Talk at RuleML + RR 2021

1. The 5th International Joint
conference on Rules and Reasoning
Sept. 8–15, 2021
(virtually in) Leuven, Belgium
An Answer Set Programming based framework for High-Utility
Pattern Mining extended with Facets and Advanced Utility
Functions
Francesco Cauteruccio and Giorgio Terracina
DEMACS, University of Calabria, Italy
{cauteruccio, terracina}@mat.unical.it

2. Outline
• Context and Motivation
• Proposed Framework
• ASP Approach
• Experimental Evaluation
• Conclusion
1/17

3. Context and Motivation
• Pattern Mining is one of the most studied data mining branches
• Find interesting patterns (set of items) in a database of transactions
• Frequent pattern mining, sequential pattern mining, etc…
• High-Utility Pattern Mining (HUPM)
• Find patterns having a high-utility (w.r.t. some utility measure)
• Example: in a sales database, the utility of a pattern may be represented by the profit of some items bought
together.
• Basic assumption: each item is associated with one, static utility .
• However…
• The utility of an item can be defined from very different point of views,
• Transactions are not only flat lists of items but they can provide different level of abstractions.
Pattern Mining and High-Utility Pattern Mining
2/17

4. Context and Motivation
• We present a framework for HUPM extending basic notions and introducing:
• A higher level of abstraction with transaction set representation
• For each transaction, an Object, a Container and a Database level of aggregation can be defined.
• The notion of facet
• A facet is an attribute which can be associated with an item, a transaction, an object or a container;
• Each element may be characterized by more than one facet.
• A taxonomy of extended utility functions
• Based on the database structure and facets,
• They can be combined in several ways to fit different notions of utility.
An extended framework for HUPM
3/17

5. Proposed Framework
• The database representation is multi-layer
• 𝐷𝑎𝑡𝑎𝑏𝑎𝑠𝑒 → 𝐶𝑜𝑛𝑡𝑎𝑖𝑛𝑒𝑟 → 𝑂𝑏𝑗𝑒𝑐𝑡 → 𝑇𝑟𝑎𝑛𝑠𝑎𝑐𝑡𝑖𝑜𝑛
• Given a database 𝐷 and a set of transactions {𝑇!, … , 𝑇"}
• 𝐷 is organized as a set of containers 𝐶 = {𝐶!, … , 𝐶"}
• 𝐶# can be associated with a set of objects 𝑂 = {𝑂!, … , 𝑂$}
• 𝑂% contains a set of transactions {𝑇!, … , 𝑇&}
Extending the database structure
Running example depicting a sales database
5/17

6. Proposed Framework
• The utility of 𝑖 may be defined from
different perspectives: facets.
• Each item 𝑖 can be associated with
one or more facets.
• Facets can also be defined for
transactions, objects and containers.
• To describe facets, we use the notion
of utility vector.
Facets
6/17

7. Proposed Framework
• Item utility vector for an item 𝑖
• 𝐼𝑈! = [𝑖𝑢", 𝑖𝑢#, … , 𝑖𝑢$], and 𝑖𝑢% describes a certain facet of 𝑖
• Transaction utility vector for a transaction 𝑇#
• 𝑇𝑈&!
= [𝑡𝑢", 𝑡𝑢#, … , 𝑡𝑢'], and 𝑡𝑢% describes a certain facet of 𝑇(
• Internal utility of 𝑖 in 𝑇( is available and denoted as 𝑞(𝑖, 𝑇()
• Object utility vector
• 𝑂𝑈) = 𝑜𝑢", 𝑜𝑢#, … , 𝑜𝑢* , and 𝑜𝑢% describes a certain facet of 𝑂
• Container utility vector
• 𝐶𝑈+ = [𝑐𝑢", 𝑐𝑢#, … , 𝑐𝑢,], and 𝑐𝑢% describes a certain facet of 𝐶
Facets and utility vectors
facets: price, weight
7/17

8. Proposed Framework
• Intra-pattern utility function
• Let 𝑃 be a pattern with 𝑟 items, and 𝑇( be a transaction containing it,
• Let 𝐼𝑈𝑆 = {𝐼𝑈", … , 𝐼𝑈-} be the set of item utility vectors of 𝑃
• The intra-pattern utility function 𝐼𝑈&!
= 𝑖𝑝(𝑃, 𝑇(, 𝐼𝑈𝑆) generates an
unique item utility vector for the pattern occurrence.
• 𝑖𝑝 ⋅ can be any function combining the utilities across the facets,
such as SUM, MAX, MIN, AVG, etc…
• Pattern utility function
• The occurrence utility vector for a pattern 𝑃 is 𝑂𝑐𝑐𝑈&!
=
[𝐼𝑈&!
, 𝑇𝑈&!
, 𝑂𝑈&!
, 𝐶𝑈&!
]
• The pattern utility vector 𝑈. is the collection of all the occurrence
utility vectors of 𝑃: 𝑈. = ⋃&!∈&"
𝑂𝑐𝑐𝑈&!
• 𝑈. is a matrix (occurrence utility vectors × facets).
Advanced utility functions
In this example, 𝑖𝑝 = ∑ 𝑓𝑎𝑐𝑒𝑡 × 𝑖𝑛𝑡𝑒𝑟𝑛𝑎𝑙𝑈𝑡𝑖𝑙𝑖𝑡𝑦
8/17

9. Proposed Framework
• The utility 𝑢 of a pattern 𝑃 can be obtained as an arbitrary
combination of the values of 𝑈! using a function 𝑢(𝑃)
• 𝑢(𝑃) can be classified as
• Horizontal first 𝑢 𝑃 = 𝑓?(𝑓@(𝑢.)) combines by row (facets), then by
column (occurrences)
• Vertical first 𝑢 𝑃 = 𝑓@(𝑓?(𝑢.)) combines by column (occurrences),
then by row (facets)
• Mixed 𝑢 𝑃 = 𝑓 𝑢. combines the values at once
• All of these classifications can be further classified in
• Inter-transaction utility
• Pattern-vs-object utility
• Pattern-vs-container utility
• These can be exploited to define utility measures relating
item/transaction facets and one of the object/container facets,
such as Pearson and Multiple correlation.
Advanced utility functions
As an example, suppose we select 𝑓# =
𝑓𝑖𝑙𝑡𝑒𝑟 ⋅ and 𝑓$ = max ⋅ , that is we first
filter for a single facet, and then we take
the maximum across all the occurrences.
9/17

10. Proposed Framework
• Given a pattern 𝑃, we say that 𝑃 is an extended high-utility pattern if its utility 𝑢(𝑃) is greater than
a minimum threshold 𝑡ℎ$ and it occurs in at least 𝑡ℎ% transactions.
• The problem of extended high-utility pattern mining (e-HUPM) is to discover all the extended
high-utility patterns in a given database 𝐷.
The e–HUPM problem
10/17

11. ASP Approach
• We want to provide as much flexibility as possible in the definition of what is a useful pattern.
• Encoding the problem in Answer Set Programming (ASP) helps achieving the desidered flexibility
and modularity.
• Classic guess-and-check scenario
• We generate one answer set for each valid pattern,
• Complex utility functions are executed by means of external functions (e.g., in DLVHEX, WASP, clingo)
• Pattern validity criteria and filter can be easily applied by encoding them as rules.
The why and the how
11/17

12. ASP Approach
The encoding
%%% Input schema:
%container(ContainerId)
%object(ObjectId,ContainerId)
%transaction(Tid, ObjectId)
%item(Item, Tid, Position, Q)
%itemUtilityVector(Item, I1, ..., Il)
%transactionUtilityVector(Tid, T1, ..., Tm)
%objectUtilityVector(ObjectId, O1, ..., On)
%containerUtilityVector(ContainerId, C1, ..., Co)
%%% Parameters
occurrencesThreshold(...). utilityTreshold(...).
%%% Item pre-filtering
usefulItem(I):- item(I,_,_,_),....any condition on the items.
%%% Candidate pattern generation
{inCandidatePattern(I)}:- usefulItem(I).
%%% Occurrences computation and check
inTransaction(Tid):- transaction(Tid,_), not incomplete(Tid).
incomplete(TiD):- transaction(Tid,_), inCandidatePattern(I), not contains(I,Tid).
contains(I,Tid):- item(I,Tid,_,_).
:- #count{ Tid : inTransaction(Tid)}=N, N < Tho, occurrencesThreshold(Tho).
%%% Utility computation
patternItemUtilityVectors(Tid,Item,I1,...,Il,Q):- inCandidatePattern(Item),
itemUtilityVector(Item, I1, ..., Il), inTransaction(Tid), item(Item, Tid, Position, Q).
intraPatternUtilityVector(Tid,I1,...,Il):-
&computeIntraPatternUtility[patternItemUtilityVectors](Tid,I1,...,Il).
occurrenceUtilityVector(Tid,I1,...,Il,T1,...Tm,O1,...On,C1,...,Co):-
inTransaction(Tid), intraPatternUtilityVector(Tid,I1,...,Il)
transactionUtilityVector(Tid, T1, ..., Tm), transaction(Tid, ObjectId),
objectUtilityVector(ObjectId, O1, ..., On), object(ObjectId , ContainerId)
containerUtilityVector(ContainerId, C1, ..., Co).
:- &computeUtility[occurrenceUtilityVector](U), U < Thu, utilityTreshold(Thu).
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13. Experimental Evaluation
• Aspect-based sentiment analysis of scientific reviews [1]
• Each review is annotated with 8 different aspects: appropriataness, clarity, originality,
empirical/theoretical soudness, meaningful comparison, substance, impact and recommendation
• Each aspect has assigned one sentiment value from {𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒, 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒, 𝑛𝑒𝑢𝑡𝑟𝑎𝑙, 𝑎𝑏𝑠𝑒𝑛𝑡}.
• 814 papers and a total of 1148 reviews.
• 2230 annotated lines with a total of 15124 distinct words.
Dataset
[1] Chakraborty, S., Goyal, P., Mukherjee, A.: Aspect-based sentiment analysis of scientific reviews. In: JCDL ’20: Proceedings of the ACM/IEEE Joint Conference on Digital Libraries in 2020, Virtual Event, China, August 1-5,
2020. pp. 207–216 (2020), ACM
13/17

14. Experimental Evaluation
• Average running time
• 𝑢(𝑃): disagreement between originality and decision (% of
pattern occurrences showing a positive originality and a
reject decision, thresholds: [15, 50, 75, 100])
Quantitative analysis
• Comparison with HUPM systems
• No analysis involving more than one
elements can be devised with such
systems
• Here, the utility of an item is the absolute
value of the appropriateness aspect in
the sentence it first appears in.
14/17

15. Experimental Evaluation
• 𝑢 𝑃 : Pearson correlation between an aspect 𝑋
and the final decision on the corresponding
paper.
• «The set of review sentences containing 𝑃 are
characterized by a direct correlation between the
sentiment on 𝑋 and the final decision on the
corresponding paper»
• 𝑢(𝑃): Multiple correlation between two aspects
𝑋 and 𝑌 and the final decision on the
corresponding paper.
Qualitative analysis
15/17

16. Conclusion
• We introduced a general framework for HUPM with several extensions.
• The framework allows to work with multi-dimensional data and with different utility measures.
• A versatile and modular ASP encoding has been developed.
• We employed a real use case on paper review to carry out both quantitative and qualitative
analyses.
• Facets and advanced utility functions help reducing the amount of relevant patterns
• Useful in providing deep insights on the data.
• Not an ending point!
• Apply the framework to new contexts,
• Derive ad-hoc algorithms for the extended utility functions.
16/17

17. Thanks for your attention!
These slides available at https://bit.ly/ehupm-ruleml21
Francesco Cauteruccio
Research Fellow @ DEMACS, University of Calabria
cauteruccio@mat.unical.it
francescocauteruccio.info
@finalfire