Automated Ranking of Database Query Results

Automated Ranking of Database Query Results
Automated Ranking of Database Query Results
Sanjay Agrawal
Surajit Chaudhuri
Gautam Das
Aristides Gionis
Microsoft Research
Microsoft Research
Microsoft Research
Computer Science Dept
Stanford University
Abstract
Ranking and returning the most relevant results
of a query is a popular paradigm in Information
Retrieval. We discuss challenges and investigate
several approaches to enable ranking in
databases, including adaptations of known
techniques from information retrieval. We
present results of preliminary experiments.
1. Introduction
Automated ranking of the results of a query is a popular
aspect of the query model in Information Retrieval (IR)
that we have grown to depend on. In contrast, database
systems support only a Boolean query model. For
example, a selection query on a SQL database returns all
tuples that satisfy the conditions in the query. Therefore,
the following two scenarios are not gracefully handled by
a SQL system:
1. Empty answers: When the query is too selective, the
answer may be empty. In that case, it is desirable to
have the option of requesting a ranked list of
approximately matching tuples without having to
specify the ranking function that captures
“proximity” to the query. An FBI agent or an analyst
involved in data exploration will find such
functionality appealing.
2. Many answers: When the query is not too selective,
too many tuples may be in the answer. In such a case,
it will be desirable to have the option of ordering the
matches automatically that ranks more “globally
important” answer tuples higher and returning only
the best matches. A customer browsing a product
catalog will find such functionality attractive.
Conceptually, the automated ranking of query results
problem is really that of taking a user query (say, a
conjunctive selection query) and mapping it to a Top-K
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Proceedings of the 2003 CIDR Conference
query with a ranking function that depends on given
conditions in the user query. The key questions are:
• How to derive such ranking functions
automatically? How well do ranking functions
from IR apply?
• Are the ranking techniques for handling empty
answers and many answers problems different?
• How to execute such Top-K queries efficiently
over large databases?
We will start off by asking ourselves how to make it
possible for relational databases to adapt ranking
functions from IR for handling the database ranking
problem. When each attribute in the relation is a
categorical attribute, we can “mimic” the IR solution by
applying the TF-IDF idea that is based on the frequency
of occurrence of attribute values in the database.
However, unlike text documents, databases contain
numeric as well as categorical information. Therefore, we
need to extend TF-IDF concepts to numerical domains.
We develop IDF Similarity, a database ranking function
that extends TF-IDF concepts to databases containing a
heterogeneous mix of categorical as well as numeric data.
While IDF Similarity works well for some database
ranking applications, sometimes its effectiveness is quite
limited. In certain instances the relevance of data values
for ranking may be due to other factors in addition to their
frequencies. This has been noted in the IR domain as well,
where sometimes one has to go beyond TF-IDF
weightings to derive accurate ranking functions. This begs
the question: what else could be the basis of generic
ranking in databases? We show that collecting the
workload on the database can be quite useful for ranking.
In a way, this may be viewed as a poor man’s choice of
relevance feedback and collaborative filtering where a
user’s final choice of relevant tuples is not recorded.
Despite its primitive nature, such workload information
can help determine the frequency with which database
attributes and values are referenced. When used in
conjunction with IDF, workload information boosts
ranking quality. We develop QF Similarity, a ranking
function that leverages such workload information.
Much of the discussion in this paper focuses on the
empty answers problem. Solving the many answers
problem poses additional challenges because a ranking
function that only depends on the conditions in the user
query is inadequate for this problem. We extend our
ranking functions with additional query independent
components that measure the “importance” of tuples in a
global sense.
Finally, even if we get the ranking functions right, for
large databases, we have to minimize their impact on
query processing. Although inverted lists are popular data
structures for efficient retrieval in IR, they are inadequate
for our purposes as we seek imprecise matches involving
categorical and numerical attributes. We study
adaptations of some recent algorithms for Top-K query
processing, which leads us to yet another contribution of
this paper; an index-based Top-K query processing
algorithm, ITA that exploits our ranking functions.
We have built a system in which our ranking
algorithms have been implemented on a relational DBMS.
The system has two major components, a pre-processing
component and a query processing component. The
preprocessing component is a ranking function extractor
that leverages data and workload characteristics. The
query processing component is a Top-K algorithm that
uses the ranking function and exploits the physical
database design. We have performed user experiments on
our system to evaluate its effectiveness. However, despite
our best efforts, our user experiments are preliminary.
Unlike IR which relies on extensive available user studies
and benchmarks, no infrastructure is available today for
evaluating database ranking.
The rest of this paper is organized as follows. In
Section 2 we discuss related work. In Sections 3 and 4
respectively, we describe two database ranking functions
for the empty answers problem, IDF Similarity and QF
Similarity. Section 5 discusses differences between the
empty answers and the many answers ranking problem,
and describes extensions to our ranking functions to solve
the latter problem. Section 6 discusses key
implementation details, especially choices among Top-K
processing techniques and our ITA algorithm. We present
experiments in Section 7, and conclude in Section 8.
2. Related work
Extracting ranking functions has been extensively
investigated in areas outside database research such as
Information Retrieval. The Cosine Similarity metric with
TF-IDF weighting of the vector space model [4] is very
successful in practice. We extend the TF-IDF weighting
technique for database ranking to handle a heterogeneous
mix of numeric and categorical data.
Ranking is an important component in collaborative
filtering research [5]. These methods require training data
using queries as well as their ranked results. In contrast,
we require workloads containing queries only.
In database research, there has been some scattered
work on the automatic extraction of similarity/ranking
functions from a database. The early work of [21]
considered vague/imprecise similarity-based querying of
databases. The problem of integrating databases and
information retrieval systems has been attempted in
several works [12, 13, 17, 18]. Information retrieval based
approaches have been extended to XML retrieval in [26].
The papers [10, 23, 24, 32] employ relevance-feedback
techniques for learning similarity in multimedia and
relational databases. A keyword-based retrieval system
over databases is proposed in [1].
The distinguishing aspects of our work from the above
are (a) we address the challenges that a heterogeneous
mix of numeric as well as categorical attributes pose, and
(b) we propose a novel and easy to implement ranking
method based on query workload analysis. Although [22]
describes a ranking application for a mix of categorical
and numeric data, the similarity function is not
automatically derived but rather is based on domain
knowledge of the application. The paper [30] proposes
distance functions for heterogeneous data, but the
emphasis is on classification applications. In [19, 20], the
authors propose SQL extensions in which users can
specify soft constraints in the form of preferences. These
extensions broaden the expressiveness of search criteria
by a user, but do not relieve the user from the onus of
having to specify suitable ranking functions.
A major concern of this paper is the query processing
techniques for supporting ranking. Several techniques
have been previously developed in database research for
the Top-K problem [6, 7, 14, 15, 31]. We adopt the
algorithm in [15] for our purposes, and discuss issues
such
as
how
the
relational
engine
and
indexes/materialized views can be leveraged for query
performance.
3. IDF Similarity: generalizing IR methods
In this section, we develop IDF Similarity, a database
ranking function based on information retrieval
techniques. We consider a database table R with
categorical and numerical attributes {A1, …, Am} and
tuples {T1, …, Tn}. The selection conditions will be
conjunctive conditions, i.e., of the form “WHERE C1
AND … AND Cm”, where each atomic Ck is of the form
“Ak = valuek”. (More general conditions are discussed in
Section 3.3. Also, our ranking techniques can be extended
for multi-table databases; see Section 6.2.2).
3.1 IDF Similarity for categorical data
If the database only had categorical attributes, a very
simple solution can be employed by essentially
“mimicking” the well-known IR technique of Cosine
Similarity with TF-IDF weighting by treating each tuple
(and query) as a small document and defining a similarity
function between tuples and queries. We note that such
approaches have been considered in several prior works
on database ranking (see Section 2). Henceforth in this
paper ranking function and similarity function will be
used interchangeably.
We start by briefly reviewing this standard IR
technique. Given a set of documents and a query (the
latter specified as a set of keywords), the problem is to
retrieve the Top-K documents most relevant, or most
similar to the query. Similarity between a document and
the query is formalized as follows. Given a vocabulary of
m words, a document is treated as an m-dimensional
vector, where the ith component is the frequency of
occurrence (also known as term frequency, or TF) of the
ith vocabulary word in the document. Since a query is a
set of words, it too has a vector representation. The
Cosine Similarity between a query and a document is
defined as the normalized dot-product of the two
corresponding vectors. The Cosine Similarity may be
further refined by scaling each component with the
inverse document frequency (IDF) of the corresponding
word (IDF(w) of a word w is defined as log(N/F(w))
where N is the number of documents, and F(w) is the
number of document in which w appears). IDF has been
used in IR to suggest that commonly occurring words
convey less information about user’s needs than rarely
occurring words, and thus should be weighted less.
We can also adopt these techniques for our problem.
More formally, for every value t in the domain of attribute
Ak, we define IDFk(t) as log(n/Fk(t)), where n is the
number of tuples in the database and Fk(t) is the frequency
of tuples in the database where Ak = t. For any pair of
values u and v in Ak’s domain, let the quantity Sk(u,v) be
defined as IDFk(u) if u = v, and 0 otherwise. Consider
tuple T = <t1,…,tm> and query Q = <q1,…,qm> (i.e. the
latter has a C-condition of the form “WHERE A1 = q1
AND … AND Am = qm”). The similarity between T and Q
is defined in Equation (1). We refer to the quantities
Sk(u,v) as similarity coefficients; thus the similarity
between T and Q is simply the sum of corresponding
similarity coefficients over all attributes. (To improve
readability in the rest of the paper, we shall omit the
subscript k where ever possible. Thus S(t,q) will refer to
the similarity coefficient Sk(t, q), while A will refer to the
attribute Ak).
SIM (T , Q ) =
m
k =1
S k (t k , q k )
(1)
This similarity function closely resembles the IR-like
Cosine Similarity with TF-IDF weightings, except that the
dot-product is un-normalized. Also note that in our case,
the term frequency TF is irrelevant since each tuple is
treated as a small document in which a word, i.e. a
<attribute, value> pair can only occur once. Henceforth
we refer to this similarity function as IDF Similarity.
IDF Similarity can be very effective in certain
database ranking applications. For example, if we query
an automobile database for a “CONVERTIBLE” made by
“NISSAN”, the system first returns all Nissan
convertibles, followed by other convertibles, and followed
by other Nissan cars. This is because “CONVERTIBLE”
is a rare car type and consequently has higher IDF than
“NISSAN”, a common car manufacturer.
3.2 Generalizing IDF Similarity for numeric data
The following interesting research challenges arise when
we try to extend IDF Similarity for more general database
schemas containing a heterogeneous mix of categorical
and numerical attributes. Intuitively, the similarity
coefficient S(u, v) between values u and v of a numeric
attribute A should be a smooth function inversely related
to the “distance” between u and v. Thus, for numeric data
it is inappropriate to adopt the definition of similarity
coefficients in Section 3.1 because of their binary nature
(where if u and v are arbitrarily close to each other yet
distinct, S(u, v) will incorrectly evaluate to 0). Moreover,
the “frequency” (and hence “IDF”) of a numeric value
should depend on nearby values. For example, if we
request for a home in a realtor database with price $300k
and 10 bedrooms, the price is less important for ranking
purposes (there may be many houses priced close to
$300k, even if few have exactly that price) than the
number of bedrooms (relatively fewer homes have around
10 bedrooms).
A simple solution is to discretize the domain of
numeric attribute A into buckets, effectively treating a
numerical attribute as categorical. However, most
bucketing approaches are problematic since (a)
inappropriate bucket boundaries may separate two values
that are actually close to each other, (b) determining the
correct number of buckets is not easy, and (c) values in
different buckets are treated as completely dissimilar,
regardless of the actual distance separating the buckets.
Instead, we propose a more robust definition of
similarity for numeric data that does not suffer from these
shortcomings. Let {t1, t2, …, tn} be the values of attribute
A that occur in the database. For any value t, we define
IDF(t) as shown in Equation (2) (where h is the
bandwidth parameter, to be defined later).
IDF ( t ) = log
n
n
e
−
1
2
(2)
ti − t
h
2
i
Intuitively, the denominator in Equation (2) represents a
numeric extension of the concept of “frequency” of t, i.e.
the sum of “contributions” to t from every the other point
ti in the database. These contributions are modeled as
(scaled) Gaussian distributions, so that the further t is
from ti, the smaller is the contribution from ti.
We then define the similarity between t and q as
shown in Equation (3), i.e. as the density at t of a
Gaussian distribution centered at q, scaled by IDF(q).
S (t , q ) = e
−
1 t −q
2 h
4. QF Similarity: leveraging workloads
2
IDF ( q )
(3)
As an illustration, consider the scenario where the
numeric data resembles categorical data: there are nt
tuples in the database with value t, and the remaining n –
nt tuples have values far from t. If q belongs to the latter,
then it is easy to see that S(t, q) is almost 0. Whereas, if q
also has the value t, then S(t, q) degenerates to log(n/nt),
which is exactly the formula for categorical data.
The above numerical extensions to IDF have been
derived using kernel density estimation techniques [25]. A
popular estimate for the bandwidth is h = 1.06 σ n−1/5,
where σ is the standard deviation of {t1, t2, …, tn}. For
theoretical justification of these extensions, see [2].
3.3 Other generalizations of IDF Similarity
In Section 3.1 we had assumed a query model where Cconditions are conjunctions of atomic conditions such as
“Ak = qk”. A useful generalization is the ability to specify
a range/set of values for numerical/categorical attributes.
Let query Q have a C-condition “C1 AND … AND
Cm”, where each Ck is generalized as “Ak IN Qk”, where Qk
is a set of values for categorical attributes, or a range
[lb,ub] for numeric attributes. For uniformity of notation,
we use IN to also specify numeric ranges, e.g. “Ak IN
[lb,ub]”, instead of the more standard BETWEEN. Let T
= <t1,…,tm> be any tuple. To generalize the similarity
function SIM(T,Q) of Equation (1), we define similarity
between tk and Qk as the maximum similarity coefficient
between tk and all values in Qk. The generalized similarity
function is shown in Equation (4).
SIM (T , Q ) =
m
k =1
max S k (t k , q )
q ∈Q k
(4)
In defining Equation (4), we considered the alternative of
using avg instead of max. However, this can lead to an
unintuitive scenario where a tuple that completely
satisfies the selection condition may be ranked lower than
a tuple that only partially satisfies the selection condition.
A more detailed discussion on this issue is omitted.
Thus far, our query model assumes that values for all
attributes are specified in a query. In most real queries it
is unlikely that all attributes are specified. We refer to
these as missing attributes. Our approach is to restrict
similarity calculations only to the attributes specified by
the query, i.e., we only consider the projection of the
database on the columns that are referenced in the query.
This has parallels with approaches in IR, where similarity
is calculated only using words that appear in the query. It
is only when numerous tuples have the same similarity
score that we use missing attributes to break ties. Details
of this scenario are discussed in Section 5.
While IDF Similarity can be very useful in many
applications of database ranking, it nevertheless has
several shortcomings that need to be addressed. In this
section we first discuss these shortcomings, and then
discuss QF Similarity, a ranking function that leverages
workload information to overcome these shortcomings.
The following examples show that a data value may
be important for ranking purposes irrespective of its
frequency of occurrence in the database.
Example 1: In a realtor database, more homes are built
in recent years such as 2000 and 2001 as compared to
earlier years such as 1980 and 1981. Thus recent years
have smaller IDF. Yet the demand for newer homes is
usually more than that for older homes.
Example 2: In a bookstore database, the demand for an
author is due to factors other than the number of books
she has written (such factors may include for example,
number of favorable reviews).
We note that the above problems can be solved by a
domain expert who can define a more accurate similarity
function (e.g. by giving more weight to later years in
Example 1). However, this can be highly dependent on
the application, so we do not attempt a general discussion
here. Instead, we show how to derive the similarity
function automatically by analyzing other more easily
available knowledge sources, such as past usage patterns
of the database (i.e. workload). An important point is that
our techniques do not require as inputs both workload
queries and their correctly ranked results; getting the
latter information is tedious and involves user feedback,
whereas gathering queries only is relatively easy since
profiling tools exist on most commercial DBMS that can
log each query string that executes on the system.
In the next subsection we describe a simple version of
QF Similarity, in which the importance of attribute values
is determined by the frequency of their occurrence in the
workload. We follow this up in Section 4.2 with a more
sophisticated variant of QF Similarity, in which similarity
between pairs of different categorical attribute values can
also be derived from the workload. In Section 4.3 we
briefly discuss a hybrid strategy, QFIDF Similarity, where
we combine information from the workload as well as the
data to derive importance of attribute values.
4.1 Query frequencies of attribute values
The idea behind the simple variant of QF Similarity is that
the importance of attribute values is directly related to the
frequency of their occurrence in query strings in the
workload. Consider the realtor database discussed in
Example 1. It is reasonable to assume that there are more
queries requesting for newer homes than for older homes.
Thus the frequency of the year 2001 appearing in the
workload will be more than of the year 1981. A simple
idea that takes advantage of this observation is to record
the frequency of attribute values appearing in the
workload, and then let similarity coefficients depend on
these frequencies. We make this precise as follows.
Assume for simplicity only categorical data; we
discuss numeric data in Section 4.3. Let RQF(q) be the
raw frequency of occurrence of value q of attribute A in
the query strings of the workload. Let RQFMax be the
raw frequency of the most frequently occurring value in
the workload. Let the query frequency, QF(q) be defined
as RQF(q)/ RQFMax. We define the similarity coefficient
S(t,q) as QF(q) if q = t, and 0 otherwise.
We note that QF(q) has resemblance with the classical
term frequency TF(q), except that it is the frequency of q
over the entire workload rather than in the specific query.
4.2 Similarity between different attribute values
In this section we discuss a more sophisticated variant of
QF Similarity. While the simple QF Similarity discussed
in Section 4.1 can resolve Examples 1 and 2, it cannot
resolve the following example; in fact, none of the
ranking functions discuss so far can resolve Example 3.
Example 3: In an automobile database, a HONDA
ACCORD and a TOYOTA CAMRY are very dissimilar as
measured by any of the previous similarity functions,
since the similarity coefficients S(TOYOTA, HONDA) and
S(CAMRY, ACCORD) are both 0. However, intuitively
we know that the two cars are quite similar, e.g. they are
family sedans, of comparable quality, and targeted to the
same market segment.
To resolve this problem, we need similarity coefficients
that are non-zero even when the pair of categorical values
is different. For example, S(TOYOTA, HONDA) may be
0.8, while S(TOYOTA, FERRARI) may be 0.1.
We discuss an approach for deriving such similarity
coefficients by leveraging workload information in further
ways. The intuition is that if certain pairs of values t <> u
often “occur together” in the workload, they are similar.
For example, there may be queries with C-conditions such
as “MFR IN {TOYOTA, HONDA, NISSAN}”. Such
workloads suggest that these manufacturers are more
similar to each other than to, say FERRARI.
Let W(t) be the subset of queries in workload W in
which categorical value t occurs in an IN clause. The
Jaccard coefficient [29] measures the similarity between
the two sets W(t) and W(q) as shown in Equation (5).
J (W (t),W(q)) =
W (t) ∩W (q)
W (t) ∪W (q)
(5)
The similarity coefficient between t and q is defined as
this Jaccard coefficient, scaled by the QF factor as shown
in Equation (6).
S (t , q ) = J (W (t ), W (q ))QF (q )
(6)
Note that in the limit when W(t) is very similar to W(q),
S(t, q) degenerates to QF(q), which is exactly the formula
for S(t, q) in Section 4.1.
4.3 Discussion
Pair-wise similarity between different attribute values can
be determined by other techniques in addition to
analyzing IN clauses of queries. For example, perhaps
there have been several recent queries in the workload by
a specific user who has repeatedly requested for
TOYOTA and HONDA cars in succession. Finding such
co-occurrence of values over sequences of queries by
specific users is the subject of ongoing work.
Numerical values that occur in the workload can also
benefit from query frequency analysis. For example, in
the realtor database, if certain home prices are very
frequently specified by workload queries, it is reasonable
to treat them (and nearby values) as important values
during similarity computations. Thus, as we did for IDF( )
in Section 3.2, we have to compute a smooth query
frequency function QF( ).
QF Similarity is purely workload-based, i.e. it does
not use the data at all. This may be a disadvantage in
situations where we have insufficient or unreliable
workloads. We experimented with a hybrid ranking
function, QFIDF Similarity, where we combined IDF and
QF weights by multiplying them, i.e., S(t, q) =
QF(q)*IDF(q) when t = q, and 0 otherwise. (In this
formula we define QF(q) = (RQF(q)+1)/ (RQFMax+1) so
that even if a value is never referenced in the workload, it
gets a small non-zero QF). Using multiplication to
combine the two factors is inspired by the TF*IDF factors
in the original TF-IDF ranking function [4]. The resulting
function noticeably improved ranking quality in certain
cases (see Section 7).
5. The many answers problem: breaking ties
In the previous two sections we have focused mainly on
the empty answers ranking problem. In this section we
discuss differences between the empty answers and many
answers problem, and describe how our ranking functions
can be extended to handle the latter problem.
For ranking the results of a query that produces many
answers, IDF Similarity and QF Similarity may
sometimes run into the following problem: many tuples
may tie for the same similarity score and thus get ordered
arbitrarily. For example, consider a query Q with a
selection condition of the form “A1 = q1 AND … AND Ai
= qi” where i < m (i.e. some of the columns, Ai+1, …, Am
have not been specified by the query). Suppose many
tuples in the database satisfy this selection condition. We
note that the projection of each of these tuples along the
attributes specified in the query is the same, i.e. <q1, …,
qi>. Thus SIM(T, Q,) for each answer tuple T will be the
same, whether we use IDF Similarity or QF Similarity.
We observe that this problem can also arise in the
empty answers problem: the top one or two tuples may
have distinct similarity scores, followed by a large group
of tuples that share the same similarity score. In general,
if we only use the attributes specified in the query for
ranking purposes, our similarity functions will partition
the database into several equivalence classes, where
tuples within each class have the same similarity score.
To break ties among the tuples in each class, it is thus
necessary to look beyond the attributes specified in the
query, i.e. missing attributes. Investigating attributes
beyond what has been specified by the query is
particularly tricky since the ranking function does not
know what the user’s preferences for the missing
attributes are. The final ranking function could be a
composition of weights of the missing attribute values.
The problem thus is how do we in a principled manner
determine these weights?
Our approach is to determine weights of missing
attribute values that reflect their “global importance” for
ranking purposes, since we cannot possibly relate them to
the preferences of the specific user who has issued the
query. For example, suppose we seek homes with four
bedrooms in a realtor database. Since there are many
homes satisfying this condition, we examine attributes
other than number of bedrooms to rank the result set. If
we knew that “BELLEVUE” is a more important location
than “CARNATION” in a global sense, we would rank
four bedroom homes in Bellevue higher than four
bedroom homes in Carnation.
We use workload information to determine global
importance of missing attribute values. The intuition is
that if Bellevue is truly a popular neighborhood, the
workload will contain many more queries requesting for
Bellevue homes compared to Carnation homes. More
formally, we define the global importance of missing
attribute value tk as log(QFk(tk)), and extend QF Similarity
to use the quantity log(QFk(tk)) to break ties in each
equivalence class (larger this quantity1, higher the rank of
the tuple) where the summation is over missing attributes.
Extending IDF Similarity by using IDF values instead
of QF values of missing attributes to break ties presents
challenges. One possibility is to rank tied tuples higher if
their missing attribute values have large IDF, i.e. occur
infrequently in the database. But this gives rise to the
undesirable scenario where, all else being equal, homes
that occur in uncommon neighbourhoods are ranked
before homes that occur in more common
neighbourhoods. An alternative strategy is to rank tied
tuples higher if their missing attribute values have small
IDF, i.e. occur more frequently in the database. This will
1
If QFk(tk) is viewed as the probability of occurrence of value tk in a
random query, the quantity log(QFk(tk)) represents the log-likelihood of
a query that requests the remaining values of T, which can be construed
as the “importance” of T for ranking purposes.
work well in the realtor example above, as homes in more
popular neighbourhoods will be ranked higher than homes
in strange neighbourhoods. Although more robust than the
previous strategy, there are situations where this approach
is also flawed. For example, suppose the database had a
Boolean attribute “Deck”. Since only a small fraction of
homes have decks, this ranking function will rank higher
homes that do not have decks, which is contrary to
intuition since a deck is usually a desirable feature.
In Section 7 we discuss experiments which show that
for ranking queries with numerous answers, the quality of
QF Similarity is noticeably better than the quality of IDF
Similarity (both functions extended as described above).
6. Implementation
In this section we discuss the implementation of the preprocessing and query processing components of our
database ranking system.
6.1 Pre-processing component
The main task of the pre-processing component is to
compute and store a representation of the similarity
function in auxiliary database tables. Computing IDF(t)
(resp. QF(t)) for all categorical values t involves scanning
the database (resp. scanning/parsing the workload) to
compute frequency of occurrences of values in the
database (resp. workload), and storing the results in
auxiliary tables. For a numeric attribute, since we do not
know what value q will be specified by a query, we
cannot pre-compute IDF(q) (resp. QF(q)); thus we have to
store an approximate representation of the smooth
function IDF( ) (resp. QF( )) so that the function value at
any q can be retrieved at runtime. We mention that since
kernel density estimation techniques have been used to
smoothen these functions, they can be approximated as
histograms in linear time by the WARPing method [25];
we omit further details from this paper. The approximated
functions are stored in auxiliary tables.
For identifying similarity coefficients for QF
Similarity between all pairs of values u and v of any
attribute A (Section 4.2), we avoid space/time
requirements quadratic in the size of A’s domain by only
storing similarity coefficients that are above a certain
threshold. They can be efficiently computed using a
frequent itemset algorithm [3].
6.2 Query processing component
The main task of the query processing component is,
given a query Q and an integer K, to efficiently retrieve
the Top-K tuples from the database using one of our
ranking functions. We assume that the ranking function
has already been extracted in a pre-processing phase
(Section 6.1). We focus exclusively on the empty answers
problem; the query processing challenges of the many
answers problem is part of our ongoing work.
Our objective was to use the available functionality of
a traditional SQL DBMS for solving this Top-K problem.
Thus, we decided not to adopt techniques that build
specialized multi-dimensional indexes for arbitrary
similarity spaces (e.g. Fast-Map [16]). Another possible
approach is to use inverted lists, a popular data structure
in information retrieval. We discarded this approach from
further consideration since (a) this requires the presence
of indexes on all columns specified in a query, which may
be impractical and (b) it does not work for numeric data.
6.2.1 Handling a simpler query processing problem
We first focus on a much simpler version of the query
processing problem; the more general problem is
discussed in Section 6.2.2.
• Inputs: (a) a database table R with m categorical
columns, clustered on key column TID, where
standard database indexes exist on a subset of
columns, (b) A query expressed as a conjunction of
m single-valued conditions of the form Ak = qk., and
(c) an integer K.
• Similarity function: We assume a very simple
similarity function which we call Overlap Similarity.
This function measures the number of values in the
tuple that match the corresponding values in the
query. In Section 6.2.2 we discuss implementations
of the more general similarity functions developed
earlier in this paper.
• Output: The Top-K tuples of R most similar to Q.
We discuss two solutions to this restricted problem.
Traditional implemention of Top-K operator: Many
SQL database systems (e.g. Microsoft SQL Server)
support Top-K query processing features. The SQL for
the above restricted problem is shown in Figure 1.
SELECT TOP K
R.*
FROM
R
ORDER BY
((CASE WHEN R.A1 = q1 THEN 1 ELSE 0 END) +
(CASE WHEN R.A2 = q2 THEN 1 ELSE 0 END) +
…
(CASE WHEN R.Am = qm THEN 1 ELSE 0 END))
DESC
Figure 1: Top-K query in SQL
Most database systems would create a computed column
(created on the fly in a pipelined manner) corresponding
to the ranking function (e.g., in the ORDER BY clause in
Figure 1) and then use a Sort_TopK operator, i.e., sort the
relation to get Top-K results. Recent papers have focused
on how to efficiently implement a Sort_TopK operator [8,
9]. It is important to note that the assumed semantics of
Top-K is nondeterministic, i.e., ties are broken arbitrarily.
An index-based Top-K implementation: In most SQL
systems, the above algorithm cannot leverage any
available indexes and has to scan every database tuple.
However, we observe that the Overlap Similarity function
(in fact, all similarity functions discussed in this paper)
satisfies a useful monotonic property: if T and U are two
tuples such that for all k, Sk(tk, qk) Sk(uk, qk), then SIM(T,
Q)
SIM(U, Q). This enables us to adapt Fagin’s
Threshold Algorithm (TA) and its derivatives [7, 15] to
retrieve the Top-K tuples without having to process all
tuples of the database.
To adapt TA for our purposes, we have to implement
two types of access methods: (a) sorted access along any
attribute Ak, in which TIDs of tuples can be efficiently
retrieved one-by-one in order of decreasing similarity of
their Ak attribute value from qk, and (b) random access, in
which the entire tuple corresponding to any given TID can
be efficiently retrieved. In brief, Fagin’s algorithm
performs sorted access along each attribute in “lock-step”,
retrieves the complete tuples corresponding to the TIDs
seen using random access, and maintains a buffer of the
Top-K tuples seen thus far. The monotonic property of the
similarity function allows the use of an early stopping
condition, by which the algorithm can detect that the final
Top-K tuples have been retrieved before all tuples have
been processed.
We leverage available database indexes such as B+
trees to efficiently implement these two access methods.
Since it is unrealistic to assume that indexes are always
present on all attributes specified by any query, we adapt
a derivative of TA [7] that works even if sorted access is
not available on some attributes. Our resulting adaptation,
called the Index-based Threshold Algorithm, or ITA, is
shown in Figure 2.
Assume that indexes are present on columns A1, ..., Ap
and not present on columns Ap+1, ..., Am. The essence of
ITA is to do index seeks on orderings L1, ..., Lp where
each Lk is defined as an ordering of tuples where tuples
with Ak = qk precede the tuples with Ak <> qk. We use the
following terminology: (a) TupleLookup(TID), where the
complete tuple for the given TID is retrieved from R, and
(b) IndexLookupGetNextTID(Lk), where given an ordering
Lk of a column Ak, the next matching TID of R is retrieved
using the available index on that column. These
operations are respectively equivalent to the random
access and sorted access operations described earlier.
TupleLookup(TID) can be implemented by traditional
indexes in a relational databases. Efficient implementation
of IndexLookupGetNextTID(Lk) using the indexing
support in relational database engine requires more care;
we omit further details from this paper.
Index seeks on L1, ..., Lp may be interleaved or ordered
in a variety of ways based on heuristics or data statistics.
The most important step is the stopping condition, i.e.
identifying that no more index seeks on any column will
be needed. We discuss this next.
Stopping Condition: We define a hypothetical tuple by
taking the “current” value a1, …, ap for A1, ..., Ap
corresponding to index seeks on L1, ..., Lp and using the
values qp+1, ..., qm for the remaining columns. This creates
the very best tuple we can hope to find in the data that is
yet to be seen. If the similarity of this hypothetical tuple
to the query is no more than the tuple in the Top-K buffer
with the lowest similarity, the algorithm successfully
terminates.
ITA: Index-based Threshold Algorithm
Initialize Top-K buffer to empty
REPEAT
FOR EACH k = 1 TO p DO
1.
TIDk = IndexLookupGetNextTID(Lk)
2.
Tk = TupleLookup(TIDi)
3.
Compute value of ranking function for Tk
4.
If rank of Tk is higher than the lowest ranking tuple in the
Top-K buffer
then update Top-K buffer
5.
If stopping condition has been reached then EXIT
END FOR
UNTIL
indexLookupGetNextTID(L1) …
indexLookupGetNextTID(Lp)
are all completed
Figure 2: Index-based Threshold Algorithm for Top-K
query processing
Although ITA does not require indexes on all columns
referenced by the query, fewer indexes imply that the
algorithm may need to do more tuple lookups using TIDs
before it can terminate. We also note that the same tuple
may be retrieved several times via TID lookup because its
TID may be encountered multiple times during index
lookups along different columns. The main disadvantage
of this approach is that it introduces random accesses, and
this can have an adverse affect on performance if too
many index lookups are needed (see Section 7.3.2).
6.2.2 Handling more general query processing
Our basic framework for Top-K query processing extends
to the more general similarity functions developed in the
paper. These extensions are described next.
Presence of QFIDF tables: Let us consider query
processing when we use one of the more general ranking
functions described in Sections 3 and 4.1. In addition to
the base table R, several small auxiliary tables, one per
categorical column of R, have been created during
preprocessing that contain information about the
similarity function. We call these tables QFIDF tables.
We assume that each such QFIDF table has two attributes
<ColVal, QFIDFVal> and is clustered on the ColVal
attribute. ColVal contains all distinct values of the
specific database column that corresponds to this QFIDF
table, while QFIDFVal contains the respective weights
(for ranking purposes) of these distinct values. The
specific QFIDFVal weights depend on the ranking
function we adopt, e.g., IDF, QF or QF*IDF.
Let us consider the impact of this generality on the
two Top-K implementations described in the previous
subsection. First, to know the QFIDFVal weights, we
need to look up the QFIDF tables. Since the QFIDF
lookup is based only on the conditions in the query and is
independent of the data tuple, this may be accomplished
by an initialization step. The retrieved QFIDFVal weights
are then used during subsequent processing in the
traditional Top-K computation for the creation of the
computed column based on the ranking function.
The above initialization step is also common to ITA.
Subsequent computation in ITA remains unaffected,
except that the ranking function computations have to
take into account the retrieved QFIDFVal weights.
Numerical columns: We consider the important case
when some of the database columns are numeric.
We adapt ITA for numeric conditions in a query as
follows. Suppose the query has a condition Ak = qk for a
numeric column Ak. Because Ak is numeric, unlike
categorical cases, it is now possible to return “nearby
matches” based on increasing value of |Ak – qk| once no
more exact matches Ai = qk exist in the data. We perform
two index scans on Ak: one that retrieves TIDs of tuples
with values greater than qk in increasing order, and
another that retrieves TIDs of tuples with values lesser
than qk in decreasing order. We then pick the TIDs from
the merged stream. Once we have ensured that each index
on a numeric attribute can produce tuples in the order of
decreasing similarity in the above fashion, the rest of the
implementation is the same as what has been described
for categorical attributes.
Handling numeric conditions in a query using
traditional Top-K SQL is straightforward and is omitted
from this paper.
Other generalizations: ITA can be extended to handle
other generalizations, such as IN and range conditions in
the query (Section 3.3), non-zero pair-wise similarity
coefficients (Section 4.2), and for breaking ties among
tuples (Section 5). Further details of these extensions to
ITA may be found in [2].
When our ranking order is over the result of a
relational query, defined over a set of tables, additional
challenges arise. Appropriate materialized views can
greatly enhance applicability of our techniques.
Furthermore, indexes on base tables can be leveraged but
the trade-off in query processing and optimization is
increasingly more complex.
7. Experiments
We implemented the techniques described in this paper
and conducted experiments to evaluate their effectiveness.
All experiments were run on a machine with an x86 450
MHz processor with 256 MB RAM and an internal 5GB
hard drive running Microsoft Windows 2000 and
Microsoft SQL Server 2000.
We first tested the ranking quality as well as
performance of the following similarity functions on
queries with empty/few answers: Overlap (Section 6.2.1),
IDF (Section 3), QF and QFIDF (Section 4). We then
tested the extensions to IDF and QF for breaking ties
among tuples (Section 5). Finally, we compared the query
processing performance of the threshold algorithm using
indexes (ITA) against SQL Server Top-K using these
similarity functions (Section 6).
7.1 Summary of results
Quality results
• For queries with empty answers, QFIDF produced
the best rankings, followed by QF, then IDF, and
finally Overlap.
• For queries with empty answers, the ranking quality
of QF improves with increasing workload size.
• For queries with numerous answers, QF produced
better rankings than IDF.
Performance results
• The preprocessing time and space requirements of all
our techniques scale linearly with data size.
• When all indexes are present, ITA is more efficient
than SQL Server Top-K for all our similarity
functions.
• Even when a subset of indexes is present, ITA can
perform well; the performance is strongly determined
by how effective the algorithm is in reducing the
number of processed tuples.
7.2 Quality experiments
Evaluating and comparing the quality of different
database ranking alternatives is challenging. Unlike
Information Retrieval which relies on extensive user
studies and available benchmarks (such as the TREC
collection [28]), such infrastructure is not available today
for evaluating database ranking. Nonetheless, we
conducted user studies on several real databases.
In this paper we only report results for one real
database, Realtor, which is part of a large real estate
database from http://homeadvisor.msn.com. We first
collected about 72,000 tuples representing homes for sale
in Washington State. Of these, we retained 4099 tuples
representing homes for sale in the Seattle Eastside. We
chose a mixture of 10 categorical and numerical attributes
for our experiments: City, Deck, Fenced, Culdesac, Price,
Datebuilt, Bedrooms, Sqft. For building a workload, we
requested eight people, some of them actual homeowners
in Seattle Eastside, to provide us with queries that they
would execute if they wanted to buy a home. An example
of a typical query was: “SELECT * FROM homes
WHERE Bedrooms > 3 AND Bathrooms > 2 AND Price
< 350000”; the user commented he had in mind young
families with not too much money, but have children and
hence need space. We collected a total of 84 queries, each
typically referencing 2-5 attributes. We used five people
to provide test queries to evaluate the quality results. We
selected a mix of 6-10 test queries similar to the ones
provided by users during workload generation. We first
describe a few sample results informally, and then present
a formal evaluation of the ranking quality.
7.2.1 Informal quality results
All ranking functions produced rankings that were quite
intuitive and reasonable. IDF was obviously superior to
Overlap in several queries; for example when requesting
for homes with price $300k located on a cul-de-sac, the
latter attribute value was given more importance since
only a small fraction of homes (around 15%) are located
on cul-de-sacs, whereas a much larger fraction of homes
have prices close to $300k.
However, there were several interesting examples
where IDF was unable to obtain the rankings generated by
the users. When requesting for a home located on a culde-sac and with a fenced yard, IDF was unable to
distinguish between the importance of these two values,
as both had approximately the same relative frequencies
in the database (around 15% of homes also had fenced
yards). But to the users a cul-de-sac location is more
important than a fence (because fences can be easily
constructed whereas a home location cannot be changed).
QF Similarity obtained better rankings as even in our
modest-sized workload there were many more queries that
requested cul-de-sacs than fences.
7.2.2 Formal quality results
We now present a formal evaluation of the ranking quality
produced by the ranking functions. Since it would have
been very tedious to have users rank the entire database
for each query, we used the following strategy. For each
test query Qi we generated a list Hi of 25 tuples likely to
contain a good mix of “relevant” and “irrelevant” tuples
to the query (we omit details from this paper, but we did
this by ranking the entire database using these ranking
functions and mixing a few highly ranked tuples with a
few randomly selected tuples). Finally, we presented the
queries along with the corresponding lists (with tuples
randomly permuted) to each user in our study. Each user’s
responsibility was to mark each tuple in Hi as relevant or
irrelevant to the query Qi. We then applied our ranking
functions against the test queries.
For formally comparing the ranking quality of the
various ranking functions with the human responses, we
used a standard collaborative filtering metric R to
measure ranking quality (Equation (7)). In the equation, ri
is the subject’s preference for the ith tuple in the ranked
list returned by the ranking function (1 if it is marked
relevant, and 0 otherwise). The intuition behind the R
metric is that if relevant tuples are ranked low, they
contribute less to the value of R with exponential decay
(see [2] for further discussion on the R metric).
ri
R =
i
2
(7)
i−1
9
We next present the R metric values obtained in various
quality experiments (R values are normalized by dividing
by the maximum possible value for R).
Comparing quality of different ranking functions: In
Figure 3 we present the average R metric for each ranking
function on the test queries.
R metric
0.8
0.7
0.6
QFIDF
QF
IDF
Overlap
Ranking functions
Figure 3: Quality of various ranking
functions on Realtor database
The best ranking function in average ranking quality was
QFIDF, followed by QF, then IDF, and finally Overlap.
All ranking functions did better than a naïve ranking
function that retrieves K random tuples (this naïve
function’s average R value is 0.66, not shown in the
chart). We mention that the differences in quality are
likely to have been more significant if our users were able
to score many more than 25 tuples per query.
Quality versus workload size:
R metric
0.7
0.6
50% w orkload
Comparing quality on queries with many answers: We
compared the quality of IDF Similarity with QF
Similarity, both extended to use missing attributes to
break ties as discussed in Section 5. For this experiment,
our users especially created 6 test queries whose selection
conditions were satisfied by many tuples (order of
hundreds). QF has better ranking quality (R = 0.76) than
IDF (R = 0.68). Again, we emphasize that the difference
in quality is likely to have been more significant if users
were able to score many more than 25 tuples per query.
7.3 Performance experiments
We evaluated the pre-processing and query processing
performance of our ranking algorithms. We used the
Realtor database for Washington State with 72,000 tuples
(Section 7.2), as well as synthetic databases generated by
using the publicly available program [11] for generating
the popular TPC-H databases [27] with differing data
skew. For our experiments we generated the lineitem fact
table with 600,000 rows and varying skew parameter z.
Here we report results for z = 2.0 (similar results occurred
for values of z from 0.5 to 3). We treated all 17 attributes
as categorical. There are 6 attributes with less than 10
distinct values, 3 attributes with order of tens distinct
values, 5 attributes with hundreds, and 3 with thousands.
Note that although we use TPC-H databases, the
workloads used in our experiments are quite different
from standard TPC-H benchmarks. Thus, our results do
not reflect the TPC-H benchmark numbers.
7.3.1 Preprocessing performance experiments
We omit reporting results as the preprocessing was very
efficient: a scan of the table R in case of IDF Similarity, a
scan/parse of the workload in case of QF Similarity (and
variants), accompanied by the creation of the appropriate
small auxiliary tables.
7.3.2 Query processing performance experiments
0.8
100% w orkload
We explored the dependence of quality to workload size
in QF Similarity by training it on randomly sampled
fractions of the entire workload. The results (Figure 4)
indicate that larger workloads lead to better quality,
because they are likely to contain more accurate QF
values.
25% w orkload
Workload size
Figure 4: Ranking quality of QF Similarity on
Realtor database as workload size varies
We report query processing experiments for the ranking
functions developed in Sections 3 and 4. We do not report
query processing performance experiments for the many
answers problem (Section 5) as it is part of ongoing work.
We implemented three versions of our index-based
threshold algorithm ITA: ITA-OL that uses Overlap
Similarity, ITA-IDF that uses IDF Similarity and ITA-QF
that uses QF Similarity. (Performance results for ITAQFIDF are essentially the same as for ITA-QF and have
been omitted). For comparison, we used the SQL Server’s
Top-K mechanism to retrieve the Top-K tuples for all of
our similarity functions. For the first two parts of the
experiment, non-clustered indexes were available on all
columns referenced in the queries.
Ratio of Time
Varying number of attributes in query: We used the
TPC-H database and generated 5 workloads W1 through
W5 of 100 queries each (Wi is a workload containing
queries each referencing i attributes). The attributes and
values in a query were randomly selected from the
underlying database.
0.5
0.4
0.3
0.2
0.1
0
ITA-OL
ITA-IDF
ITA-QF
1
2
3
4
Number of attributes
5
Figure 5: Time taken by ITA compared to SQL
Server’s Top-K processing as number of attributes
varies
As Figure 5 shows, the running times (as a ratio of time
taken by SQL Server’s Top-K processing) increased as
the number of attributes increased, which was expected.
We also observed the query performance of all the three
techniques to be almost identical to each other, but
significantly better than SQL Server’s Top-K processing
(as the number of tuples processed was orders of
magnitude less than SQL Server’s Top-K processing).
Ratio of Time
Varying K in Top-K: Here we used the TPC-H database
and a workload with 100 queries. The number of
attributes in a query was randomly selected between 1 and
5. Figure 6 shows that all the techniques had almost
identical performance (ITA-OL was slightly faster than
both ITA-IDF and ITA-QF as it involves the least
processing during querying) and outperformed SQL
Server’s Top-K processing by almost a factor of 5.
0.19
0.18
ITA-OL
0.17
ITA-IDF
ITA-QF
0.16
0.15
1
10
K
100
1000
Figure 6: Time taken by ITA compared to SQL
Server’s Top-K processing as K varies
Note the decrease in time when K is increased from 10 to
100; this is because the time taken for SQL Server’s Top-
K increased as well (extra time was spent in maintaining
the larger Top-K buffer).
Varying number of indexes in database: We
investigated the performance when only some of the
columns specified in a query have indexes. For a given
number of available indexes N for a query Q we used two
strategies: (a) ITA-QF-Exhaustive where the best running
time was selected from amongst all possible subsets of N
column indexes relevant for Q and (b) ITA-QF-Random
where the N indexes to be retained for Q were randomly
selected from amongst all relevant indexes for Q. We
report results on the Realtor database with 72,000 tuples
for this experiment. We generated a workload of 100
queries (each query referenced 4 attributes; the specific
attributes and values were selected randomly from the
underlying database). We fixed K = 10 and varied the
number of available indexes N for each query from 4
down to 1.
Number of
available
Indexes N
4
Ratio of Time
for ITA-QFExhaustive
0.13
Ratio of Time
for ITA-QFRandom
0.13
3
0.10
2.90
2
0.12
4.30
1
2.76
7.80
Figure 7: Time taken by ITA compared to SQL
Server Top-K processing as indexes are dropped
Figure 7 shows the running time of ITA-QF-Exhaustive
and ITA-QF-Random for different values of N, expressed
as a ratio of the time taken by SQL Server’s Top-K
processing. We observed that as the number of available
indexes was decreased from 4 to 2, the running time of
ITA-QF-Exhaustive remained almost the same, yet
significantly (an order of magnitude) better than SQL
Server’s Top-K processing. This is due to the fact that the
available indexes can still be used to answer the Top-K
queries efficiently. At N = 1 there was a steep increase in
running time (outperformed by SQL Server’s Top-K
processing) even though the number of tuples processed
was still about 30% of the total tuples. This is due to the
significantly higher cost of random access in databases
compare to sequential access. We observed that the
running time of ITA-QF-Random was much (3-8 times)
worse than SQL Server’s Top-K processing for N = 3, 2
and 1. ITA-QF-Random could not leverage the stopping
criteria effectively; it accessed a large number of tuples
(more than 30% of total data).
These experiments demonstrate that ITA-QF can be
efficient even when a subset of indexes is available, but
the performance is strongly tied with the nature of subset.
The choice of determining such an optimal subset of
indexes is a part of ongoing work.
8. Conclusions
In this paper, we have presented our experience in
attempting to build a generic automated ranking
infrastructure for SQL databases. This is consistent with
our research philosophy of seeding the relational database
management infrastructure with functionality necessary
and useful for data exploration.
Our attempt was to extend TF-IDF based techniques
from information retrieval to numerical and mixed data,
as well as develop techniques of workload tracking as a
weak form of collaborative filtering. Our approaches have
shown promise, and are worthy of further investigation,
especially more conclusive user studies. Equally
important is to develop benchmarks. While TREC has
served the IR community wonderfully well, there is no
such infrastructure to move forward this nascent field.
We were also aware that a meaningful solution has to
take into account the impact on query processing. Our
proposals lead to an implementation of the ranking
function that exploits indexed access by drawing on
insights from Fagin’s Threshold Algorithm.
Are we trying to solve too hard a problem? One could
argue that ranking is extremely domain and/or user
specific and we cannot hope to automate such a difficult
task. We remind the readers that one could have raised
similar concerns about IR ranking as well. To explore
what information a database system can intelligently
bring to bear at a modest cost to solve database ranking to
reduce the burden of an application designer or user is a
dream worth pursuing.
Acknowlegment
We thank Nico Bruno for his insightful comments on the
algorithms and presentation of the paper.
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