Matching Items (4)
Description
K-Nearest-Neighbors (KNN) search is a fundamental problem in many application domains such as database and data mining, information retrieval, machine learning, pattern recognition and plagiarism detection. Locality sensitive hash (LSH) is so far the most practical approximate KNN search algorithm for high dimensional data. Algorithms such as Multi-Probe LSH and LSH-Forest improve upon the basic LSH algorithm by varying hash bucket size dynamically at query time, so these two algorithms can answer different KNN queries adaptively. However, these two algorithms need a data access post-processing step after candidates' collection in order to get the final answer to the KNN query. In this thesis, Multi-Probe LSH with data access post-processing (Multi-Probe LSH with DAPP) algorithm and LSH-Forest with data access post-processing (LSH-Forest with DAPP) algorithm are improved by replacing the costly data access post-processing (DAPP) step with a much faster histogram-based post-processing (HBPP). Two HBPP algorithms: LSH-Forest with HBPP and Multi- Probe LSH with HBPP are presented in this thesis, both of them achieve the three goals for KNN search in large scale high dimensional data set: high search quality, high time efficiency, high space efficiency. None of the previous KNN algorithms can achieve all three goals. More specifically, it is shown that HBPP algorithms can always achieve high search quality (as good as LSH-Forest with DAPP and Multi-Probe LSH with DAPP) with much less time cost (one to several orders of magnitude speedup) and same memory usage. It is also shown that with almost same time cost and memory usage, HBPP algorithms can always achieve better search quality than LSH-Forest with random pick (LSH-Forest with RP) and Multi-Probe LSH with random pick (Multi-Probe LSH with RP). Moreover, to achieve a very high search quality, Multi-Probe with HBPP is always a better choice than LSH-Forest with HBPP, regardless of the distribution, size and dimension number of the data set.
ContributorsYu, Renwei (Author) / Candan, Kasim S (Thesis advisor) / Sapino, Maria L (Committee member) / Chen, Yi (Committee member) / Sundaram, Hari (Committee member) / Arizona State University (Publisher)
Created2011
Description
Finding the optimal solution to a problem with an enormous search space can be challenging. Unless a combinatorial construction technique is found that also guarantees the optimality of the resulting solution, this could be an infeasible task. If such a technique is unavailable, different heuristic methods are generally used to improve the upper bound on the size of the optimal solution. This dissertation presents an alternative method which can be used to improve a solution to a problem rather than construct a solution from scratch. Necessity analysis, which is the key to this approach, is the process of analyzing the necessity of each element in a solution. The post-optimization algorithm presented here utilizes the result of the necessity analysis to improve the quality of the solution by eliminating unnecessary objects from the solution. While this technique could potentially be applied to different domains, this dissertation focuses on k-restriction problems, where a solution to the problem can be presented as an array. A scalable post-optimization algorithm for covering arrays is described, which starts from a valid solution and performs necessity analysis to iteratively improve the quality of the solution. It is shown that not only can this technique improve upon the previously best known results, it can also be added as a refinement step to any construction technique and in most cases further improvements are expected. The post-optimization algorithm is then modified to accommodate every k-restriction problem; and this generic algorithm can be used as a starting point to create a reasonable sized solution for any such problem. This generic algorithm is then further refined for hash family problems, by adding a conflict graph analysis to the necessity analysis phase. By recoloring the conflict graphs a new degree of flexibility is explored, which can further improve the quality of the solution.
ContributorsNayeri, Peyman (Author) / Colbourn, Charles (Thesis advisor) / Konjevod, Goran (Thesis advisor) / Sen, Arunabha (Committee member) / Stanzione Jr, Daniel (Committee member) / Arizona State University (Publisher)
Created2011
Description
Modern software and hardware systems are composed of a large number of components. Often different components of a system interact with each other in unforeseen and undesired ways to cause failures. Covering arrays are a useful mathematical tool for testing all possible t-way interactions among the components of a system.
The two major issues concerning covering arrays are explicit construction of a covering array, and exact or approximate determination of the covering array number---the minimum size of a covering array. Although these problems have been investigated extensively for the last couple of decades, in this thesis we present significant improvements on both of these questions using tools from the probabilistic method and randomized algorithms.
First, a series of improvements is developed on the previously known upper bounds on covering array numbers. An estimate for the discrete Stein-Lovász-Johnson bound is derived and the Stein- Lovász -Johnson bound is improved upon using an alteration strategy. Then group actions on the set of symbols are explored to establish two asymptotic upper bounds on covering array numbers that are tighter than any of the presently known bounds.
Second, an algorithmic paradigm, called the two-stage framework, is introduced for covering array construction. A number of concrete algorithms from this framework are analyzed, and it is shown that they outperform current methods in the range of parameter values that are of practical relevance. In some cases, a reduction in the number of tests by more than 50% is achieved.
Third, the Lovász local lemma is applied on covering perfect hash families to obtain an upper bound on covering array numbers that is tightest of all known bounds. This bound leads to a Moser-Tardos type algorithm that employs linear algebraic computation over finite fields to construct covering arrays. In some cases, this algorithm outperforms currently used methods by more than an 80% margin.
Finally, partial covering arrays are introduced to investigate a few practically relevant relaxations of the covering requirement. Using probabilistic methods, bounds are obtained on partial covering arrays that are significantly smaller than for covering arrays. Also, randomized algorithms are provided that construct such arrays in expected polynomial time.
The two major issues concerning covering arrays are explicit construction of a covering array, and exact or approximate determination of the covering array number---the minimum size of a covering array. Although these problems have been investigated extensively for the last couple of decades, in this thesis we present significant improvements on both of these questions using tools from the probabilistic method and randomized algorithms.
First, a series of improvements is developed on the previously known upper bounds on covering array numbers. An estimate for the discrete Stein-Lovász-Johnson bound is derived and the Stein- Lovász -Johnson bound is improved upon using an alteration strategy. Then group actions on the set of symbols are explored to establish two asymptotic upper bounds on covering array numbers that are tighter than any of the presently known bounds.
Second, an algorithmic paradigm, called the two-stage framework, is introduced for covering array construction. A number of concrete algorithms from this framework are analyzed, and it is shown that they outperform current methods in the range of parameter values that are of practical relevance. In some cases, a reduction in the number of tests by more than 50% is achieved.
Third, the Lovász local lemma is applied on covering perfect hash families to obtain an upper bound on covering array numbers that is tightest of all known bounds. This bound leads to a Moser-Tardos type algorithm that employs linear algebraic computation over finite fields to construct covering arrays. In some cases, this algorithm outperforms currently used methods by more than an 80% margin.
Finally, partial covering arrays are introduced to investigate a few practically relevant relaxations of the covering requirement. Using probabilistic methods, bounds are obtained on partial covering arrays that are significantly smaller than for covering arrays. Also, randomized algorithms are provided that construct such arrays in expected polynomial time.
ContributorsSarakāra, Kauśika (Author) / Colbourn, Charles J. (Thesis advisor) / Czygrinow, Andrzej (Committee member) / Richa, Andréa W. (Committee member) / Syrotiuk, Violet R. (Committee member) / Arizona State University (Publisher)
Created2016
Description
Similarity search in high-dimensional spaces is popular for applications like image
processing, time series, and genome data. In higher dimensions, the phenomenon of
curse of dimensionality kills the effectiveness of most of the index structures, giving
way to approximate methods like Locality Sensitive Hashing (LSH), to answer similarity
searches. In addition to range searches and k-nearest neighbor searches, there
is a need to answer negative queries formed by excluded regions, in high-dimensional
data. Though there have been a slew of variants of LSH to improve efficiency, reduce
storage, and provide better accuracies, none of the techniques are capable of
answering queries in the presence of excluded regions.
This thesis provides a novel approach to handle such negative queries. This is
achieved by creating a prefix based hierarchical index structure. First, the higher
dimensional space is projected to a lower dimension space. Then, a one-dimensional
ordering is developed, while retaining the hierarchical traits. The algorithm intelligently
prunes the irrelevant candidates while answering queries in the presence of
excluded regions. While naive LSH would need to filter out the negative query results
from the main results, the new algorithm minimizes the need to fetch the redundant
results in the first place. Experiment results show that this reduces post-processing
cost thereby reducing the query processing time.
processing, time series, and genome data. In higher dimensions, the phenomenon of
curse of dimensionality kills the effectiveness of most of the index structures, giving
way to approximate methods like Locality Sensitive Hashing (LSH), to answer similarity
searches. In addition to range searches and k-nearest neighbor searches, there
is a need to answer negative queries formed by excluded regions, in high-dimensional
data. Though there have been a slew of variants of LSH to improve efficiency, reduce
storage, and provide better accuracies, none of the techniques are capable of
answering queries in the presence of excluded regions.
This thesis provides a novel approach to handle such negative queries. This is
achieved by creating a prefix based hierarchical index structure. First, the higher
dimensional space is projected to a lower dimension space. Then, a one-dimensional
ordering is developed, while retaining the hierarchical traits. The algorithm intelligently
prunes the irrelevant candidates while answering queries in the presence of
excluded regions. While naive LSH would need to filter out the negative query results
from the main results, the new algorithm minimizes the need to fetch the redundant
results in the first place. Experiment results show that this reduces post-processing
cost thereby reducing the query processing time.
ContributorsBhat, Aneesha (Author) / Candan, Kasim Selcuk (Thesis advisor) / Davulcu, Hasan (Committee member) / Sapino, Maria Luisa (Committee member) / Sarwat, Mohamed (Committee member) / Arizona State University (Publisher)
Created2016