Dynamic Distribution-Sensitive Point Location

We propose a dynamic data structure for the distribution-sensitive point location problem in the plane. Suppose that there is a fixed query distribution within a convex subdivision S , and we are given an oracle that can return in O (1) time the probability of a query point falling into a polygonal region of constant complexity. We can maintain S such that each query is answered in O opt (S) ) expected time, where opt ( S ) is the expected time of the best linear decision tree for answering point location queries in S . The space and construction time are O(n log 2 n ), where n is the number of vertices of S . An update of S as a mixed sequence of k edge insertions and deletions takes O(k log 4 n) amortized time. As a corollary, the randomized incremental construction of the Voronoi diagram of n sites can be performed in O(n log 4 n ) expected time so that, during the incremental construction, a nearest neighbor query at any time can be answered optimally with respect to the intermediate Voronoi diagram at that time.

Potential field data interpolation by Taylor series expansion

Data interpolation is critical in the analysis of geophysical data when some data is missing or inaccessible. We propose to interpolate irregular or missing potential field data using the relation between adjacent data points inspired by the Taylor series expansion (TSE). The TSE method first finds the derivatives of a given point near the query point using data from neighboring points, and then uses the Taylor series to obtain the value at the query point. The TSE method works by extracting local features represented as derivatives from the original data for interpolation in the area of data vacancy. Compared with other interpolation methods, the TSE provides a complete description of potential field data. Specifically, the remainder in TSE can measure local fitting errors and help obtain accurate results. Implementation of the TSE method involves two critical parameters – the order of the Taylor series and the number of neighbors used in the calculation of derivatives. We have found that the first parameter must be carefully chosen to balance between the accuracy and numerical stability when data contains noise. The second parameter can help us build an over-determined system for improved robustness against noise. Methods of selecting neighbors around the given point using an azimuthally uniform distribution or the nearest-distance principle are also presented. The proposed approach is first illustrated by a synthetic gravity dataset from a single survey line, then is generalized to the case over a survey grid. In both numerical experiments, the TSE method has demonstrated an improved interpolation accuracy in comparison with the minimum curvature method. Finally we apply the TSE method to a ground gravity dataset from the Abitibi Greenstone Belt, Canada, and an airborne gravity dataset from the Vinton Dome, Louisiana, USA.

Query-Points Visibility Constraint Minimum Link Paths in Simple Polygons

We study the query version of constrained minimum link paths between two points inside a simple polygon P with n vertices such that there is at least one point on the path, visible from a query point. The method is based on partitioning P into a number of faces of equal link distance from a point, called a link-based shortest path map (SPM). Initially, we solve this problem for two given points s, t and a query point q. Then, the proposed solution is extended to a general case for three arbitrary query points s, t and q. In the former, we propose an algorithm with O(n) preprocessing time. Extending this approach for the latter case, we develop an algorithm with O(n3) preprocessing time. The link distance of a q-visible path between s, t as well as the path are provided in time O(log n) and O(m + log n), respectively, for the above two cases, where m is the number of links.

Exact Nearest Neighbour Search within Constrained Neighbourhood Using the Forest of Vp-Tree-Like Structures

In this paper, we address the problem of fast nearest neighbour search. Unfortunately, well-known indexing data structures, such as vp-trees perform poorly on some datasets and do not provide significant acceleration compared to the brute force approach. In the paper, we consider an alternative solution, which can be applied if we are not interested in some fraction of distant nearest neighbours. This solution is based on building the forest of vp-tree-like structures and guarantees the exact nearest neighbour search in the epsilon-neighbourhood of the query point.

Multi-Task Gaussian Process Upper Confidence Bound for Hyperparameter Tuning

In many scientific and engineering applications, Bayesian optimization (BO) is a powerful tool for hyperparameter tuning of a machine learning model, materials design and discovery, etc. BO guides the choice of experiments in a sequential way to find a good combination of design points in as few experiments as possible. It can be formulated as a problem of optimizing a “black-box” function. Different from single-task Bayesian optimization, Multi-task Bayesian optimization is a general method to efficiently optimize multiple different but correlated “black-box” functions. The previous works in Multi-task Bayesian optimization algorithm queries a point to be evaluated for all tasks in each round of search, which is not efficient. For the case where different tasks are correlated, it is not necessary to evaluate all tasks for a given query point. Therefore, the objective of this work is to develop an algorithm for multi-task Bayesian optimization with automatic task selection so that only one task evaluation is needed per query round. Specifically, a new algorithm, namely, multi-task Gaussian process upper confidence bound (MT-GPUCB), is proposed to achieve this objective. The MT-GPUCB is a two-step algorithm, where the first step chooses which query point to evaluate, and the second step automatically selects the most informative task to evaluate. Under the bandit setting, a theoretical analysis is provided to show that our proposed MT-GPUCB is no-regret under some mild conditions. Our proposed algorithm is verified experimentally on a range of synthetic functions as well as real-world problems. The results clearly show the advantages of our query strategy for both design point and task.

Multi-Task Gaussian Process Upper Confidence Bound for Hyperparameter Tuning

In many scientific and engineering applications, Bayesian optimization (BO) is a powerful tool for hyperparameter tuning of a machine learning model, materials design and discovery, etc. BO guides the choice of experiments in a sequential way to find a good combination of design points in as few experiments as possible. It can be formulated as a problem of optimizing a “black-box” function. Different from single-task Bayesian optimization, Multi-task Bayesian optimization is a general method to efficiently optimize multiple different but correlated “black-box” functions. The previous works in Multi-task Bayesian optimization algorithm queries a point to be evaluated for all tasks in each round of search, which is not efficient. For the case where different tasks are correlated, it is not necessary to evaluate all tasks for a given query point. Therefore, the objective of this work is to develop an algorithm for multi-task Bayesian optimization with automatic task selection so that only one task evaluation is needed per query round. Specifically, a new algorithm, namely, multi-task Gaussian process upper confidence bound (MT-GPUCB), is proposed to achieve this objective. The MT-GPUCB is a two-step algorithm, where the first step chooses which query point to evaluate, and the second step automatically selects the most informative task to evaluate. Under the bandit setting, a theoretical analysis is provided to show that our proposed MT-GPUCB is no-regret under some mild conditions. Our proposed algorithm is verified experimentally on a range of synthetic functions as well as real-world problems. The results clearly show the advantages of our query strategy for both design point and task.

Fair near neighbor search via sampling

Similarity search is a fundamental algorithmic primitive, widely used in many computer science disciplines. Given a set of points S and a radius parameter r > 0, the rnear neighbor (r-NN) problem asks for a data structure that, given any query point q, returns a point p within distance at most r from q. In this paper, we study the r-NN problem in the light of individual fairness and providing equal opportunities: all points that are within distance r from the query should have the same probability to be returned. In the low-dimensional case, this problem was first studied by Hu, Qiao, and Tao (PODS 2014). Locality sensitive hashing (LSH), the theoretically strongest approach to similarity search in high dimensions, does not provide such a fairness guarantee.

NN Search based on Non-uniform Space Partition on Air

It is one of most important challenges in information services based on location to support a huge number of clients to process the NN query for a given query point. A scheme of NN query processing based on wireless data broadcasting is an effective way to overcome the challenge. In this paper, we propose an indexing scheme NSPI (Non-uniform Space Partition Index) for quick NN search over wireless data broadcasting. For implementing the aim, we use a non-uniform spatial partition and provide an index based on the partition for equidistance between indexes on the wireless channel. The index scheme enables the clients to process NN quickly by lessening the time for the clients to meet the index on the channel. To show the effectiveness of the proposed scheme, we compare the access time and tuning time of the clients with existing indexing schemes by simulation studies. The proposed NSPI shows shorter access time than the other existing scheme. Also, NSPI outperforms in the aspect of tuning time than the others.

Predicting Heavy Oil Combustion Kinetics with Machine Learning

Heavy oil resources are becoming increasingly important for the global oil supply, and consequently there has been renewed interest in techniques for extracting heavy oil. Among these, in-situ combustion (ISC) has tremendous potential for late-stage heavy oil fields, as well as high viscosity, very deep, or other unconventional reservoirs. A critical step in evaluating the use of ISC in a potential project is developing an accurate chemical reaction model to employ for larger-scale simulations. Such models can be difficult to calibrate, however, that in turn can lead to large errors in upscaled simulations. Data-driven models of ISC kinetics overcome these issues by foregoing the calibration step and predicting kinetics directly from laboratory data. In this work, we introduce the Non-Arrhenius Machine Learning Approach (NAMLA). NAMLA is a machine learning-based method for predicting O2 consumption in heavy oil combustion directly from ramped temperature oxidation (RTO) experimental data. Our model treats the O2 consumption as a function of only temperature and total O2 conversion and uses a locally-weighted linear regression model to predict the conversion rate at a query point. We apply this method to simulated and experimental data from heavy oil samples and compare its ability to predict O2 consumption curves with a previously proposed interpolation-based method. Results show that the presented method has better performance than previously proposed interpolation models when the available experimental data is very sparse or the query point lies outside the range of RTO experiments in the dataset. When available data is sufficiently dense or the query point is within the range of RTO curves in the training set, then linear interpolation has comparable or better accuracy than the proposed method. The biggest advantage of the proposed method is that it is able to compute confidence intervals for experimentally measured or estimated O2 consumption curves. We believe that future methods will be able to use the efficiency and accuracy of interpolation-based methods with the statistical properties of the proposed machine learning approach to better characterize and predict heavy oil combustion.

A parametric approximation algorithm for spatial group keyword queries

With the application of big data, various queries arise for information retrieval. Spatial group keyword queries aim to find a set of spatial objects that cover the query keywords and minimize a goal function such as the total distance between the objects and the query point. This problem is widely found in database applications and is known to be NP-hard. Efficient algorithms for solving this problem can only provide approximate solutions, and most of these algorithms achieve a fixed approximation ratio (the upper bound of the ratio of an approximate goal value to the optimal goal value). Thus, to obtain a self-adjusting algorithm, we propose an approximation algorithm for achieving a parametric approximation ratio. The algorithm makes a trade-off between the approximation ratio and time consumption enabling the users to assign arbitrary query accuracy. Additionally, it runs in an on-the-fly manner, making it scalable to large-scale applications. The efficiency and scalability of the algorithm were further validated using benchmark datasets.