faset: a set theory model for faceted search

FaSet: A Set Theory Model for

Faceted Search

Dario Bonino, Fulvio Corno, Laura Farinetti

Politecnico di TorinoDipartimento di Automatica e Informatica

http://elite.polito.it

Outline

FaSetWI/IAT 2009, Milano, Italy2

Faceted Search

Goal

The FaSet Set-Theoretical Model

FaSet Relational Implementation

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

FaSet3 WI/IAT 2009, Milano, Italy

Example


Color

Yellow

Red

Orange

Green

Blue

White

Black

Shape

Cube

Sphere

Cone

Cylinder

Taste

Sweet

Bitter

Neutral

Acid

Facets

Allowed foci for

each facet

Choice of the foci

describing the item

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


Examples


Facets in the real world


Multi-valued

classification

During classification

During search

AND vs OR semantics?

Hierarchical (nested)

facets

Parents selectable?

Incomplete classification

Numerical ranges

Color

Yellow

Red

Orange

Green

Blue

White

Black

Other

Shape

Squared ▼

Cube

Parallelepiped

Rounded ▼

Sphere

Cylinder

Weight

0-50 g

50-100 g

100+ g

Facets in the Literature

User Interfaces Data and logic model


Active research field since ~2000

Usability studies Mainly for search

interfaces

Application case studies

Web vs desktop environment

Mainly for multimedia data

Methodologies from Library science (Broughton, Vickery)

Formal models Dynamic Taxonomies

(Sacco)

Uniformities, Lattices (Priss)

Granular computing

Less applicable results

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


Facets and Foci

Facets: disjoint sets

Fa, Fb, Fc, …

Facet space:

U = Fa Fb Fc …

Focus L: subset

La Fa

Many foci for each facet

Focus name: index list

La<i,j,k,…>


Fa

Fb

U

Fa

La<2>

La<1>

La<1,1>

La<1,2>

Hierarchy

Hierarchical nesting of

foci is represented by

subset containment

La<narrower>

La<broader>

Locus names are

chosen to represent

hierarchical containment

La<i,j,k> La<i,j>

Reminds of Dewey Decimal

Classification

Incomplete taxonomy

No overlap allowed

A focus may be larger

than the union of its sub-

foci


La<2>

La<1>

La<1,1>

La<1,2>

Fa

Classification (Facet)

Resources r are

classified w.r.t. the facet

space

“Projection”: r Fa

We may only represent

projections built by

combining foci

r Fa = ∪p La<p>

Just the focus names

are needed

{<1,1>,<2>}


La<2>

La<1>

La<1,1>

La<1,2>

r Fa

Fa

Classification (Multidimensional)

On the multi-

dimensional space, the

cartesian product is

taken

r U = rFa rFb ...

Just the focus names

are needed


r Fa

r Fb

r U

Searching in FaSet

Resources r

Classified as r U

Query q

Expressed uniformly as q U

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


Fb q

r1

r2

Fa

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>


Example

L<>

L<1> L<2>

L<1,1> L<1,2> L<1,3> L<2,1> L<2,2>

<1,3> <2>

<1>

<2,2>

<1,2> <1,3>

<1,1> <1,2>


q

r1

r2

r3

r4

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)



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


Resource

Database

constant


The FaSet search algorithm uses

Set operations

Universal and existential quantification

Aggregate operations for computing ranking measures

Directly supported by Relational DBMS primitives


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


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!

faset: a set theory model for faceted search

Technology