In Voronoi-based nearest neighbor search, the Voronoi cell of every point p in a database can be used to check whether p is the closest to some query point q. We extend the notion of Voronoi cells to support uncertain objects, whose attribute values are inexact. Particularly, we propose the Possible Voronoi cell (or PV-cell). A PV-cell of a multi-dimensional uncertain object o is a region R, such that for any point p ∈ R, o may be the nearest neighbor of p. If the PV-cells of all objects in a database S are known, they can be used to identify objects that have a chance to be the nearest neighbor of q. However, there is no efficient algorithm for computing an exact PV-cell. We hence study how to derive an axis-parallel hyper-rectangle (called the Uncertain Bounding Rectangle, or UBR) that tightly contains a PV-cell. We further develop the PV-index, a structure that stores UBRs, to evaluate probabilistic nearest neighbor queries over uncertain data. An advantage of the PV-index is that upon updates on S, it can be incrementally updated. Extensive experiments on both synthetic and real datasets are carried out to validate the performance of the PV-index. / published_or_final_version / Computer Science / Master / Master of Philosophy

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 91-95). Also available in electronic version. Access restricted to campus users.

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2005. / Includes bibliographical references (leaves 60-61). Also available in electronic version.

We present an algorithm for c-approximate nearest neighbor problem in a d-dimensional Euclidean space, achieving query time ofO(dn^{1/c^2+o(1)}) and space O(dn + n^{1+1/c^2+o(1)}).

The purpose of the present thesis is to show that hyperspectral data can be used for discrimination between different tree species. The data set used in this study contains the hyperspectral measurements of leaves of seven savannah tree species. The data is high-dimensional and shows large within-class variability combined with small between-class variability which makes discrimination between the classes challenging. We employ two classification methods: G-nearest neighbour and feed-forward neural networks. For both methods, direct 7-class prediction results in high misclassification rates. However, binary classification works better. We constructed binary classifiers for all possible binary classification problems and combine them with Error Correcting Output Codes. We show especially that the use of 1-nearest neighbour binary classifiers results in no improvement compared to a direct 1-nearest neighbour 7-class predictor. In contrast to this negative result, the use of neural networks binary classifiers improves accuracy by 10% compared to a direct neural networks 7-class predictor, and error rates become acceptable. This can be further improved by choosing only suitable binary classifiers for combination.

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There is a lack of precise and universally accepted approach in the quantification of carbon sequestered in aboveground woody biomass using remotely sensed data. Drafting of the Kyoto Protocol has made the subject of carbon sequestration more important, making the development of accurate and cost-effective remote sensing models a necessity. There has been much work done in estimating aboveground woody biomass from spectral data using the traditional multiple linear regression analysis approach and the Finnish k-nearest neighbor approach, but the accuracy of these methods to estimate biomass has not been compared. The purpose of this study is to compare the ability of these two methods in estimating above ground biomass (AGB) using spectral data derived from Landsat ETM+ imagery.

The approximate nearest neighbor(ANN) search over high dimensional data has become an unavoidable service for online applications. Fast and high-quality results of unknown queries are the largest challenge that most algorithms faced with. Locality Sensitive Hashing(LSH) is a well-known ANN search algorithm while suffers from inefficient index structure, poor accuracy in distributed scheme. The traditional index structures have most significant bits(MSB) problem, which is their indexing strategies have an implicit assumption that the bits from one direction in the hash value have higher priority. In this thesis, we propose a new content-based index called Random Draw Forest(RDF), which not only uses an adaptive tree structure by applying the dynamic length of compound hash functions to meet the different cardinality of data, but also applies the shuffling permutations to solve the MSB problem in the traditional LSH-based index. To raise the accuracy in the distributed scheme, we design a variable steps lookup strategy to search the multiple step sub-indexes which are most likely to hold the mistakenly partitioned similar objects. By analyzing the index, we show that RDF has a higher probability to retrieve the similar objects compare to the original index structure. In the experiment, we first learn the performance of different hash functions, then we show the effect of parameters in RDF and the performance of RDF compared with other LSH-based methods to meet the ANN search. / Thesis / Master of Science (MSc)

An extension of the original Ott-Grebogy-Yorke control scheme is used on a simple double pendulum. The base point of the double pendulum moves in both horizontal and vertical directions which leads to rather complicated behavior.A delay coordinate is used to reconstruct the attractor. The required dimension is determined by the False Nearest Neighbor analysis. A newly developed Fixed Point Transformation method is used to identify the unstable periodic orbit (UPO). Two different system parameters are used to control the motion. Minimum parameter constraints are studied. The use of discrete values for parameter changes is also investigated. Based on these investigations, a new on-off control scheme is proposed to simplify the implementation of the controller and minimize the delay in applying the control. / Ph. D.

Nearest-neighbor search is a very natural and universal problem in computer science. Often times, the problem size necessitates approximation. In this thesis, I present new paradigms for nearest-neighbor search (along with new algorithms and theory in these paradigms) that make nearest-neighbor search more usable and accurate. First, I consider a new notion of search error, the rank error, for an approximate neighbor candidate. Rank error corresponds to the number of possible candidates which are better than the approximate neighbor candidate. I motivate this notion of error and present new efficient algorithms that return approximate neighbors with rank error no more than a user specified amount. Then I focus on approximate search in a scenario where the user does not specify the tolerable search error (error constraint); instead the user specifies the amount of time available for search (time constraint). After differentiating between these two scenarios, I present some simple algorithms for time constrained search with provable performance guarantees. I use this theory to motivate a new space-partitioning data structure, the max-margin tree, for improved search performance in the time constrained setting. Finally, I consider the scenario where we do not require our objects to have an explicit fixed-length representation (vector data). This allows us to search with a large class of objects which include images, documents, graphs, strings, time series and natural language. For nearest-neighbor search in this general setting, I present a provably fast novel exact search algorithm. I also discuss the empirical performance of all the presented algorithms on real data.