Politecnico di Torino
Dipartimento di Automatica e Informatica
http://elite.polito.it
FaSet: A Set Theory Model for
Faceted Search
Dario Bonino, Fulvio Corno, Laura Farinetti

Outline
 Faceted Search
 Goal
 The FaSet Set-Theoretical Model
 FaSet Relational Implementation
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Faceted Classification
 Originated in Library Science
 Ranganathan, 1962
 Content-based classification scheme
 Multi-dimensional
 Facet = classification dimension
 Multi-valued
 Focus = allowed value in one of the facets
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Example
Color Shape Taste Facets
Yellow Cube Sweet
Red Sphere Bitter
Orange Cone Neutral
Allowed foci for
Green Cylinder Acid
each facet
Blue
White
Black
Choice of the foci
describing the item
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Faceted Search Systems
 Faceted Classification
 Simple, intuitive, versatile, powerful
 Adopted by more and more web sites
 As a classification system for their
products/items/documents/resources/…
 As a model for the user interface in search, filtering,
refinement
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Examples
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Examples
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Examples
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Facets in the real world
 Multi-valued Color Shape
classification Yellow Squared ▼
Red Cube
 During classification
Orange Parallelepiped
 During search
Green Rounded ▼
 AND vs OR semantics? Sphere
Blue
 Hierarchical (nested) White Cylinder
facets Black
 Parents selectable? Other
Weight
 Incomplete classification 0-50 g
 Numerical ranges 50-100 g
100+ g
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Facets in the Literature
User Interfaces Data and logic model
 Active research field  Methodologies from
since ~2000 Library science
 Usability studies (Broughton, Vickery)
 Mainly for search  Formal models
interfaces  Dynamic Taxonomies
 Application case studies (Sacco)
 Web vs desktop  Uniformities, Lattices
(Priss)
environment
 Granular computing
 Mainly for multimedia
data  Less applicable results
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Goal of the paper
 Propose a formal model: FaSet
 for representing
 Faceted Classification of resources
 Faceted Search Interfaces for such resource sets
 Searching, Filtering, Ranking operations
 compatible with modern web applications
 Mathematically simple
 Easy mapping to Relational Algebra
 Decouple classification and resources
 versatile and flexible
 Supports all “real-world” variations on Facets
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Facets and Foci
 Facets: disjoint sets U
 Fa, Fb, Fc, … Fb
 Facet space:
 U = Fa  Fb  Fc  … Fa
 Focus L: subset
 La  Fa Fa
 Many foci for each facet
La<2>
 Focus name: index list La<1>
 La<i,j,k,…> La<1,1>
La<1,2>
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Hierarchy
 Hierarchical nesting of Fa
La<2>
foci is represented by
La<1>
subset containment
La<1,1>
 La<narrower> 
La<1,2>
La<broader>
 Locus names are  Incomplete taxonomy
chosen to represent  No overlap allowed
hierarchical containment  A focus may be larger
 La<i,j,k>  La<i,j> than the union of its sub-
 Reminds of Dewey Decimal
foci
Classification
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Classification (Facet)
 Resources r are Fa
La<2>
classified w.r.t. the facet
La<1>
space
La<1,1>
 “Projection”: r  Fa
La<1,2>
 We may only represent
projections built by r  Fa
combining foci
 r  Fa = ∪p La<p>
 Just the focus names
are needed
 {<1,1>,<2>}
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Classification (Multidimensional)
 On the multi-
dimensional space, the rU
cartesian product is r  Fb
taken
 r  U = rFa  rFb  ...
 Just the focus names r  Fa
are needed

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Searching in FaSet
 Resources r r1
 Classified as r  U Fb q
r2
 Query q
 Expressed uniformly as q  U Fa
 Search = Filtering + Ranking
 Filtering: r is relevant to q iff: (r  U) ⋂ (q  U)  
 Ranking: estimate the similarity S(q, r) of r to q
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Filtering
 All resources that match, even partially, with the
query
 (r  U) ⋂ (q  U)  
 May be easily computed by checking focus names
 Prefix-compatibility: La<p1> ≍ La<p2> iff
 p1 = p2, or
 p1 is a prefix of p2, or
 p2 is a prefix of p1
 At least one couple of foci, per each facet, must be
prefix-compatible
 ∀Fa : ∃ La<p1> ∈ q, La<p2> ∈ r : La<p1> ≍ La<p2>
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Example
L<>
L<1> L<2>
L<1,1> L<1,2> L<1,3> L<2,1> L<2,2>
<1,3> <2> q
<1> r1
<2,2> r2
<1,2> <1,3> r3
<1,1> <1,2> r4
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Ranking
 Compute similarity between resource and query
 Often neglected by Faceted Search Interfaces
 Define a Similarity Measure S(q, r) ∈ [0,1]
 Compute similarity between matching foci (deeper
matches give higher scores)
 Aggregate focus-based similarity measures in the same
facet (fuzzy sum)
 Normalize facet-level results
 Aggregate facet-based similarity measures across all
facets (fuzzy product)
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FaSet Relational Implementation
 The FaSet classification requires
 A constant set of Facets
 A constant set of Foci
 An “index” table storing the list of focus names for each
resource constant
Resource
Database
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FaSet Relational Implementation
 The FaSet search algorithm uses
 Set operations
 Universal and existential quantification
 Aggregate operations for computing ranking measures
 Directly supported by Relational DBMS primitives
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Future work
 Experimentation of FaSet on sample data sets
 Performance evaluation
 Integration with front-end AJAX interfaces
 CMS module
 MIT Exhibit
 Evaluation of the ranking
algorithm from the
Information Retrieval
point of view
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Conclusions - FaSet
 Formally defined faceted Representation & Search
model
 Light formalism
 Supports hierarchies, nesting, multiple classification,
incomplete specifications, …
 Compatible with modern web development
technologies
Thank
you!
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