Automated Ranking Of Database Query Results  Sanjay Agarwal - Microsoft Research  Surajit Chaudhuri - Microsoft Research  Gautam Das - Microsoft Research  Aristides Gionis - Computer Science Dept Stanford University Ramya Somuri Nov ‘ Presented at the first Conference on Innovative Data Systems Research (CIDR) in the year 2003

 Introduction  Problem Formulation  Similarity Functions  Implementation  Experiments  Conclusion

Similarity, Relevance, Preference What do we want? A Ranked List What do we want? Query Semantics: True/False { BOOLEAN MODEL} Query Results Representation: Empty Answers Many Answers Select * From Realtor R Where 400K<Price<600K AND #Bedrooms= 4 ? Boolean Semantics of SQL: Success and Barrier? Problems: Example:

 In this case it would be desirable to return a ranked list of ‘approximately’ matching tuples without burdening the user to specify any additional conditions.  In other words, an automated approach for ranking and returning approximately matching tuples.

 As the name suggests ‘Ranking’ is the process of ordering a set of values (or data items) based on some parameter that is of high relevance to the user of ranking process.  Ranking and returning the most relevant results of user’s query is a popular paradigm in information retrieval.

 Automated ranking of query results is the process of taking a user query and mapping it to a Top-K query with a ranking function that depends on conditions specified in the user query.

Architecture Of Ranking Systems

 Develop a method for automatically ranking database records by relevance to a given query  Derive a Similarity Function  Apply Similarity Function between Query & Records in database  Rank the Result-Set and return Top-K records Focus of Paper

W o rkflow W o rkflow

 IDF Similarity - Mimics the TF-IDF concept for Heterogeneous data.  QF Similarity - Utilizes workload information.  QFIDF Similarity - Combination of QF and IDF.

Problem Formulation Problem Formulation

Attributes VkVk Numerical Attribute Categorical Attribute SNOMFRPRICECOLORMODELTYPE 1AUDI REDQ5SUV 2BMW REDZ4 3TOYOTA BLUECAMRYSEDAN 4HONDA GREENACCORDSEDAN 5NISSAN WHITE350ZCONVE RTIBLE TuplesTuples

 R- Relation  {A l, …,A m }- Set of Attributes  V k – Set of valid attribute values for an attribute A k  {t l,……, t m }- Tuples/records  A tuple t is expressed as t = for a tuple with values t k ε V k for each k  Q -

 Where clause of Query Q is of the form “WHERE C l AND …….AND C k ” Each C i is of the form A i IN {value l, ………..,value k } / A i IN [lb,ub]  Similarity coefficient S k (u,v) can be defined as “similarity” for the attribute values [u,v]  S k (u,v) =1 if u=v =0 if u,v are dissimilar  W k – “importance” of attribute/Attribute weight 0<w k <1; Σw k =1

IR technique Q = set of key words IDF(w) = log(N/F(w)) N - No of documents F(w) - No of occurrences of documents in which w appears TF(w,d)=Frequency of occurrence of w in d Cosine similarity between query and document is normalized dot product of the two corresponding vector Similarity function known as cosine similarity with TF-IDF weightings d w Database(only categorical attribute) T= Q= Condition is “WHERE is A 1= q 1 ” IDF k (t)=log(n/F k (t)) n-number of tuples in database F k (t) -Frequency of tuples in database where A k =t Similarity between T and Q is Sum of corresponding similarity coefficients over all attributes Dot product is un-normalized TF is irrelevant Similarity function known as IDF similarity tuple

 Select model from automobile_database Where TYPE=“convertible” and MFR=“Nissan”;  System generates tuples in the following order  Nissan Convertibles  Convertibles by other manufacturer  Other cars/types by Nissan  “Convertible” is rare and has higher IDF than “Nissan” which is a common car manufacturer

 No  Example Select * From automobile_database Where price=3000  S k (u,v) = 1 if (u=v) otherwise 0 is a bad definition since two numerical values might be close but not equal.

 S k (u,v) = 1-d/ | u k -l k | where d=|v-u| is the distance between the value & [ l k, u k ] is the domain of A k  Example: Select * from Realtor R where #rooms=4 Bedroomsd=|v-u|S k (u,v) |u k -l k |

 For numeric data  Inappropriate to use previous similarity coefficients/functions.  frequency of numeric value depends on nearby values.  Discretizing numeric to categorical attribute is problematic.  Solution:  {t 1,t 2 …..t n } be the values of attribute A. For every value t,  Similarity function is sum of ”contributions” of t from every other point it contributions modeled as Gaussian distribution

 Problem: In a realtor database, more homes are built in recent years such as 2007 and 2008 as compared to 1980 and1981. Thus recent years have small IDF.Yet newer homes have higher demand.  Solution: QF Similarity.

 Importance of attribute values is directly related to the frequency of their occurrence in workload.  In the previous example, it is reasonable to assume that more queries are requesting for newer homes than for older homes. Thus the frequency of the year 2008 appearing in the workload will be more than that of year 1981.

 Query frequency QF(q) = RQF(q)/ RQFMax RQF(q)- raw frequency of occurrence of value q of attribute A in query strings of workload RQFMax- raw frequency of most frequently occurring value in workload  S(t,q)= QF(q), if q=t 0, otherwise

Consider a workload W = { Q1,Q2,Q3,Q4} Q1- Select * from Realtor R where year=“2009” Q2- Select * from Realtor R Where year=“2009” Q3- Select * from Realtor R Where year=“2008” Q4- Select * from Realtor R Where year=“2007” Attribute Year= { 1981,……., 2009} QF (2008) = RQF(2008)/RQFMax = 1/2. If a query requests for an attribute value not in the workload, then QF=0. Ex- QF(1981)=0

 Problem/Example: S MFR (Toyota,Honda) =0 S MODEL (Camry, Accord) =0  Solution: Similarity Coefficients that are non-zero even when the pair of categorical attributes is different Eg:S MFR (Toyota,Honda) =0.9

 Similarity between pairs of different categorical attribute values can also be derived from workload  The similarity coefficient between tuple and query in this case is defined by jaccard coefficient scaled by QF factor as shown below. S(t,q)=J(W(t),W(q))QF(q)

 Analyzing IN clauses of queries: If certain pair of values often occur together in the workload,they are similar.e.g. queries with C as “MFR IN {TOYOTA,HONDA,NISSAN}”  Several recent queries in workload by a specific user repeatedly requesting for TOYOTA and HONDA.  Numerical values that occur in the workload can also benefit from query frequency analysis.

Why QFIDF?  QF is purely workload-based.  Doesn't use data at all.  Fails in case of insufficient & unreliable workloads. What is QFIDF?  QFIDF is a hybrid ranking function obtained by combing IDF, QF weights by multiplying them  For QFIDF Similarity  S(t,q)=QF(q) *IDF(q),when t=q 0, otherwise where QF(q)=(RQF(q)+1)/(RQFMax+1).  Thus we get small non zero QF even if value is never referenced in workload model.

 In case of many answers problem, the recently discussed ranking functions might fail to perform.  This is because many tuples may tie for the same similarity score. Such a scenario could arise for empty answer problem also.  To break this tie, requires looking beyond the attributes specified in the query, i.e., missing attributes.

Many Answers Problem: Breaking Ties Many Answers Problem: Breaking Ties

 Solution: Determine the weights of missing attribute values that reflect their “global importance” for ranking purposes by using workload information.  Extend QF similarity,use quantity Σlog(QF k (t k )) to break ties. Consider a query requesting for 4 bedroom houses. -Result set= many # of homes -Examine the other attributes other than # of bed rooms(missing attributes). Ex- Location - Dallas is more important than Arlington. -Rank the 4 bed room homes in Dallas higher than that of Arlington

 Rank the tuples with large IDF for missing attributes higher - Arlington homes are given more preference than Dallas homes since Arlington has a higher IDF, but this scenario is not true in real practice.  Rank the tuples with small IDF for missing attributes higher Consider homes with decks, but since we are considering smaller IDF preference will be given to homes without decks since they have a smaller IDF which is not true in real practice.

 Pre-processing component  Query–processing component

 Compute and store a representation of similarity function in auxiliary database tables.  For categorical data: Compute IDF(t) (resp QF(t)),to compute frequency of occurrences of values in database and store the results in auxiliary database tables.  For numeric data: An approximate representation of smooth function IDF() (resp(QF()) is stored, so that function value of q is retrieved at runtime.

 Main task: Given a query Q and an integer K, retrieve Top-K tuples from the database using one of the ranking functions.  Ranking function is extracted in pre-processing phase.  SQL-DBMS functionality used for solving top-K problem.  Handling simpler query processing problem  Input: table R with M categorical columns, Key column TID, C is conjunction of form A k =q k..... and integer K.  Output: top-K tuples of R similar to Q.  Similarity function: Overlap Similarity.

 Traditional approach ?  Indexed based approach  overlap similarity function satisfies the following monotonic property.  If T and U are two tuples such that for all K, S k (t k,q k )< S k (u k,q k ) then SIM(T,Q) < SIM(U,Q)  To adapt TA implement Sorted and Random access methods.  Performs sorted access for each attribute, retrieve complete tuples with corresponding TID by random access and maintains buffer of Top-K tuples seen so far.

Read all grades of an object once seen from a sorted access No need to wait until the lists give k common objects Do sorted access (and corresponding random accesses) until you have seen the top k answers. How do we know that grades of seen objects are higher than the grades of unseen objects ? Predict maximum possible grade unseen objects: a: 0.9 b: 0.8 c: L1L1 L2L2 d: 0.9 a: 0.85 b: 0.7 c: f: 0.65 d: 0.6 f: 0.6 Seen Possibly unseen Threshold value Threshold Algorithm (TA) T = min(0.72, 0.7) = 0.7

IDA1A1 A2A2 Min(A 1,A 2 ) Step 1: - parallel sorted access to each list (a, 0.9) (b, 0.8) (c, 0.72) (d, 0.6) L1L1 L2L2 (d, 0.9) (a, 0.85) (b, 0.7) (c, 0.2) a d For each object seen: - get all grades by random access - determine Min(A1,A2) - amongst 2 highest seen ? keep in buffer Example – Threshold Algorithm

IDA1A1 A2A2 Min(A 1,A 2 ) a: 0.9 b: 0.8 c: 0.72 d: L1L1 L2L2 d: 0.9 a: 0.85 b: 0.7 c: Step 2: - Determine threshold value based on objects currently seen under sorted access. T = min(L1, L2) a d T = min(0.9, 0.9) = objects with overall grade ≥ threshold value ? stop else go to next entry position in sorted list and repeat step 1 Example – Threshold Algorithm

IDA1A1 A2A2 Min(A 1,A 2 ) Step 1 (Again): - parallel sorted access to each list (a, 0.9) (b, 0.8) (c, 0.72) (d, 0.6) L1L1 L2L2 (d, 0.9) (a, 0.85) (b, 0.7) (c, 0.2) a d For each object seen: - get all grades by random access - determine Min(A1,A2) - amongst 2 highest seen ? keep in buffer b Example – Threshold Algorithm

IDA1A1 A2A2 Min(A 1,A 2 ) a: 0.9 b: 0.8 c: 0.72 d: L1L1 L2L2 d: 0.9 a: 0.85 b: 0.7 c: Step 2 (Again): - Determine threshold value based on objects currently seen. T = min(L1, L2) a b T = min(0.8, 0.85) = objects with overall grade ≥ threshold value ? stop else go to next entry position in sorted list and repeat step 1 Example – Threshold Algorithm

IDA1A1 A2A2 Min(A 1,A 2 ) a: 0.9 b: 0.8 c: 0.72 d: L1L1 L2L2 d: 0.9 a: 0.85 b: 0.7 c: Situation at stopping condition a b T = min(0.72, 0.7) = 0.7 Example – Threshold Algorithm

Sorted access Random access

Stopping Condition  Hypothetical tuple – current value a 1,…, a p for A 1,… A p, corresponding to index seeks on L 1,…, L p and q p+1,….. q m for remaining columns from the query directly.  Termination – Similarity of hypothetical tuple to the query< tuple in Top-k buffer with least similarity.

 Automated Ranking Infrastructure for SQL databases.  Extended TF-IDF based techniques from Information retrieval to numeric and mixed data.  Implementation of Ranking function that exploited indexed access (Fagin’s TA)