The document proposes a framework for extending high-utility pattern mining (HUPM) with facets and advanced utility functions. It introduces a multi-layer transaction representation using containers, objects, and transactions. Facets can be associated with items or different transaction levels to define utility. Advanced utility functions combine utility vectors in various ways to calculate pattern utility. An ASP encoding is developed to find patterns satisfying minimum occurrence and utility thresholds. The framework is evaluated on a sentiment analysis dataset, demonstrating quantitative and qualitative benefits over classical HUPM.

1. the 37th International Conference on
Logic Programming
Sept. 20–27, 2021 (virtual event)
Extending High-Utility Pattern Mining with Facets and Advanced
Utility Functions (Extended Abstract)
Francesco Cauteruccio and Giorgio Terracina
DEMACS, University of Calabria, Italy
{cauteruccio, terracina}@mat.unical.it

2. 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;
• Examples: 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 items sold 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

3. Context and Motivation
• We present a framework for HUPM extending basic notions and introducing:
• 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.
An extended framework for HUPM
Transaction set representation
Facets
Advanced utility functions
For each transaction, different levels of
aggregation can be defined.
+
+
Attributes that can be associated with
any level of aggregation of the
framework.
A taxonomy of functions that can be
combined in several ways to fit
different notions of utility.

4. Proposed Framework
• A multi-layer database representation
• 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$}
• 𝑂% contains a set of transactions {𝑇!, … , 𝑇&}
• The facets define the utility of an item 𝑖
• Each item 𝑖 can be associated with one or more facets.
• Facets can also be defined for transactions, objects and containers.
• Values of facets are represented by utility vectors
• Item utility vector: 𝐼𝑈! = [𝑖𝑢", 𝑖𝑢#, … , 𝑖𝑢$], and 𝑖𝑢% describes a certain facet of 𝑖
• Same applies for transactions, objects and containers.
Extending the database structure and introducing facets
Running example depicting a sales database
Item utility vector for the item 𝑖! containing
values for price and weight facets

5. Proposed Framework
• The advanced utility functions combine utility vectors in different ways:
1. Intra-pattern utility function
• Given a pattern and its occurrences, combine item utility vectors across all the occurrences.
2. Pattern utility function
• Combine the intra-pattern utility function with the facets from the transaction set representation.
• Generates a matrix 𝑈& (occurrences × facets).
3. Utility function 𝒖 𝑷
• Computes the utility of a pattern over 𝑈&.
• Several classifications for 𝑢(𝑃)
• Horizontal-first, vertical-first, inter-transaction utility, pattern-vs-object utility, etc…
Advanced utility functions

6. 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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• Classic guess-and-check approach
• We generate one answer set for each
valid pattern,
• The advanced utility functions are
executed by means of external
functions (e.g., in DLVHEX, WASP,
clingo)
• Pattern validity criteria and filters can
be applied by encoding them.

7. Experimental Evaluation
• Dataset: aspect-based sentiment analysis of
scientific reviews [1]
• Each sentence is annotated with different
aspects, each aspect as a value.
Dataset, quantitative and qualitative analysis
[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
• Quantitative analysis: Running time, comparison with
HUPM systems (in a classical setting).
• Qualitative analysis:
• Mining patterns where the advanced utility function is the
Pearson correlation between the sentiment on a sentence
aspect 𝑋 and the final decision on the corresponding paper.
• Similar results have been obtained where the advanced
utility function is the Multiple correlation.
The use case scenario in the e-HUPM model
The use case scenario in the e-HUPM model

8. 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 scientific reviews 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 particular classes of advanced utility functions.

9. Thanks for your attention!
These slides are available at https://bit.ly/ehupm-iclp21
Francesco Cauteruccio
Research Fellow @ DEMACS, University of Calabria
cauteruccio@mat.unical.it
francescocauteruccio.info
@finalfire