18,477 research outputs found
Doctor of Philosophy in Computing
dissertationIn the last two decades, an increasingly large amount of data has become available. Massive collections of videos, astronomical observations, social networking posts, network routing information, mobile location history and so forth are examples of real world data requiring processing for applications ranging from classi?cation to predictions. Computational resources grow at a far more constrained rate, and hence the need for ef?cient algorithms that scale well. Over the past twenty years high quality theoretical algorithms have been developed for two central problems: nearest neighbor search and dimensionality reduction over Euclidean distances in worst case distributions. These two tasks are interesting in their own right. Nearest neighbor corresponds to a database query lookup, while dimensionality reduction is a form of compression on massive data. Moreover, these are also subroutines in algorithms ranging from clustering to classi?cation. However, many highly relevant settings and distance measures have not received similar attention to that of worst case point sets in Euclidean space. The Bregman divergences include the information theoretic distances, such as entropy, of most relevance in many machine learning applications and yet prior to this dissertation lacked ef?cient dimensionality reductions, nearest neighbor algorithms, or even lower bounds on what could be possible. Furthermore, even in the Euclidean setting, theoretical algorithms do not leverage that almost all real world datasets have signi?cant low-dimensional substructure. In this dissertation, we explore different models and techniques for similarity search and dimensionality reduction. What upper bounds can be obtained for nearest neighbors for Bregman divergences? What upper bounds can be achieved for dimensionality reduction for information theoretic measures? Are these problems indeed intrinsically of harder computational complexity than in the Euclidean setting? Can we improve the state of the art nearest neighbor algorithms for real world datasets in Euclidean space? These are the questions we investigate in this dissertation, and that we shed some new insight on. In the ?rst part of our dissertation, we focus on Bregman divergences. We exhibit nearest neighbor algorithms, contingent on a distributional constraint on the datasets. We next show lower bounds suggesting that is in some sense inherent to the problem complexity. After this we explore dimensionality reduction techniques for the Jensen-Shannon and Hellinger distances, two popular information theoretic measures. In the second part, we show that even for the more well-studied Euclidean case, worst case nearest neighbor algorithms can be improved upon sharply for real world datasets with spectral structure
Indexability, concentration, and VC theory
Degrading performance of indexing schemes for exact similarity search in high
dimensions has long since been linked to histograms of distributions of
distances and other 1-Lipschitz functions getting concentrated. We discuss this
observation in the framework of the phenomenon of concentration of measure on
the structures of high dimension and the Vapnik-Chervonenkis theory of
statistical learning.Comment: 17 pages, final submission to J. Discrete Algorithms (an expanded,
improved and corrected version of the SISAP'2010 invited paper, this e-print,
v3
DRSP : Dimension Reduction For Similarity Matching And Pruning Of Time Series Data Streams
Similarity matching and join of time series data streams has gained a lot of
relevance in today's world that has large streaming data. This process finds
wide scale application in the areas of location tracking, sensor networks,
object positioning and monitoring to name a few. However, as the size of the
data stream increases, the cost involved to retain all the data in order to aid
the process of similarity matching also increases. We develop a novel framework
to addresses the following objectives. Firstly, Dimension reduction is
performed in the preprocessing stage, where large stream data is segmented and
reduced into a compact representation such that it retains all the crucial
information by a technique called Multi-level Segment Means (MSM). This reduces
the space complexity associated with the storage of large time-series data
streams. Secondly, it incorporates effective Similarity Matching technique to
analyze if the new data objects are symmetric to the existing data stream. And
finally, the Pruning Technique that filters out the pseudo data object pairs
and join only the relevant pairs. The computational cost for MSM is O(l*ni) and
the cost for pruning is O(DRF*wsize*d), where DRF is the Dimension Reduction
Factor. We have performed exhaustive experimental trials to show that the
proposed framework is both efficient and competent in comparison with earlier
works.Comment: 20 pages,8 figures, 6 Table
A quick search method for audio signals based on a piecewise linear representation of feature trajectories
This paper presents a new method for a quick similarity-based search through
long unlabeled audio streams to detect and locate audio clips provided by
users. The method involves feature-dimension reduction based on a piecewise
linear representation of a sequential feature trajectory extracted from a long
audio stream. Two techniques enable us to obtain a piecewise linear
representation: the dynamic segmentation of feature trajectories and the
segment-based Karhunen-L\'{o}eve (KL) transform. The proposed search method
guarantees the same search results as the search method without the proposed
feature-dimension reduction method in principle. Experiment results indicate
significant improvements in search speed. For example the proposed method
reduced the total search time to approximately 1/12 that of previous methods
and detected queries in approximately 0.3 seconds from a 200-hour audio
database.Comment: 20 pages, to appear in IEEE Transactions on Audio, Speech and
Language Processin
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