partitioning data into chunks and performing the same operation on them, (map phase), eventually combining the partial results at the end (reduce phase). Thus, the applied partitioning technique can tremendously affect the performance of a parallel execution, since it is the key point for obtaining balanced map tasks and exploiting the parallelism as much as possible. When uniformly distributed datasets are considered, this goal can be easily obtained by using a regular grid covering the whole reference space for partitioning the geometries of the input dataset; conversely, with skewed distributed datasets, this might not be the right choice and other techniques have to be applied. for instance, SpatialHadoop can produce a global index also by means of a Quadtree-based grid or an Rtree-based grid, which in turn are more expensive index structures to build. This paper proposes a technique based on both a box counting function and a heuristic, rooted on theoretical properties and experimental observations, for detecting the degree of skewness of an input spatial dataset and then deciding which partitioning technique to apply in order to improve as much as possible the performance of subsequent operations. Experiments on both synthetic and real datasets are presented to confirm the effectiveness of the proposed approach

Using Deep Learning for Big Spatial Data Partitioning

This article explores the use of deep learning to choose an appropriate spatial partitioning technique for big data. The exponential increase in the volumes of spatial datasets resulted in the development of big spatial data frameworks. These systems need to partition the data across machines to be able to scale out the computation. Unfortunately, there is no current method to automatically choose an appropriate partitioning technique based on the input data distribution. This article addresses this problem by using deep learning to train a model that captures the relationship between the data distribution and the quality of the partitioning techniques.We propose a solution that runs in two phases, training and application. The offline training phase generates synthetic data based on diverse distributions, partitions them using six different partitioning techniques, and measures their quality using four quality metrics. At the same time, it summarizes the datasets using a histogram and well-designed skewness measures. The data summaries and the quality metrics are then use to train a deep learning model. The second phase uses this model to predict the best partitioning technique given a new dataset that needs to be partitioned.We run an extensive experimental evaluation on big spatial data, andwe experimentally showthe applicability of the proposed technique.We showthat the proposed model outperforms the baseline method in terms of accuracy for choosing the best partitioning technique by only analyzing the summary of the datasets

Efficient similarity search in high-dimensional data spaces

Similarity search in high-dimensional data spaces is a popular paradigm for many modern database applications, such as content based image retrieval, time series analysis in financial and marketing databases, and data mining. Objects are represented as high-dimensional points or vectors based on their important features. Object similarity is then measured by the distance between feature vectors and similarity search is implemented via range queries or k-Nearest Neighbor (k-NN) queries. Implementing k-NN queries via a sequential scan of large tables of feature vectors is computationally expensive. Building multi-dimensional indexes on the feature vectors for k-NN search also tends to be unsatisfactory when the dimensionality is high. This is due to the poor index performance caused by the dimensionality curse. Dimensionality reduction using the Singular Value Decomposition method is the approach adopted in this study to deal with high-dimensional data. Noting that for many real-world datasets, data distribution tends to be heterogeneous, dimensionality reduction on the entire dataset may cause a significant loss of information. More efficient representation is sought by clustering the data into homogeneous subsets of points, and applying dimensionality reduction to each cluster respectively, i.e., utilizing local rather than global dimensionality reduction. The thesis deals with the improvement of the efficiency of query processing associated with local dimensionality reduction methods, such as the Clustering and Singular Value Decomposition (CSVD) and the Local Dimensionality Reduction (LDR) methods. Variations in the implementation of CSVD are considered and the two methods are compared from the viewpoint of the compression ratio, CPU time, and retrieval efficiency. An exact k-NN algorithm is presented for local dimensionality reduction methods by extending an existing multi-step k-NN search algorithm, which is designed for global dimensionality reduction. Experimental results show that the new method requires less CPU time than the approximate method proposed original for CSVD at a comparable level of accuracy. Optimal subspace dimensionality reduction has the intent of minimizing total query cost. The problem is complicated in that each cluster can retain a different number of dimensions. A hybrid method is presented, combining the best features of the CSVD and LDR methods, to find optimal subspace dimensionalities for clusters generated by local dimensionality reduction methods. The experiments show that the proposed method works well for both real-world datasets and synthetic datasets

Sonar image interpretation for sub-sea operations

Mine Counter-Measure (MCM) missions are conducted to neutralise underwater explosives. Automatic Target Recognition (ATR) assists operators by increasing the speed and accuracy of data review. ATR embedded on vehicles enables adaptive missions which increase the speed of data acquisition. This thesis addresses three challenges; the speed of data processing, robustness of ATR to environmental conditions and the large quantities of data required to train an algorithm. The main contribution of this thesis is a novel ATR algorithm. The algorithm uses features derived from the projection of 3D boxes to produce a set of 2D templates. The template responses are independent of grazing angle, range and target orientation. Integer skewed integral images, are derived to accelerate the calculation of the template responses. The algorithm is compared to the Haar cascade algorithm. For a single model of sonar and cylindrical targets the algorithm reduces the Probability of False Alarm (PFA) by 80% at a Probability of Detection (PD) of 85%. The algorithm is trained on target data from another model of sonar. The PD is only 6% lower even though no representative target data was used for training. The second major contribution is an adaptive ATR algorithm that uses local sea-floor characteristics to address the problem of ATR robustness with respect to the local environment. A dual-tree wavelet decomposition of the sea-floor and an Markov Random Field (MRF) based graph-cut algorithm is used to segment the terrain. A Neural Network (NN) is then trained to filter ATR results based on the local sea-floor context. It is shown, for the Haar Cascade algorithm, that the PFA can be reduced by 70% at a PD of 85%. Speed of data processing is addressed using novel pre-processing techniques. The standard three class MRF, for sonar image segmentation, is formulated using graph-cuts. Consequently, a 1.2 million pixel image is segmented in 1.2 seconds. Additionally, local estimation of class models is introduced to remove range dependent segmentation quality. Finally, an A* graph search is developed to remove the surface return, a line of saturated pixels often detected as false alarms by ATR. The A* search identifies the surface return in 199 of 220 images tested with a runtime of 2.1 seconds. The algorithm is robust to the presence of ripples and rocks

Efficient Analysis in Multimedia Databases

The rapid progress of digital technology has led to a situation where computers have become ubiquitous tools. Now we can find them in almost every environment, be it industrial or even private. With ever increasing performance computers assumed more and more vital tasks in engineering, climate and environmental research, medicine and the content industry. Previously, these tasks could only be accomplished by spending enormous amounts of time and money. By using digital sensor devices, like earth observation satellites, genome sequencers or video cameras, the amount and complexity of data with a spatial or temporal relation has gown enormously. This has led to new challenges for the data analysis and requires the use of modern multimedia databases. This thesis aims at developing efficient techniques for the analysis of complex multimedia objects such as CAD data, time series and videos. It is assumed that the data is modeled by commonly used representations. For example CAD data is represented as a set of voxels, audio and video data is represented as multi-represented, multi-dimensional time series. The main part of this thesis focuses on finding efficient methods for collision queries of complex spatial objects. One way to speed up those queries is to employ a cost-based decompositioning, which uses interval groups to approximate a spatial object. For example, this technique can be used for the Digital Mock-Up (DMU) process, which helps engineers to ensure short product cycles. This thesis defines and discusses a new similarity measure for time series called threshold-similarity. Two time series are considered similar if they expose a similar behavior regarding the transgression of a given threshold value. Another part of the thesis is concerned with the efficient calculation of reverse k-nearest neighbor (RkNN) queries in general metric spaces using conservative and progressive approximations. The aim of such RkNN queries is to determine the impact of single objects on the whole database. At the end, the thesis deals with video retrieval and hierarchical genre classification of music using multiple representations. The practical relevance of the discussed genre classification approach is highlighted with a prototype tool that helps the user to organize large music collections. Both the efficiency and the effectiveness of the presented techniques are thoroughly analyzed. The benefits over traditional approaches are shown by evaluating the new methods on real-world test datasets

Handbook of Mathematical Geosciences

This Open Access handbook published at the IAMG's 50th anniversary, presents a compilation of invited path-breaking research contributions by award-winning geoscientists who have been instrumental in shaping the IAMG. It contains 45 chapters that are categorized broadly into five parts (i) theory, (ii) general applications, (iii) exploration and resource estimation, (iv) reviews, and (v) reminiscences covering related topics like mathematical geosciences, mathematical morphology, geostatistics, fractals and multifractals, spatial statistics, multipoint geostatistics, compositional data analysis, informatics, geocomputation, numerical methods, and chaos theory in the geosciences