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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Knowledge Driven Behavioural Analysis in Process Intelligence</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Antonia Azzini</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Paolo Ceravolo</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Ernesto Damiani</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Francesco Zavatarelli</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Computer Science Department, Universita` degli Studi di Milano via Bramante</institution>
          ,
          <addr-line>65 - 26013 - Crema</addr-line>
          ,
          <country country="IT">Italy</country>
        </aff>
      </contrib-group>
      <fpage>97</fpage>
      <lpage>111</lpage>
      <abstract>
        <p>In this paper we illustrate how the knowledge driven Behaviour Analysis, which has been used in the KITE.it process management framework, can support the evolution of analytics from descriptive to predictive. We describe how the methodology uses an iterative three-step process: first the descriptive knowledge is collected, querying the knowledge base, then the prescriptive and predictive knowledge phases allow us to evaluate business rules and objectives, extract unexpected business patterns, and screen exceptions. The procedure is iterative since this novel knowledge drives the definition of new descriptive analytics that can be combined with business rules and objectives to increase our level of knowledge on the combination between process behaviour and contextual information.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1 Introduction</title>
      <p>
        Process Intelligence (PI), i.e. the convergence of operational business intelligence [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]
and real-time application integration, has gain a lot of attention in the last years,
especially around applications involving sensor networks [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]. The final aim is to provide
more accurate and fast decisions on the strategic and operational management levels.
Most of the current studies on PI focus on the analysis of the process behavior and
support performance improvement limited to this aspects [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ]. But, descriptive analysis
is contextual in nature [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ], its value is clarified by the knowledge you have on a
process, for instance in terms of business rules that apply and constrain a process [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ]. In
particular our claim is that, to insert PI into a consistent knowledge acquisition process
[
        <xref ref-type="bibr" rid="ref6">6</xref>
        ], the level of its maturity and practical implementation has to evolve in the following
directions:
      </p>
      <p>
        For this purpose, we introduced the KITE Knowledge Acquisition Process [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ], a
methodology dealing with the evolution of analytics from descriptive to prescriptive,
to predictive intention. In KITE an initial set of metrics offer the initial descriptive
knowledge. Then our analytics support the evaluation of process instances based on
their consistency with policies, business rules and KPI, defined at the strategic level.
These constrains are refereed in general as prescriptions. Process instances violating
prescriptions offer a crucial source of knowledge acquisition as predictive analytics
can evaluate the incidence of specific variables on violations, to then derive predictive
knowledge. Indeed, predictive analytics involves searching for meaningful relationships
among variables and representing those relationships in models. There are response
variables - things we are trying to predict, in our case violations to prescriptions. There
are explanatory variables or predictors - things we observe. To generalise, as much as
possible our predictive power, predictors in our case are any data related to resource
auxiliary to process execution. Actually, in our approach, metrics measure process
behaviour in an extended sense, as the information retrieved is not limited to the workflow,
but include data related to any resource auxiliary to the process execution, as already
discussed in [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ]. Our approach differs from traditional predictive analytics because it is
centred on the knowledge provided by the organization via Business Rules and other
documentation. This approach was framed by KITE in the firm belief that it can put in
contact PI and predictive analytics with Knowledge Management.
      </p>
      <p>The paper is organized as follow. Section 2 starts the discussion with the related
work. Sections 3 and 4 describe the KITE framework. Section 5 describes how KITE
knowledge acquisition process works. Section 6 deals with behavioural and predictive
analysis. Section 7 illustrate our ideas through an example. Section 8 proposes some
conclusions.</p>
    </sec>
    <sec id="sec-2">
      <title>2 Related Work</title>
      <p>
        Predictive analytics applied to process monitoring is often limited, or strongly
depended, to temporal analysis. For instance in [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ] temporal logic rules are adopted to
define business constraints. The approach is then focused on the evaluation of these
constraints at execution time, to generate alerts that can prevent the development of
violations. In [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ], the authors present a set of approaches based on annotated
transition systems containing time information extracted from event logs. The aim is again
to check time conformance at execution time, as executions not aligned with annotated
transitions predict the remaining processing time, and recommend countermeasures to
the end users. An approach for prediction of abnormal termination of business processes
has been presented in [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ]. Here, a fault detection algorithm (local outlier factor) is used
to estimate the probability of abnormal termination. Alarms are provided to early notify
probable abnormal terminations to prevent risks rather than merely reactive correction
of risk eventualities. Other approaches go beyond temporal analysis extending
predictive analytics to include ad-hoc contextual information. In [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ], a clustering approach
on SLA properties is coupled with behavioral analysis to discovered and model
performance predictors. In [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ], the authors propose an approach running statistical analysis
on process-related data, notably the activities performed, their sequence, resource
availability, capabilities and interaction patterns. In [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ], the authors propose an approach
for Root Cause Analysis based on classification algorithms. After enriching a log with
information like workload, occurrence of delay and involvement of resources, they use
decision trees to identify the causes of overtime faults. In such an analysis, the
availability of attributes/features that may explain the root cause of some phenomena is crucial.
On the side of knowledge acquisition procedures the literature presents several works
specifically oriented to the area of business process management [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ]. However only a
few are really considering analytics as a key element of this process. For instance in [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ]
the authors exploit the notion of knowledge maintenance process. process mining is
applied to analyze the knowledge maintenance logs to discover process and then construct
a more appropriate knowledge maintenance process model. The proposed approach has
been applied in the knowledge management system.
      </p>
      <p>Our work is characterized by the introduction of an extended notion of process
behavior that provide a generalized systematic approach to captures process features
beyond workflow execution. This element is the exploited within a knowledge
acquisition methodology that exploits prescriptive and predictive analytics to acquire novel
and unexpected knowledge.</p>
    </sec>
    <sec id="sec-3">
      <title>3 The KITE Methodology</title>
      <p>
        KITE.it is a project co-funded by the Italian Ministry for Economic Development,
within the “Industria 2015” Program, in the area of “New technologies for Made in
Italy” [
        <xref ref-type="bibr" rid="ref16">16</xref>
        ]. The exit from the great global crisis towards a new cycle of development
requires to move from organizational and inter-organizational models, based on a strict
definition of roles and organizational boundaries. In this context, KITE.it is aimed at
developing a business and social cooperation framework that enables interoperability
among enterprises and other knowledge workers, making available a variety of tools
and technologies developed to connect the processes of an organization to those of
suppliers or to involve customers in planning and assessing activities. In fact, the KITE.it
framework should be capable of supporting procedures such as i) creation,
contextualization and execution of metrics, ii) connection between metrics and strategic level, and
iii) inception and capitalization of the results. The final goal is driving the monitoring
process to derive previously unknown and potentially unexpected knowledge.
To circumscribe our discussion, in this paper we examine a single aspect of the KITE.it
Framework, focusing on how it was extended to cover data integration and
interoperability, as discussed in Section 4. Moreover, we are considering how these
characteristics was exploited in guiding the Knowledge Acquisition Process, as discussed in Sec
5.
      </p>
    </sec>
    <sec id="sec-4">
      <title>4 The KITE Knowledge Base</title>
      <p>The KITE Knowledge Base (KKB) has to integrate a variety of heterogeneous data
from the different sources composing the KITE.it Framework.</p>
      <p>
        This requirement is faced adopting a graph-based model to structure and link data
according to the Web Standards, the so-called Resource Description Framework.
Generally speaking, the Resource Description Framework (RDF) [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ] provides a standard for
defining vocabularies, which can be adopted to generate directed labeled graphs [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ],
in which entities edges and value are associated with terms of the vocabulary. For this
reason, RDF is an extremely generic data representation model that can be extended
easily with any domain-specific information. Moreover, RDF is a monotonic declarative
language, i.e. the acquisition of new data cannot invalidate the information previously
acquired.
      </p>
      <p>The atomic elements of a RDF graph are triples1. Triples are composed by three
elements: resources, relations between resources and attributes of resources. These
elements are modeled within the labelled oriented graph, as the atomic structure &lt; s; p; o &gt;
where s is subject, p is predicate and o is object, combined as shown in Figure 1.</p>
      <p>New information is inserted into an RDF graph by adding new triples to the data set.
It is therefore easy to understand why such a representation can provide big benefits for
real time business process analysis: data can be appended ‘on the fly’ to the existing one,
and it will become part of the graph, available for any analytical application, without
the need for reconfiguration or any other data preparation steps.</p>
      <p>Assuming pairwise disjoint infinite sets I, B, L (IRIs2, Blank nodes, RDF Literals).
Definition 1 A tuple (s; p; o) 2 (I [ B) I (I [ B [ L) is called an RDF triple.</p>
      <p>An RDF graph G is a set of RDF triples. An interesting feature of RDF standards
is that multiple graphs can be stored in a single RDF Dataset. As stated in the
specifications “An RDF Dataset comprises one graph, the default graph, which does not have
a name, and zero or more named graphs, where each named graph is identified by an
IRI”.</p>
      <p>
        RDF standard vocabularies allow external applications to query data through SPARQL
query language [
        <xref ref-type="bibr" rid="ref19">19</xref>
        ]. SPARQL is a standard query language for RDF graphs based on
conjunctive queries on triple patterns, identifying paths in the RDF graph. Thus, queries
can be seen as graph views. SPARQL is supported by most of the triples stores available.
      </p>
      <p>If we now introduce a novel infinite set V for variables, disjoint from I, B, and L we
can define SPARQL patterns as in the following.</p>
      <p>Definition 2 A tuple t 2 (I [ L [ V ) (I [ V ) (I [ L [ V ) is called a SPARQL triple
pattern. Where the blank nodes act as non-distinguished variables in graph patterns.
Definition 3 A finite set of SPARQL triple patterns can be constructed in a Graph
Pattern (GP) using OPTIONAL, UNION, FILTER and JOIN. A Basic Graph Pattern is a
set of triple patterns connect by the JOIN operator.</p>
      <p>
        The semantics of SPARQL is based on the notion of mapping, defined in [
        <xref ref-type="bibr" rid="ref20">20</xref>
        ] as a
partial function μ : V ! (I [ L [ B). Where, if GP is a graph pattern and var(GP) denotes
1 An alternative terminology adopted in documentation is statements or eventually tuples.
2 IRIs are the RDF URI references, IRIs allow all characters beyond the US-ASCII charset.
the set of variables occurring in GP; given a triple pattern t and a mapping μ such that
var(t) dom(μ), μ is the triple obtained by replacing the variable in t according to μ.
      </p>
      <p>
        In [
        <xref ref-type="bibr" rid="ref21">21</xref>
        ], the authors present a framework based on RDF for business process
monitoring and analysis. They define an RDF model to represent a generic business process
that can be easily extended in order to describe any specific business process by only
extending the RDF vocabulary and adding new triples to the triple store. The model
is used as a reference by both monitoring applications (i.e., applications producing the
data to be analyzed) and analyzing tools. On one side, a process monitor creates and
maintains the extension of the generic business process vocabulary either at start time,
if the process is known a priori, or at runtime while capturing process execution data, if
the process is not known. Process execution data is then saved as triples with respect to
the extended model. On the other side, the analyzing tools may send SPARQL queries
to the continuously updated process execution RDF graph.
      </p>
      <p>Figure 2 shows the schema of an RDF Dataset composed by the union of two graphs.
The resources describing the generic model of a business process are tagged in blue.
They can represent a sequence of different tasks, each having a start/end time and
having zero or more sub-tasks. The resources tagged in yellow represent domain-specific
concepts describing the repair and overhaul process in avionics. In this very simple
extract we defined a process, in connection with its tasks, and the customer purchasing
the overhaul operations.</p>
      <p>Once this schema is defined any process execution is stored in the KKB in terms
an RDF Dataset composed of triples conforming with the schema. For instance, in 1 a
legal dataset is presented.</p>
      <p>av:p1 rdf:type av:Overhaul
av:p1 bpm:hasTask av:t1
av:p1 bpm:hasTask av:t2
av:t1 bpm:followedBy av:t2
av:t1 bpm:startTime "2013-06-06 10:38:45"ˆˆxsd:date
av:t1 bpm:endTime "2013-06-06 18:12:35 "ˆˆxsd:date
av:t1 rdf:type av:Inspect
(1)</p>
    </sec>
    <sec id="sec-5">
      <title>5 The KITE Knowledge Acquisition Process</title>
      <p>
        The methodology considers the KITE Knowledge Acquisition Process (KKAP) as an
investigation over the process executions, as registered in the KKB. In particular, this
methodology is organised in iterations over three fundamental steps.
– Descriptive Knowledge: querying triples on the process execution, or any other
auxiliary resource, you have a descriptive summary of the process in terms of frequency,
dimension, and central tendency [
        <xref ref-type="bibr" rid="ref22">22</xref>
        ].
– Prescriptive Knowledge: evaluating the achievement of the business rules or the
objectives associated to a process, as well as identifying unexpected patterns, you can
screen of process executions isolating exceptions that are violating some prescription
[
        <xref ref-type="bibr" rid="ref23">23</xref>
        ].
– Predictive Knowledge: process executions screened by prescriptions can be further
investigated evaluating the incidence of specific properties on specific partitions of
the KKB. This allows to acquire novel knowledge on the process that eventually can
result in new descriptive or prescriptive knowledge.
      </p>
      <p>Before providing further definitions let us clarify our purpose by a simple example
of two iterations.</p>
      <sec id="sec-5-1">
        <title>5.1 First iteration</title>
        <p>The engine maintenance is a very complex process performed by the aerospace industry.
Generally speaking, maintenance operations are needed on a regular time basis (Inspect
Only, Minor Revision or General Revision, according to the number of flown hours)
or when a part has failed (Out o f Order), as shown in table 1. The activities vary
accordingly.</p>
        <p>General Rev.</p>
        <p>Minor Rev.</p>
        <p>Inspect Only
Out of Order</p>
        <p>Yes
Yes</p>
        <p>Yes
Inspect Disassembly Inspect Repair Clean Assembly Bench
(I) (DA) Mod. (IM) (R) (C) (A) Test (BT)</p>
        <p>Yes Yes Yes Yes</p>
        <p>Yes
Yes</p>
        <p>Yes</p>
        <p>Yes</p>
        <p>Yes</p>
        <p>Yes</p>
        <p>Yes</p>
        <p>Checkout
(CO)
Yes
Yes
Yes
Yes</p>
        <p>Suppose to focus on minor and general revision processes, and collect the
duration in days of all the process executions involving the activities Inspect, Clean and
CheckOut (I C CO in short) in case of minor revision, or Disassembly, Inspect
Module, Clean, Assembly and CheckOut (DA IM C A CO in short) when
general revision is performed. Results can be summarised as illustrated in table 2. In
this way you have Descriptive Knowledge about the processes.</p>
        <p>
          To acquire Prescriptive Knowledge you have to compare your data with some
prescriptions. By this term here we refer to any constraint or property the business
processes execution should satisfy. In the Business Process Management literature, this
function is typically associated with Business Rules [
          <xref ref-type="bibr" rid="ref24">24</xref>
          ], even if their scope is not
limited at assessing the business behavior but involves the business structure as well (for
instance defining the corporate governance). Business Rules can derive from internal
objectives and strategies or from external factors such as contractual constrains or legal
requirements. However, Business Rules can also be discovered by data mining [
          <xref ref-type="bibr" rid="ref25">25</xref>
          ] or
process mining [
          <xref ref-type="bibr" rid="ref26">26</xref>
          ], for instance by identifying recurrent behavior.
        </p>
        <p>Once a prescription is defined you are able to partition the dataset based on the
violations of this prescription. If the violation can be associated to an intensity the
partitions depend on a degree, otherwise the partition is binary. For instance Business
Rules could prescribe the expected duration of process executions: Duration 7 days
if Minor Revision and Duration 11 days if General Revision. Table 3 shows the
result of this operation. The prescription that have been learned from a dataset d can be
applied to other datasets D, under the assumption that d is a representative sample of D.</p>
        <p>The notion of violation is crucial in the KITE methodology as it identify an
observation that is not consistent with our expectations and we would like to avoid for
future executions. Investigating the incidence of specific resources on the sub set of the
violations we can induce additional knowledge to support explanation or resolution of
process executions violating our prescription. To draw conclusions of our example let
us introduce an additional resource in our view of the dataset, as illustrated in Table 4. If
we can observe a significant incidence of this resource to the subset of the violations we
ProcessID Task Sequence Duration Violation
p12 Minor Revision 3 NO
p39 Minor Revision 3 NO
p31 Minor Revision 4 NO
p33 Minor Revision 5 NO
p05 Minor Revision 5 NO
p102 General Revision 11 NO
p104 General Revision 11 NO
... ... ... ...
p11 Minor Revision 8 YES
p101 General Revision 12 YES
p103 General Revision 13 YES</p>
        <p>... ... ... ...
can attest the acquisition of novel knowledge that should be exploited for the definition
of a second iteration of the KKAP.</p>
      </sec>
      <sec id="sec-5-2">
        <title>5.2 Second iteration</title>
        <p>As previously stated, this is an iterative process, which takes the last data as a starting
point for the second iteration, see Figure 3.</p>
        <p>We start our second iteration as shown in table 5, where some other kind of
processes (Inspect Only and Out o f Order) are added to the dataset for a better
understanding. We also introduce additional resources, in this case the notion whether the
activities were performed by internal company staff or outsourced to somebody else.</p>
        <p>Defining another prescription we are able again to partition the dataset based on
the violations of the new business rule. Consider for example to define the following</p>
        <p>Fig. 3. iterations
prescription: operations must not be outsourced if the engine belongs to a military
customer. Table 6 shows the result of this operation.</p>
        <p>ProcessID Task Sequence
p11 Minor Revision
p101 General Revision
p103 General Revision
p202 Inspect Only
p301 Out of Order
... ...</p>
        <p>Customer Type Staff</p>
        <p>Military Outsourced
Military Internal
Military Internal
Military Internal
Military Outsourced
... ...</p>
        <p>Investigating again the incidence of a specific resource on the subset of the violation
we can induce additional knowledge and support explanation. In our case, in order to
draw conclusions we introduce an additional resource in our view of the dataset, as
illustrated in Table 7. When we observe a significant incidence of this resource to the
subset of the violations we have acquisition of novel knowledge.
ProcessID Task Sequence Customer Type Staff
p101 General Revision Military Internal
p103 General Revision Military Internal
p202 Inspect Only Military Internal
... ... ... ...
p11 Minor Revision Military Outsourced
p301 Out of Order Military Outsourced
... ... ... ...</p>
        <p>Violating Certified</p>
        <p>NO YES
NO YES
NO YES
... ...</p>
        <p>YES NO
YES NO
... ...</p>
      </sec>
    </sec>
    <sec id="sec-6">
      <title>6 Predictive Analytics</title>
      <p>
        As illustrated in [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ] we extended the notion of Behavioral Analysis as a weaker form
of classic behavior equivalence, where two compatible behaviors have to be equivalent
with respect to activities they have in common [
        <xref ref-type="bibr" rid="ref27">27</xref>
        ]. To characterise a process execution
log, for instance for detecting ordering relations among events, it is common to start by
the definition of process execution tracks, workflow trace as defined in [
        <xref ref-type="bibr" rid="ref28">28</xref>
        ]. In our
approach, we extended this definition by auxiliary resources, considering any data related
to the events in a trace that are consistent with a graph pattern over the KKB.
      </p>
      <p>
        As already mentioned the KKAP includes predictive analytics aimed at identifying
the incidence of KKB’s resources on process execution. In general, predictive analytics
encompasses a variety of statistical techniques from modeling, machine learning, and
data mining that uncovers relationships and patterns within large volumes of data that
can be used to predict behavior and events [
        <xref ref-type="bibr" rid="ref29">29</xref>
        ]. Here we adopt the term to refer to
this part of our methodology that is is forward-looking, i.e. uses past events to better
understand the process. In particular our aim is to investigate data about resources
auxiliary to process execution, searching for incidence with those process instances that are
violating prescriptions. Now, our aim is to define how this incidence is evaluated.
      </p>
      <p>
        The approach adopted in KITE is based on Bayesian statistics [
        <xref ref-type="bibr" rid="ref30">30</xref>
        ]. Bayesian
statistics offers the theoretical framework for combining experimental and extra-experimental
knowledge. In particular, Bayesian procedures, for evaluating the predictive power of
a parameter in a statistical model, take into account both experimental data and
information on the parameter incorporated in the so-called prior distribution3. This is
an important point of distinction with frequentist approaches, most commonly used.
The most practical consequence is that frequentist approaches impose assumptions on
the distribution for both the random sample and the model tested. Different hypothesis
tests have different model assumptions. For many tests, the model assumptions consist
of several conditions. If any one of these conditions is not true, we do not know that the
test is valid. But these assumptions cannot be easily verified on any kind of data sets, in
particular when dealing with data flows acquired or consumed at low interval rates.
3 It is however well know that the conflict between Bayesian and frequentist procedures tends
to disappear as the sample size increases. Indeed, the discrepancies are limited when sampling
information dominates the prior distribution or pre-experimental information may influence
the estimates on prior distribution.
      </p>
      <p>Following a Bayesian approach, we consider H an unknown hypothesis; X =
fX1; :::; Xng is a set of independent and identically distributed observations. Let xn =
(x1; :::; xn) be an observed sample; p(H) is the prior probability of the hypothesis under
test; p(XjH) the likelihood; and the posterior distribution is defined as in equation 2.
p(HjX) =</p>
      <p>p(XjH)p(H)
ån p(XnjHn)p(Hn)
(2)</p>
      <p>Predictive modeling involves finding good subsets of predictors or explanatory
variables. Models that fit the data well are better than models that fit the data poorly. Simple
models are better than complex models. Working with a list of useful predictors, we can
fit many models to the available data, then evaluate those models by their simplicity and
by how well they fit the data.</p>
    </sec>
    <sec id="sec-7">
      <title>7 A Preliminary Example</title>
      <p>To illustrate the approach proposed in KITE.it, we now provide a running example. Let
us start from a sample business rule stating that: “On an equipment fault, operators will
visit customers premises within 12 hours from fault reporting”. Our aim is to discover
new knowledge from the information detected by monitoring the process in connection
to this policy. We then formulate a predictive analysis considering the incidence of
“previous visits to the same client by the same operator” to violations to these policies.</p>
      <p>We start by a descriptive metrics that can be computed using a query listing the
excess time, expressed in hours and computed as the difference between visit time and
fault time, for a set of tuples extracted from specific traces identified by ProcessID.
Table 8 illustrate an sample of the results returned querying a data set.</p>
      <p>The prescription we want to apply to these traces imposes a constraint of form
excess time &gt; 12. Filtering traces by this constraint we obtain the set of violations V :
f12; 33; 29; 21; 11; 05g. This set must be compared to the set of traces ordered by the
the number of previous visits by same operator to clients. Another descriptive metrics
is then defined to extract these data, getting a distribution E. Table 9 illustrate an sample
of the results returned.</p>
      <p>ClientID VisitID OpId VisitPriorToFault</p>
      <p>C121 AEFF 1 3
C313 AB07 3 2
C236 AA01 7 6
C118 AA08 4 4
C259 AAB0 9 1
C329 AA04 13 1
C311 AA42 14 2
C111 AB17 8 4
C319 AA22 12 6</p>
      <p>C209 AA78 19 3</p>
      <p>The predictive analysis is then executed by evaluating the incidence of different
partition E on V . More specifically, referring to the equation 2, V is the hypotheses
H we are testing and E is the observation X. We are in other words evaluating how
confident we are that observing a trace included in E this trace will also be in V .
If X is an ordinal variable we can test these incidence for each subset of the distribution
by imposing a threshold a for defining membership of the subset under consideration.</p>
      <p>Xa = fx a; 8x 2 Xg (3)</p>
      <p>So we can straightforwardly proceed to calculate the posterior probability p(V jEa).
For instance taking a = 3 we have six process instances in Ea, with five of them in V :
p(V jEa) = 56 = 0:83. Table 10 shows the results imposing a thresholds a for each value
in E.</p>
      <p>We find that process instances related to 3 or more “visit prior to fault time” present
high probability to violate the business rules defining the expected execs time from fault
to visit. In particular this is shaping a behavior that is potential dysfunctional, e.g. due
to a “cry wolf” effect.</p>
      <p>
        It is important to note that in this example we used “educated guesses” to decide
the set of parameters to be used for the process behavior metrics. An exhaustive search
of the right parameter set to identifying inductive metrics would be computationally
very expensive. Clearly several not exhaustive approaches are possible. Ranging from
considering the expert intuitions to game-theoretical algorithm aimed at identifying
parameter sets based on their effectiveness in the winning strategy for an attacker wishing
to fail the KPI without being caught, as explained in [
        <xref ref-type="bibr" rid="ref31">31</xref>
        ].
      </p>
    </sec>
    <sec id="sec-8">
      <title>8 Conclusion</title>
      <p>Most of the time, the literature has disregarded a notion of process behaviour that
comprehensively includes alla data related to resources auxiliary to process execution. As a
consequence, the method proposed for implementing Predictive Analytics usually are
not fully integrated with a Knowledge Acquisition procedure, for instance, without
providing concrete guidelines on how to move form one measurement step to another.</p>
      <p>In this paper we put forward the idea that the full integration of PI capabilities
requires to introduce a notion of Extended Behaviour, as the value of the information
available in processes becomes one of the most important source for Predictive
Analytics bringing to the acquisition of novel knowledge. .</p>
    </sec>
    <sec id="sec-9">
      <title>Acknowledgment</title>
      <p>This work was partly funded by the Italian Ministry of Economic Development under
the “Industria 2015” contract - KITE.IT Project.</p>
    </sec>
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