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Lecture Notes in Computer Science 2341
Edited by G. Goos, J. Hartmanis, and J. van Leeuwen

3
Berlin
Heidelberg
New York
Barcelona
Hong Kong
London
Milan
Paris
Tokyo

Cui Yu
High-Dimensional
Indexing
Transformational Approaches
to High-Dimensional Range and Similarity Searches
1 3

Series Editors
Gerhard Goos, Karlsruhe University, Germany
Juris Hartmanis, Cornell University, NY, USA
Jan van Leeuwen, Utrecht University, The Netherlands
Author
Cui Yu
Monmouth University, Department of Computer Science
West Long Branch, NJ 07764, USA
National University of Singapore, Department of Computer Science
Kent Ridge, Singapore 117543, Singapore
E-mail:cyu@monmouth.edu
Cataloging-in-Publication Data applied for
Bibliographic information published by Die Deutsche Bibliothek
Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie;
detailed bibliographic data is available in the Internet at <http://dnb.ddb.de>.
CR Subject Classification (1998): H.3.1, H.2.8, H.3, H.2, E.2, E.1, H.4, H.5.1
ISSN 0302-9743
ISBN 3-540-44199-9 Springer-Verlag Berlin Heidelberg New York
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is
concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting,
reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication
or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965,
in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are
liable for prosecution under the German Copyright Law.
Springer-Verlag Berlin Heidelberg New York
a member of BertelsmannSpringer Science+Business Media GmbH
http://www.springer.de
© Springer-Verlag Berlin Heidelberg 2002
Printed in Germany
Typesetting: Camera-ready by author, data conversion by Boller Mediendesign
Printed on acid-free paper SPIN: 10869935 06/3142 5 4 3 2 1 0

Preface
Many new applications, such as multimedia databases, employ the so-called
feature transformation which transforms important features or properties
of data objects into high-dimensional points. Searching for ‘similar’ objects
based on these features is thus a search of points in this feature space. Another
high-dimensional database example is stock price information systems, where
time series data are stored and searched as high-dimensional data points. To
support efficient query processing and knowledge discovery in these high-
dimensional databases, high-dimensional indexes are required to prune the
search space and efficient similarity join strategies employing these indexes
have to be designed.
High-dimensional indexing has been considered an important means to
facilitate fast query processing in data mining, fast retrieval, and similarity
search in image and scientific databases. Existing multi-dimensional indexes
such as R-trees are not scalable in terms of the number of dimensions. It
has been observed that the performances of R-tree-based index structures
deteriorate rapidly when the dimensionality of data is high [11, 12]. This
is due to rapid growth in overlap in the directory with respect to growing
dimensionality of data, requiring a large number of subtrees to be searched
for each query. The problem is further exacerbated by the fact that a small
high-dimensional query covering a very small fraction of the data space has
actually a very large query width along each dimension. Larger query widths
imply that more subtrees need to be searched. In this monograph, we study
the problem of high-dimensional indexing to support range, similarity, and
K-nearest neighbor (KNN) queries, and similarity joins.
To efficiently support window/range queries, we propose a simple and yet
efficient transformation-based method called the iMinMax(θ). The method
maps points in high-dimensional spaces to single dimensional values deter-
mined by their maximum or minimum values among all dimensions. With
such representations, we are able to index high-dimensional data points us-
ing a conventional B+
-tree. By varying the tuning ‘knob’, θ, we can obtain a
different family of iMinMax structures that are optimized for different distri-
butions of data sets. Hence, the method is tunable to yield best performance
based on data distributions. For a d-dimensional space, a window query needs
to be transformed into d subqueries. However, some of these subqueries can

VI Preface
be pruned away without evaluation, further enhancing the efficiency of the
scheme. Extensive experiments were conducted, and experimental compari-
son with other existing methods such as the VA-file and Pyramid-tree pro-
vides an insight on the efficiency of the proposed method.
To efficiently support similarity or K-nearest neighbor (KNN) queries,
we propose a specialized metric-based index called iDistance, and an exten-
sion of the iMinMax(θ). In the iDistance, a metric-based index, the high-
dimensional space is split into partitions, and each partition is associated
with an ‘anchor’ point (called a reference point) whereby other points in the
same partitions can be made reference to. With such a representation, the
transformed points can then be indexed using a B+
-tree, and KNN search in
the high-dimensional space is performed as a sequence of increasingly larger
range queries on the single dimensional space. Such an approach supports
efficient filtering of data points that are obviously not in the answer set with-
out incurring expensive distance computation. Furthermore, it facilitates fast
initial response time by providing users with approximate answers online that
are progressively refined till all correct answers are obtained (unless the users
terminate prematurely). Unlike KNN search, similarity range search on iDis-
tance is straightforward and is performed as a spherical range query with
fixed search radius. Extensive experiments were conducted, and experimen-
tal results show that the iDistance is an efficient index structure for nearest
neighbor search.
The iMinMax(θ) is designed as a generic structure for high-dimensional
indexing. To extend the iMinMax(θ) for KNN search, we design KNN process-
ing strategies based on range search to retrieve approximate nearest neighbor
data points with respect to a given query point. With proper data sampling,
accuracy up to 90% can be supported very efficiently. For a more accurate
retrieval, bigger search ranges must be used, which is less efficient.
In conclusion, both iMinMax(θ) and iDistance methods are flexible, ef-
ficient, and easy to implement. Both methods can be crafted into existing
DBMSs easily. This monograph shows that efficient indexes need not neces-
sarily be complex, and the B+
-tree, which was designed for traditional single
dimensional data, could be just as efficient for high-dimensional indexing.
The advantage of using the B+
-tree is obvious. The B+
-tree is well tested
and optimized, and so are its other related components such as concurrency
control, space allocation strategies for index and leaf nodes, etc. Most impor-
tantly, it is supported by most commercial DBMSs. A note of caution is that,
while it may appear to be straightforward to apply transformation on any
data set to reuse B+
-trees, guaranteeing good performance is a non-trivial
task. In other words, a careless choice of transformation scheme can lead to
very poor performance. I hope this monograph will provide a reference for
and benefit those who intend to work on high-dimensional indexing.
I am indebted to a number of people who have assisted me in one way or
another in materializing this monograph. First of all, I wish to express my

Preface VII
appreciation to Beng Chin Ooi, for his insight, encouragement, and patience.
He has taught me a great deal, instilled courage and conﬁdence in me, and
shaped my research capability. Without him, this monograph, which is an
extended version of my PhD thesis [104], would not have materialized.
I would like to thank Kian-Lee Tan and Stéphane Bressan for their advice
and suggestions. Kian-Lee has also proof-read this monograph and provided
detailed comments that greatly improved the literary style of this monograph.
I would like to thank H.V. Jagadish, for his insight, comments, and sugges-
tions regarding iDistance; Rudolf Bayer and Mario Nascimento, for their
comments and suggestions concerning the thesis; and many kind colleagues,
for making their source codes available. I would like to thank Shuguang
Wang, Anirban Mondal, Hengtao Shen, and Bin Cui, and the editorial staﬀ
of Springer-Verlag for their assistance in preparing this monograph. I would
like to thank the School of Computing, National University of Singapore,
for providing me with a graduate scholarship and facility for completing this
monograph.
Last but not least, I would like to thank my family for their support, and
I would like to dedicate this monograph to my parents for their love.
May 2002 Cui Yu

Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 High-Dimensional Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 The Objectives and Contributions . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Organization of the Monograph . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2. High-Dimensional Indexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Hierarchical Multi-dimensional Indexes . . . . . . . . . . . . . . . . . . . . 11
2.2.1 The R-tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.2 Use of Larger Fanouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.3 Use of Bounding Spheres . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.4 The kd-tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Dimensionality Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.1 Indexing Based on Important Attributes . . . . . . . . . . . . 18
2.3.2 Dimensionality Reduction Based on Clustering . . . . . . . 18
2.3.3 Mapping from Higher to Lower Dimension . . . . . . . . . . . 20
2.3.4 Indexing Based on Single Attribute Values. . . . . . . . . . . 22
2.4 Filtering and Reﬁning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.1 Multi-step Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.2 Quantization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.5 Indexing Based on Metric Distance . . . . . . . . . . . . . . . . . . . . . . . 29
2.6 Approximate Nearest Neighbor Search . . . . . . . . . . . . . . . . . . . . 32
2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3. Indexing the Edges – A Simple and Yet Eﬃcient Approach
to High-Dimensional Range Search . . . . . . . . . . . . . . . . . . . . . . . 37
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2 Basic Concept of iMinMax. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2.1 Sequential Scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.2 Indexing Based on Max/Min . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.3 Indexing Based on iMax. . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.4 Preliminary Empirical Study . . . . . . . . . . . . . . . . . . . . . . . 45
3.3 The iMinMax Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

X Contents
3.4 Indexing Based on iMinMax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.5 The iMinMax(θ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.6 Processing of Range Queries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.7 iMinMax(θ) Search Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.7.1 Point Search Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.7.2 Range Search Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.7.3 Discussion on Update Algorithms . . . . . . . . . . . . . . . . . . 58
3.8 The iMinMax(θi) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.8.1 Determining θi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.8.2 Refining θi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.8.3 Generating the Index Key . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4. Performance Study of Window Queries . . . . . . . . . . . . . . . . . . . 65
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.3 Generation of Data Sets and Window Queries . . . . . . . . . . . . . . 66
4.4 Experiment Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.5 Effect of the Number of Dimensions. . . . . . . . . . . . . . . . . . . . . . . 67
4.6 Effect of Data Size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.7 Effect of Skewed Data Distributions . . . . . . . . . . . . . . . . . . . . . . 70
4.8 Effect of Buffer Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.9 CPU Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.10 Effect of θi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.11 Effect of Quantization on Feature Vectors . . . . . . . . . . . . . . . . . 80
4.12 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5. Indexing the Relative Distance – An Efficient Approach to
KNN Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.2 Background and Notations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.3 The iDistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.3.1 The Big Picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.3.2 The Data Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.3.3 KNN Search in iDistance . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.4 Selection of Reference Points and Data Space Partitioning . . . 95
5.4.1 Space-Based Partitioning . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.4.2 Data-Based Partitioning. . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.5 Exploiting iDistance in Similarity Joins . . . . . . . . . . . . . . . . . . . 102
5.5.1 Join Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.5.2 Similarity Join Strategies Based on iDistance . . . . . . . . 103
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Contents XI
6. Similarity Range and Approximate KNN Searches with
iMinMax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.2 A Quick Review of iMinMax(θ) . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.3 Approximate KNN Processing with iMinMax . . . . . . . . . . . . . . 110
6.4 Quality of KNN Answers Using iMinMax . . . . . . . . . . . . . . . . . . 115
6.4.1 Accuracy of KNN Search . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.4.2 Bounding Box Vs. Bounding Sphere . . . . . . . . . . . . . . . . 118
6.4.3 Effect of Search Radius . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7. Performance Study of Similarity Queries . . . . . . . . . . . . . . . . . 123
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
7.2 Experiment Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
7.3 Effect of Search Radius on Query Accuracy . . . . . . . . . . . . . . . . 123
7.4 Effect of Reference Points on Space-Based Partitioning
Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
7.5 Effect of Reference Points on Cluster-Based Partitioning
Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.6 CPU Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.7 Comparative Study of iDistance and iMinMax . . . . . . . . . . . . . 133
7.8 Comparative Study of iDistance and A-tree . . . . . . . . . . . . . . . . 134
7.9 Comparative Study of the iDistance and M-tree . . . . . . . . . . . . 136
7.10 iDistance – A Good Candidate for Main Memory Indexing? . . 137
7.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
8. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
8.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
8.2 Single-Dimensional Attribute Value Based Indexing . . . . . . . . . 141
8.3 Metric-Based Indexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
8.4 Discussion on Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

1. Introduction
Database management systems (DBMSs) have become a standard tool for
manipulating large volumes of data on secondary storage. To enable fast
access to stored data according to its content, organizational methods or
structures known as indexes are used. While indexes are optional, as data
can always be located by sequential scanning, they are the primary means of
reducing the volume of data that must be fetched and examined in response to
a query. In practice, large database files must be indexed to meet performance
requirements. In fact, it has been noted [13] that indexes are the primary and
most direct means in reducing redundant disk I/O.
Many new applications, such as multimedia databases, employ the so
called feature transformation which transforms important features or proper-
ties of data objects into high-dimensional points. Searching for objects based
on these features is thus a search of points in this feature space. Another
high-dimensional database example is stock price information systems, where
time series data are stored and searched as high-dimensional data points. To
support efficient retrieval in these high-dimensional databases, indexes are
required to prune the search space. Indexes for low-dimensional databases
such as spatial databases and temporal databases are well studied [12, 69].
Most of these application specific indexes are not scalable with the number
of dimensions, and they are not designed to support similarity search and
high-dimensional joins. In fact, they suffer from what has been termed as
‘dimensionality curse’, and degradation in performance is so bad that se-
quential scanning is making a return as a more efficient alternative. Many
high-dimensional indexes have been designed. While some have the problem
of performance, the others have the problem of data duplication, high up-
date and maintenance cost. In this monograph, we examine the problem of
high-dimensional indexing, and present two efficient indexing structures.
1.1 High-Dimensional Applications
The need for efficient access to large collections of multi-dimensional data is
a major concern in designing new generation database systems, such as mul-
timedia database systems. Multimedia database systems manage and manip-
ulate content rich data types such as video, image, audio and text in addition
C. Yu: High-Dimensional Indexing, LNCS 2341, pp. 1-8, 2002.
© Springer-Verlag Berlin Heidelberg 2002

2 1. Introduction
to conventional alphanumeric data type. Unlike a conventional database ap-
plication, multimedia applications often require retrieval of data which are
similar in features (such as color, shape and texture content) to a given ref-
erence object. For some applications, only the K most similar objects are of
interest. Features are represented as points in multi-dimensional databases,
and retrieval entails complex distance functions to quantify similarities of
multi-dimensional features.
Let us consider image database systems [33] as our application. In systems
such as QBIC [39], VIPER [78] and VisualSEEK [94], apart from text-based
and semantic-based retrieval, content-based retrieval, where the content of
an image (such as objects, color, texture, and shape) is used, may also form
the basis for retrieval. Such attributes can usually be automatically extracted
from the images. Automatic extraction of content enables retrieval and ma-
nipulation of images based on contents. Existing content-based retrieval tech-
niques include template matching, global features matching, and local features
matching. Global features such as color, texture or shape information have
been widely used to retrieve images. Retrieval by shape information usually
works well only in specialized application domains, such as a criminal picture
identification system where the images have very distinct shape. Color and
texture are more suitable for general-purpose application domains. Several
systems have also integrated multiple global features to improve the effec-
tiveness of image retrieval [71, 94].
Due to the large size of images and the large quantity of images, efficient
and effective indexing mechanisms are necessary to facilitate speedy search-
ing. To facilitate content-based retrievals, the general approach adopted in
the literature has been to transform the content information into a form that
can be supported by an indexing method. A useful and increasingly common
approach to indexing these images based on their contents is to associate
their characteristics to points in a multi-dimensional feature space. Each fea-
ture vector thus consists of d values, which correspond to coordinates in a
d-dimensional space.
Shape features can be represented as a collection of rectangles which form
a rectangular cover of the shape [50]. An existing multi-dimensional indexing
scheme can then be used to index the rectangular cover. Another representa-
tion of shape is the boundary information, in which case, retrieval is achieved
by means of string matching and hence string matching algorithms can be
used to build the index [51]. Alternatively, shape features can be represented
as geometric properties (such as shape factors, moment features and curved
line features) and a geometric index can be used to facilitate fast retrievals
[98]. More recently, concepts from morphology are employed to map shapes
of tumor in medical databases to points in a high-dimensional space, and
the R-tree [46] has been used as the indexing structure [59]. For color, the
color histogram that captures the color composition is mapped into a high-
dimensional point, and a multi-dimensional point access method (such as

1.1 High-Dimensional Applications 3
R-tree) is used [34]. Unfortunately, it has been shown recently that existing
multi-dimensional indexes do not scale up when the number of dimensions
goes up [12].
Here, we shall describe an example process of indexing the shape of im-
ages, which is illustrated in Figure 1.1. Given an image, we first extract
the outline of the image as 128 * 128 pixel images, outputting 128*128
high-dimensional points. We then decompose the outline into basic shapes.
Next, we can use some form of wavelet transformation to transform the high-
dimensional points into a single continuous signal that is normalized in the
range of [0,1] so that the shapes can be independent of the location and
size of the shapes in the original image. Finally, each shape is represented
by its wavelet features and the shapes of images can be indexed by a high-
dimensional indexing method. The similarity between the wavelet features
can be used to measure the similarity between two shapes. One advantage of
wavelet features is that they have reasonable dimensions. Depending upon the
application, different transformation operations may be necessary to achieve,
for example, invariance with respect to scaling or rotation. The feature vec-
tors form the high-dimensional data points in the feature space. To support
fast similarity search, a high-dimensional index is used to index the data
points and using this index as the underlying structure, efficient retrieval al-
gorithms are designed. Retrieval in an image system usually involves query
by example (see the lower half of Figure 1.1). A sample image is used as the
starting point to locate similar images, which are used by the users in the
relevance feedback loop to refine the answers. During relevance feedback, the
query point is moved or features are assigned new weightage to indicate their
importance. Most indexes are used for filtering purposes as it is too bulky to
store the exact data in the index, and hence refinement is often required.
Other applications that require similar or nearest neighbor search support
include DNA databases, medical databases, financial databases and knowl-
edge discovery in general. In medical database systems, the ability to retrieve
quickly past cases with similar symptoms would be useful to doctors in di-
agnosis. N-grams in DNA databases and time-series such as stock prices in
financial databases are often indexed as multi-dimensional features, and re-
trieval for similar patterns is common.
From the above prelude, it is clear that in high-dimensional databases,
indexes are required to support either or both of the following queries:
– range/window queries: “find all objects whose attribute values fall within
certain given ranges”,
– similarity queries:
– similarity range queries: “find all objects in the database which are
within a given distance from a given object”,
– K-nearest neighbor (KNN) queries: “find the K-most similar objects in
the database with respect to a given object”.

4 1. Introduction
Fig. 1.1. Transformation and indexing of high-dimensional features
Similarity range queries are a specialized form of KNN queries, as the
similarity range query has a fixed search sphere, while the KNN query has to
enlarge its search sphere till K most similar objects are obtained. In terms
of search operation, KNN is therefore more complicated.
1.2 Motivations
Various types of indexing structures, such as B-trees [4, 28], ISAM indexes,
hashing and binary trees [57], have been designed as a means for efficient
access, insertion and deletion of data in large databases. All these techniques
are designed for indexing data based on single-dimensional keys, and in some
cases, the constraints of primary keys apply. These techniques are not suitable
for a database where range or similarity searching on multiple search keys is
a common operation. For this type of applications, multi-dimensional struc-
tures, such as grid-files [72], multi-dimensional B-trees [60, 81, 90], kd-trees
[6] and quad-trees [38] were proposed to index multi-attribute data.
Many indexes have been designed to handle multi-dimensional points and
objects with spatial extents such as regions in a Geographic Information Sys-
tem (GIS)[73]. There are two major approaches to multi-dimensional index-
ing. First, multi-dimensional point objects are ordered and numbered based
on some curve-filling methods [80, 49]. These objects are then indexed by

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NEW NOVELS AT
ALL LIBRARIES.
A FELLOW OF TRINITY.
By Alan St. Aubyn
and Walt Wheeler. 3
vols.
THE WORD AND THE
WILL. By James Payn.
3 vols.
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By George Randolph.
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London: CHATTO &
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W.

MY SHIPMATE LOUISE
The Romance of a Wreck
BY
W. CLARK RUSSELL
IN THREE VOLUMES
VOL. I.
London
CHATTO & WINDUS, PICCADILLY
1890

PRINTED BY
SPOTTISWOODE AND CO., NEW-STREET SQUARE
LONDON
TO
LEOPOLD HUDSON, ESQ.
Fellow of the Royal College of Surgeons of England
Warden of Middlesex Hospital College
IN GRATITUDE

CONTENTS
OF
THE FIRST VOLUME
CHAPTER PAGE
I. DOWN CHANNEL 1
II. THE FRENCH LUGGER 20
III. MY FELLOW PASSENGERS 43
IV. LOUISE TEMPLE 60
V. A MYSTERIOUS VOICE 84
VI. WE LOSE A MAN 108
VII. A SEA FUNERAL 130
VIII. A STRANGE CARGO 161
IX. A SECRET BLOW 182
X. THE HUMOURS OF AN INDIAMAN 203
XI. A STRANGE SAIL 223
XII. A STORM OF WIND 246
XIII. FIRE! 270
XIV. CRABB 292

CHAPTER I
DOWN CHANNEL
We had left Gravesend at four o’clock in the morning, and now, at
half-past eight o’clock in the evening, we were off the South
Foreland, the ship on a taut bowline heading on a due down Channel
course.
It was a September night, with an edge of winter in the gusts and
blasts which swept squall-like into the airy darkling hollows of the
canvas. There was a full moon, small as a silver cannon-ball, with a
tropical greenish tinge in its icy sparkling, and the scud came
sweeping up over it in shreds and curls and feathers of vapour,
sailing up dark from where the land of France was, and whitening
out into a gossamer delicacy of tint as it soared into and fled
through the central silver splendour. The weight of the whole range
of Channel was in the run of the surge that flashed into masses of
white water from the ponderous bow of the Indiaman as she
stormed and crushed her way along, the tacks of her courses
groaning to every windward roll, as though the clew of each sail
were the hand of a giant seeking to uproot the massive iron bolt that
confined the corner of the groaning cloths to the deck.
The towering foreland showed in a pale and windy heap on the
starboard quarter. The land ran in a sort of elusive faintness along
our beam, with the Dover lights hanging in the pallid shadow like a
galaxy of fireflies: beyond them a sort of trembling nebulous sheen,
marking Folkestone; and on high in the clear dusk over the quarter
you saw the Foreland light like some wild and yellow star staring
down upon the sea clear of the flight of the wing-like scud.
The ship was the Countess Ida, a well-known Indiaman of her day—
now so long ago that it makes me feel as though I were two
centuries old to be able to relate that I was a hearty young fellow in

those times. She was bound to Bombay. Most of the passengers had
come aboard at Gravesend, I amongst them; and here we were now
thrashing our way into the widening waters of the Channel, mighty
thankful—those of us who were not sea-sick, I mean—that there had
come a shift of wind when the southern limb of the Goodwin Sands
was still abreast, to enable us to keep our anchors at the cathead
and save us a heart-wearying spell of detention in the Downs.
The vessel looked noble by moonlight; she was showing a
maintopgallant sail to the freshening wind, and the canvas soared to
high aloft in shadowy spaces, which came and went in a kind of
winking as the luminary leapt from the edge of the hurrying clouds
into some little lagoon of soft indigo, flashing down a very rain of
silver fires, till the long sparkling beam travelling over the foaming
heads of the seas, like a spoke of a revolving wheel, was
extinguished in a breath by the sweep of a body of vapour over the
lovely planet. I stood at the rail that ran athwart the break of the
poop, surveying this grand night-picture of the outward-bound
Indiaman. From time to time there would be a roaring of water off
her weather-bow, that glanced in the moonshine in a huge fountain
of prismatic crystals. The figures of a couple of seamen keeping a
look-out trudged the weather-side of the forecastle, their shadows at
their feet starting out upon the white plank to some quick and
brilliant hurl of moonlight, clear as a sketch in ink, upon white paper.
Amidships, forward, loomed up the big galley, with a huge long-boat
stowed before it roofed with spare booms; on either hand rose the
high bulwarks with three carronades of a side stealing out of the
dusk between the tall defences of the ship like the shapes of beasts
crouching to obtain a view of the sea through the port-holes. A red
ray of light came aslant from the galley and touched with its rusty
radiance a few links of the huge chain cable that was ranged along
the decks, a coil of rope hanging upon a belaying pin, and a
fragment of bulwarks stanchion. Now and again a seaman would
pass through this light, the figure of him coming out red against the
greenish silver in the atmosphere. A knot of passengers hung
together close under the weather poop ladder, with a broad white

space of the quarter-deck sloping from their feet to the lee
waterways, whence at intervals there would come a sound of
choking and gasping as the heave of the ship brought the dark
Channel surge brimming to the scupper holes. The growling hum of
the voices of the men blended in a strange effect upon the ear with
the shrill singing of the wind in the rigging and the ceaseless
washing noises over the side and the long-drawn creaking sounds
which arise from all parts of a ship struggling against a head sea
under a press of canvas.
Aft on the poop where I was standing the vessel had something of a
deserted look. The pilot had been dropped off Deal; the officer of
the watch (the chief mate) was stumping the weather-side of the
deck from the ladder to abreast of the foremost skylight; the dark
figure of the captain swung in a sort of pendulum-tramping from the
mizzen rigging to the grating abaft the wheel. Dim as a distant
firebrand over the port quarter, windily flickering upon the stretch of
throbbing waters, shone the lantern of the lightship off the South
Sand Head; and it was odd to mark how it rose and fell upon the
speeding night sky to the swift yet stately pitching of our ship, with
the figure of the man at the helm somehow showing the vaguer for
it, spite of the shining of the binnacle lamp flinging a little golden
haze round about the compass stand, abaft which the shape of the
fellow showed vague as the outline of a ghost.
Ha! thought I, this is being at sea now indeed! Why, though we were
in narrow waters yet, there was such a note of ocean yearning in the
thunderous wash of the weather billows sweeping along the bends
that, but for the pale glimmer of the line of land trending away to
starboard, I might easily have imagined the whole waters of the
great Atlantic to be under our bow.
It was a bit chilly, and I caught myself hugging my peacoat to me
with a half-formed resolution to make for my cabin, where there
were yet some traps of mine remaining to be stowed away. But I
lingered—lover of all sea-effects, as I then was and still am—to
watch a fine brig blowing past us along to the Downs, the strong

wind gushing fair over her quarter, and her canvas rising in marble-
like curves to the tiny royals; every cloth glancing in pearl to the
dance of the moon amongst the clouds, every rope upon her
glistening out into silver wire, with the foam, white as sifted snow,
lifting to her hawse-pipes to the clipper shearing of her keen stem,
and not a light aboard of her but what was kindled by the luminary
in the glass and brass about her decks as she went rolling past us
delicate as a vision, pale as steam, yet of an exquisite grace as
determinable as a piece of painting on ivory.
I walked aft to the companion hatch and entered the cuddy, or, as it
is now called, the saloon. The apartment was the width of the ship,
and was indeed a very splendid and spacious state-cabin, with a
bulkhead at the extremity under the wheel, where the captain’s
bedroom was, and a berth alongside of it, where the skipper worked
out his navigation along with the officers, and where the
midshipmen went to school. There were also two berths right
forward close against the entrance to the cuddy by way of the
quarter-deck, occupied by the first and second mates; otherwise, the
interior was as clear as a ballroom, and it was like entering a
brilliantly illuminated pavilion ashore, to pass out of the windy dusk
of the night and the flying moonshine of it into the soft brightness of
oil-flames burning in handsome lamps of white and gleaming metal,
duplicated by mirrors, with hand-paintings between and polished
panels in which the radiance cloudily rippled. A long table went
down the centre of this cuddy, and over it were the domes of the
skylights, in which were many plants and flowers of beauty swinging
in pots, and globes of fish and silver swinging trays. Right through
the heart of the interior came the shaft of the mizzen mast, rich with
chiselled configurations, and of a delicate hue; a handsome piano
stood lashed to the deck abaft the trunk of giant spar. The planks
were finely carpeted, and sofas and arm-chairs ran the length of this
glittering saloon on either side of it.
There were a few people assembled at the fore-end of the table as I
made my way to the hatch whose wide steps led to the sleeping
berths below. It was not hard to perceive that one of them was an

East Indian military gentleman whose liver was on fire through years
of curry. His white whiskers of the wire-like inflexibility of a cat’s,
stood out on either side his lemon-coloured cheeks; his little blood-
shot eyes of indigo sparkled under overhanging brows where the
hair lay thick like rolls of cotton-wool. This gentleman I knew to be
Colonel Bannister, and as I cautiously made my way along—for the
movements of the decks were staggering enough to oblige me to
tread warily—I gathered that he was ridiculing the medical
profession to Dr. Hemmeridge, the ship’s surgeon, for its inability to
prescribe for sea-sickness.
‘It iss der nerves,’ I heard a fat Dutch gentleman say—afterwards
known to me as Peter Hemskirk, manager of a firm in Bombay.
‘Nerves!’ sneered the colonel, with a glance at the Dutchman’s
waistcoat. ‘Don’t you know the difference between the nerves and
the stomach, sir?’
‘Same thing,’ exclaimed Dr. Hemmeridge soothingly; ‘sea-sickness
means the head, any way; and pray, colonel, what are the brains
but’——
‘Ha! ha!’ roared the colonel, interrupting him; ‘there I have you. If it
be the brains only which are affected, why, then, ha! ha! no wonder
Mynheer here doesn’t suffer, though it’s his first voyage, he says.’
But my descent of the steps carried me out of earshot of this
interesting talk. My cabin was well aft. There was a fairly wide
corridor, and the berths were ranged on either hand of it. From
some of them, as I made my way along, came in muffled sounds
various notes of lamentation and suffering. A black woman, with a
ring through her nose and her head draped in white, sat on the deck
in front of the closed door of a berth, moaning in a sea-sick way
over a baby that she rocked in her arms, and that was crying at the
top of its pipes. The door of a cabin immediately opposite opened,
and a young fellow with a ghastly face putting his head out
exclaimed in accents strongly suggestive of nausea: ‘I thay,
confound it! thtop that noithe, will you? The rolling ith bad enough

without that thindy. Thteward!’ The ship gave a lurch, and he swung
out, but instantly darted back again, being indeed but half clothed: ‘I
thay, are you the thteward?’
‘No,’ said I. ‘Keep on singing out. Somebody’ll come to you.’
‘Won’t they thmother that woman?’ he shouted, and he would have
said more, but a sudden kickup of the ship slammed his cabin door
for him, and the next moment my ear caught a sound that indicated
too surely his rashness in leaving his bunk.
I entered my berth, and found the lamp alight in it, and the young
gentleman who was to share the cabin with me sitting in his
bedstead, that was above mine, dangling his legs over the edge of
it, and gazing with a disordered countenance upon the deck. I had
chatted with him during the afternoon and had learnt who he was.
Indeed, his name was in big letters upon his portmanteau—‘The
Hon. Stephen Colledge;’ and incidentally he had told me that he was
a son of Lord Sandown, and that he was bound to India on a
shooting tour. He was a good-looking young man, with fair whiskers,
white teeth, a genial smile, yet with something of affectation in his
way of speaking.
‘It’s doocid rough, isn’t it, Mr. Dugdale?’ said he; ‘and isn’t it raining?’
‘No,’ said I.
‘Oh, but look at the glass here,’ he exclaimed, indicating the scuttle
or porthole, the thick glass of which showed gleaming, but black as
coal against the night outside.
‘Why,’ said I, ‘the wet there is the sea; it is spray; nothing but spray.’
‘Hang all waves!’ he said in a low voice. ‘Why the dickens can’t the
ocean always be calm? If I’d have known that this ship pitched so,
I’d have waited for a steadier vessel. Will you do me the kindness to
lift the lid of that portmanteau? You’ll find a flask of brandy in it.
Hang me if I like to move. Sorry now I didn’t bring a cot, though
they’re doocid awkward things to get in and out of.’

I found the flask, and gave it to him, and he took a pull at it. I
declined his offer of a dram, and went to work to stow away some
odds and ends which were in my trunk.
‘Don’t you feel ill?’ said he.
‘No,’ said I.
‘Oh, ah, I remember now!’ he exclaimed; ‘you were a sailor once,
weren’t you?’
‘Yes; I had a couple of years of it.’
‘Wish I’d been a sailor, I know,’ said he. ‘I mean, after I’d given it up.
As to being a sailor—merciful goodness! think of four, perhaps five
months of this.’
‘Oh, you’ll be as good a sailor as ever a seaman amongst us in a day
or two,’ said I encouragingly.
‘Don’t feel like it now, though,’ he exclaimed. ‘Let’s see: I think you
said you were going out to do some painting?—Oh no! I beg pardon:
it was a chap named Emmett who told me that. You—you——’ He
looked at me with a slightly inebriated cock of the head, from which
I might infer that the ‘pull’ he had taken at his flask was by no
means his first ‘drain’ within the hour.
‘No,’ said I, with a laugh; ‘I am going out to see an old relative up
country. And not more for that than for the fun of a voyage.’
‘The fun of the voyage!’ he echoed with a stupid face; then with a
sudden brightening up of his manner, though his gloomy
countenance quickly returned to him, he exclaimed, ‘I say, Dugdale
—beg pardon, you know; no good in mistering a chap that you’re
going to sleep with for four or five months—call me Colledge, old
fellow—but I say, though, seen anything more of that ripping girl
since dinner? By George! what eyes, eh?’
He drew his legs up, and with a slight groan composed himself in a
posture for sleep, manifestly heedless of any answer I might make
to his question.

I lingered awhile in the berth, and then, filling a pipe, mounted to
the saloon, and made my way to the quarter-deck to smoke in the
shelter of the recess in the cuddy front. Colonel Bannister lay
sprawling upon a sofa, holding a tumbler of brandy grog. There were
other passengers in the cuddy, scattered, and all of them grimly
silent, staring hard at the lamps, yet with something of vacancy in
their regard, as though their thoughts were elsewhere. As I stepped
on to the quarter-deck, the cries and chorusing of men aloft, came
sounding through the strong and hissing pouring of the wind
between the masts and through the harsh seething of the seas,
which the bows of the ship were smiting into snowstorms as she
went sullenly ploughing through the water with the weather-leech of
the maintopgallant-sail trembling in the green glancings of the
moonlight like the fly of a flag in a breeze of wind. They were taking
a reef in the fore and mizzen topsails. The chief mate, Mr. Prance,
from time to time, would sing out an order over my head that was
answered by a hoarse ‘Ay, ay, sir,’ echoing out of the gloom in which
the fore-part of the ship was plunged. I lighted my pipe and sat
myself down on the coamings of the booby hatch to enjoy a smoke.
I was alone, and this moon-touched flying Channel night-scene
carried my memory back to the times when I was a sailor, when I
had paced the deck of such another vessel as this, as a midshipman
of her. It seemed a long time ago, yet it was no more than six years
either. The old professional instinct was quickened in me by the
voices of the fellows aloft, till I felt as though it were my watch on
deck, that I was skulking under the break of the poop here, and that
I ought to be aloft jockeying a lee yard-arm or dangling to windward
on the flemish horse.
Presently all was quiet on high, and by the windy sheen in the
atmosphere, caused by the commingling of white waters and the
frequent glance of the moon through some rent in the ragged scud,
I could make out the figures of the fellows on the fore descending
the shrouds. A little while afterwards a deep sea voice broke out into
a strange wild song, that was caught up and re-echoed in a
hurricane chorus by the tail of men hauling upon the halliards to

masthead the yard. It was a proper sort of note to fit such a night as
that. A minute after, a chorus of a like gruffness but of a different
melody resounded on the poop, where they were mastheading the
topsail yard after reefing it. The combined notes flung a true oceanic
character into the picture of the darkling Indiaman swelling and
rolling and pitching in floating launches through it, with her wide
pinions rising in spaces of faintness to the scud, and the black lines
of her royal yards sheering to and fro against the moon that, when
she showed, seemed to reel amidst the rushing wings of vapour to
the wild dance of our mastheads. The songs of the sailors, the clear
shrill whistling of a boatswain’s mate forward, the orders uttered
quickly by the chief officer, the washing noises of the creaming
surges, the sullen shouting of the wind in the rigging resembling the
sulky breaker-like roar of a wood of tall trees swept by a gale—all
this made one feel that one was at sea in earnest.
I knocked the ashes out of my pipe and went on to the poop. The
land still showed very dimly to starboard, with here and there little
oozings of dim radiance that might mark a village or a town. You
could see to the horizon, where the water showed in a sort of
greenish blackness with some speck of flame of a French lighthouse
over the port quarter, and the September clouds soaring up off the
edge of the sea like puffs and coils of smoke from a thousand
factory chimneys down there, and now and again a bright star
glancing out from amongst them as they came swiftly floating up to
the moon, turning of a silvery white as they neared the glorious
planet.
There were windows in the cuddy front, and as I glanced through
one of them I saw the captain come down the companion steps into
the brightly lighted saloon and seat himself at the table, where in a
moment he was joined by the fiery-eyed little colonel. Decanters and
glasses were placed by one of the stewards on a swing-tray, and the
scene then had something of a homely look spite of the cuddy’s
aspect of comparative desertion. Captain Keeling, I think, was about
the most sailorly-looking man I ever remember meeting. I had heard
of him ashore, and learnt that he had used the sea for upwards of

forty-five years. He had served in every kind of craft, and had
obtained great reputation amongst owners and underwriters for his
defence and preservation of an Indiaman he was in command of
that was attacked in the Bay of Bengal by a heavily armed French
picaroon full of men. Cups and swords and services of plate and
purses of money were heaped upon him for his conduct in that
affair; and indeed in his way he was a sort of small Commodore
Dance.
I looked at him with some interest as he sat beside the colonel with
the full light of the lamp over against him shining upon his face and
figure. There had been little enough to see of him during the day,
and it was not until we dropped the pilot that he showed himself. His
countenance was crimsoned with long spells of tropic weather, and
hardened into ruggedness like the face of a rock by the years of
gales he had gone through. He was about sixty years of age; and his
short-cropped hair was as white as silver, with a thin line of whisker
of a like fleecy sort slanting from his ear to the middle of his cheek.
His nose was shaped like the bowl of a clay-pipe, and was of a
darker red than the rest of his face. His small sea-blue eyes were
sunk deep, as though from the effect of long staring to windward;
and almost hidden as they were by the heavy ridge of silver
eyebrow, they seemed to be no more than gimlet holes in his head
for the admission of light. He had thrown open his peacoat, and
discovered a sort of uniform under it: a buff-coloured waistcoat with
gilt buttons, an open frock-coat of blue cloth with velvet lapels.
Around his neck was a satin stock, in which were three pins,
connected by small chains. His shirt collar was divided behind, and
rose in two sharp points under his chin, which obliged him to keep
his head erect in a quite military posture. Such was Captain Keeling,
commander of the famous old Indiaman Countess Ida.
I guessed he would not remain long below, otherwise I should have
been tempted to join him in a glass of grog, spite of the company of
Colonel Bannister, who was hardly the sort of man to make one feel
happy on such an occasion as the first night out at sea with memory

bitterly recent of leave-taking, of kisses, of the hand-shakes of folks
one might never see again.

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High Dimensional Indexing Transformational Approaches to High-Dimensional Range and Similarity Searches 1st edition by Cui Yu

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