Methods for the specification and verification of business processes MPB (6 cfu, 295AA)


 Rachel Bradley
 2 years ago
 Views:
Transcription
1 Methods for the specification and verification of business processes MPB (6 cfu, 295AA) Roberto Bruni Process Mining 1
2 Object We overview the key principles of process mining 2
3 Process Mining Process mining is a relative young research discipline that sits between machine learning and data mining on the one hand and process modeling and analysis on the other hand. The idea of process mining is to discover, monitor and improve real processes (i.e., not assumed processes) by extracting knowledge from event logs readily available in today s systems. 3
4 Processes, Cases, Events, Attributes A process consists of cases. A case consists of events such that each event relates to precisely one case. Events within a case are ordered. Events can have attributes. Examples of typical attribute names are activity, time, costs, and resource. 4
5 Event Logs Let us assume that it is possible to sequentially record events such that each event: refers to an activity (i.e., a welldefined step in the process) and is related to a particular case (i.e., a process instance). 5
6 Event Log Example 1.4 Analyzing an Example Log 13 Table 1.1 A fragment of some event log: each line corresponds to an event Case id Event id Properties Timestamp Activity Resource Cost :11.02 Register request Pete :10.06 Examine thoroughly Sue :15.12 Check ticket Mike :11.18 Decide Sara :14.24 Reject request Pete :11.32 Register request Mike :12.12 Check ticket Mike :14.16 Examine casually Pete :11.22 Decide Sara :12.05 Pay compensation Ellen :14.32 Register request Pete :15.06 Examine casually Mike
7 Mining Scheme 1.3 Process Mining 9 Fig. 1.4 Positioning of the three main types of process mining: discovery, conformance, and engiovedì 13 dicembre 2012
8 Discovery A discovery technique takes an event log and produces a model without using any apriori information. If the event log contains information about resources, one can also discover resourcerelated models, e.g., a social network showing how people work together in an organization. 8
9 Conformance An existing process model is compared with an event log of the same process. Conformance checking can be used to check if reality, as recorded in the log, conforms to the model and vice versa. Conformance checking may be used to detect, locate and explain deviations, and to measure the severity of these deviations. 9
10 Enhancement The idea is to extend/improve an existing process model using information about the actual process recorded in some event log. Whereas conformance checking measures the alignment between model and reality, this third type of process mining aims at changing or extending the apriori model. 10
11 Enhancement: Repair One type of enhancement is repair, i.e., modifying the model to better reflect reality. For example, if two activities are modeled sequentially but in reality can happen in any order, then the model may be corrected to reflect this. 11
12 Four Perspectives 12
13 ControlFlow Perspective The controlflow perspective focuses on the controlflow, i.e., the ordering of activities. The goal of mining this perspective is to find a good characterization of all possible paths, e.g., expressed in terms of a Petri net or some other notation (e.g., EPC, BPMN, and UML AD). We shall focus on this perspective 13
14 Organizational Perspective The organizational perspective focuses on information about resources hidden in the log, i.e., which actors (e.g., people, systems, roles, and departments) are involved and how are they related. The goal is to either structure the organization by classifying people in terms of roles and organizational units or to show the social network. 14
15 Case Perspective The case perspective focuses on properties of cases. Obviously, a case can be characterized by its path in the process or by the originators working on it. However, cases can also be characterized by the values of the corresponding data elements. For example, if a case represents a replenishment order, it may be interesting to know the supplier or the number of products ordered. 15
16 Time Perspective The time perspective is concerned with the timing and frequency of events (performance checking). When events bear timestamps it is possible to discover bottlenecks, measure service levels, monitor the utilization of resources, and predict the remaining processing time of running cases. 16
17 Playin, Playout, Replay 17
18 Playin 1.5 Playin, Playout, and Replay 19 18
19 1.5 Playin, Playout, and Replay 19 Playout 19
20 Replay Fig. 1.8 Three ways of relating event logs (or other sources of information containing example behavior) and process models: Playin, Playout, and Replay than 56 cigarettes tend to die young ) and association rules ( people that buy diapers also buy beer ). Unfortunately, it is not possible to use conventional data mining techniques to Playin process models. 20 Only recently, process mining tech niques have become readily available to discover process models based on event
21 An Example 21
22 Event Log Example 1.4 Analyzing an Example Log 13 Table 1.1 A fragment of some event log: each line corresponds to an event Case id Event id Properties Timestamp Activity Resource Cost :11.02 Register request Pete :10.06 Examine thoroughly Sue :15.12 Check ticket Mike :11.18 Decide Sara :14.24 Reject request Pete :11.32 Register request Mike :12.12 Check ticket Mike :14.16 Examine casually Pete :11.22 Decide Sara :12.05 Pay compensation Ellen :14.32 Register request Pete :15.06 Examine casually Mike
23 Table 1.1 A fragment of some event log: each line corresponds to an event Case id Event id Properties Timestamp Activity Resource Cost :11.02 Register request Pete Event Log Example Table 1.1 (Continued) :14.16 Examine casually Pete :10.45 Pay compensation Ellen :15.02 Register request Pete :12.06 Check ticket Mike :14.43 Examine thoroughly Sean :12.02 Decide Sara :15.44 Reject request Ellen :09.02 Register request Ellen :10.16 Examine casually Mike :11.22 Check ticket Pete :13.28 Decide Sara :16.18 Reinitiate request Sara :14.33 Check ticket Ellen :15.50 Examine casually Mike :11.18 Decide Sara :12.48 Reinitiate request Sara :09.06 Examine casually Sue :11.34 Check ticket Pete :13.12 Decide Sara :14.56 Reject request Mike Table 1.1 (Continued) Case id Event id Properties :15.02 R :16.06 E Timestamp Activity Resource Cost :16.22 C 14 1 Introduction :16.52 D :15.02 Register request Mike :10.06 Examine thoroughly Sue :16.06 Examine casually Ellen :15.12 Check ticket Mike :16.22 Check ticket Mike :11.18 Decide Sara :16.52 Decide Sara :14.24 Reject request Pete Case id Event id Properties :11.47 Pay compensation Mike :11.32 Register request Mike :12.12 Check ticket Mike 100 Timestamp... Activity Resource Cost :11.47 P :11.22 Decide Sara :15.02 Table 1.2 A more compact :12.05 Pay compensation Ellen Table Register representation of log shown Case 1.2request id A more compact MikeTrace :14.32 Register request Pete in Table 1.1: a = register representation of log shown Case id :16.06 Examine casually Ellen request, b = examine 1 a, b, d, e, h :15.06 Examine casually Mike thoroughly, c = examine in Table 1.1: a = register :16.34 Check ticket Ellen : Check2 ticket Mike a, d, c, e, g casually, d = check ticket, request, :09.18 Decide Sara b = examine 1 a, c, d, e, f, b, d, e, g :16.52 e = decide, f = reinitiate :12.18 Reinitiate request Sara request, g = pay thoroughly, Decide4 c = examine Sara a, d, b, e, 2h :13.06 Examine thoroughly Sean : compensation, and h = casually, Pay rejectcompensation 5 d = check ticket, Mike a, c, d, e, f, d, 200 c, e, f, c, d, e,... h request :11.43 Check ticket Pete a, c, d, e, 3g e = decide, f = reinitiate :09.55 Decide Sara request, g = pay compensation, and h = reject 5 request Table 1.2 A more compact representation of log shown in Table 1.1: a = register request, b = examine thoroughly, c = examine casually, d = check ticket, e = decide, f = reinitiate request, g = pay compensation, and h = reject request Case id Trace 1 a, b, d, e, h 2 a, d, c, e, g Fig. 1.5 The process model discovered by the αalgorithm [103] based on the set of traces { a, b, d, e, h, a, d, c, e, g, a, c, d, e, f, b, d, e, g, a, d, b, e, h, a, c, d, e, f, d, c, e, f, c, d, e, h, a, c, d, e, g } After executing h, the case ends in the desired final marking with just a token in place end. Similarly, it can be checked that the other five traces shown in Table a, c, d, e, f, b, d, e, g 4 a, d, b, e, h 5 a, c, d, e, f, d, c, e, f, c, d, e, h 6 a, c, d, e, g......
24 e = decide, f = reinitiate request, g = pay compensation, and h = reject request 4 a, d, b, e, h 5 a, c, d, e, f, d, c, e, f, c, d, e, h 14 6 a, c, d, e, g 1 Introduction Discovery Example Table 1.1 (Continued) Case id Event id Properties Timestamp Activity Resource Cost :15.02 Register request Mike :16.06 Examine casually Ellen :16.22 Check ticket Mike :16.52 Decide Sara :11.47 Pay compensation Mike Table 1.2 A more compact Fig. 1.5 The process model discovered representation by theofαalgorithm log shown [103] Case based id on the set of traces Trace { a, b, d, e, h, a, d, c, e, g, a, inc, Table d, e, f, 1.1: b, d, a e, = g, register a, d, b, e, h, a, c, d, e, f, d, c, e, f, c, d, e, h, a, c, d, e, g } request, b = examine 1 a, b, d, e, h thoroughly, c = examine 2 a, d, c, e, g casually, d = check ticket, After executing h, the case ends in the desired final marking 3 with just a token in a, c, d, e, f, b, d, e, g e = decide, f = reinitiate place end. Similarly, it can request, be checked g = that pay the other five traces 4 shown in Table 1.2 a, d, b, e, h are also possible in the model compensation, and that alland of these h = reject traces result 5 in the marking with a, c, d, e, f, d, c, e, f, c, d, e, h just a token in place end. request 6 a, c, d, e, g
25 e = decide, f = reinitiate request, g = pay compensation, and h = reject request 4 a, d, b, e, h 5 a, c, d, e, f, d, c, e, f, c, d, e, h 14 6 a, c, d, e, g 1 Introduction Discovery Example Table 1.1 (Continued) Case id Event id Properties Timestamp Activity Resource Cost :15.02 Register request Mike :16.06 Examine casually Ellen :16.22 Check ticket Mike :16.52 Decide Sara :11.47 Pay compensation Mike Table 1.2 A more compact All cases start Fig. 1.5 The process model discovered representation with by theofαalgorithm log a shown [103] Case based id on the set of traces Trace { a, b, d, e, h, a, d, c, e, g, a, inc, Table d, e, f, 1.1: b, d, a e, = g, register a, d, b, e, h, a, c, d, e, f, d, c, e, f, c, d, e, and h, a, c, end d, e, g } with either g or h. request, b = examine 1 a, b, d, e, h thoroughly, c = examine 2 a, d, c, e, g casually, d = check ticket, After executing h, the case ends in the desired final marking 3 with just a token in a, c, d, e, f, b, d, e, g e = decide, f = reinitiate place end. Similarly, it can request, be checked g = that pay the other five traces 4 shown in Table 1.2 a, d, b, e, h are also one possible of inthe model examination compensation, and that alland of these h = reject traces result 5 in the marking with a, c, d, e, f, d, c, e, f, c, d, e, h just a token in place end. request activities (b or c). 6 a, c, d, e, g Every e is preceded by d and
26 e = decide, f = reinitiate request, g = pay compensation, and h = reject request 4 a, d, b, e, h 5 a, c, d, e, f, d, c, e, f, c, d, e, h 14 6 a, c, d, e, g 1 Introduction Discovery Example Table 1.1 (Continued) Case id Event id Properties Timestamp Activity Resource Cost :15.02 Register request Mike :16.06 Examine casually Ellen :16.22 Check ticket Mike :16.52 Decide Sara :11.47 Pay compensation Mike Table 1.2 A more compact Moreover, e Fig. 1.5 The process model discovered representation followed by theofαalgorithm log shown [103] Case based id on the set of traces Trace { a, b, d, e, h, a, d, c, e, g, a, inc, Table d, e, f, 1.1: b, d, a e, = g, register a, d, b, e, h, a, c, d, e, f, d, c, e, f, c, d, e, h, a, c, d, e, by g } f, g, or h. request, b = examine 1 a, b, d, e, h thoroughly, c = examine 2 a, d, c, e, g casually, d = check ticket, After executing h, the case ends in the desired final marking 3 with just a token in a, c, d, e, f, b, d, e, g The repeated e = execution decide, f = reinitiate place end. Similarly, it can request, be checked g = that pay the other five traces 4 shown in Table 1.2 a, d, b, e, h are of also b possible or c, ind, the model and compensation, and e that suggests alland of these h = reject traces result 5 in the marking with a, c, d, e, f, d, c, e, f, c, d, e, h just a token in place end. request the presence of a loop. 6 a, c, d, e, g
27 e = decide, f = reinitiate request, g = pay compensation, and h = reject request 4 a, d, b, e, h 5 a, c, d, e, f, d, c, e, f, c, d, e, h 14 6 a, c, d, e, g 1 Introduction Discovery Example Table 1.1 (Continued) Case id Event id Properties Timestamp Activity Resource Cost :15.02 Register request Mike :16.06 Examine casually Ellen :16.22 Check ticket Mike :16.52 Decide Sara :11.47 Pay compensation Mike Table 1.2 A more compact These characteristics Fig. 1.5 process model discovered representation by theofαalgorithm logare shown [103] Case based id on the set of traces Trace { a, b, d, e, h, a, d, c, e, g, a, inc, Table d, e, f, 1.1: b, d, a e, = g, register a, d, b, e, h, a, c, d, e, f, d, c, e, f, c, d, e, h, a, c, d, e, g } request, b = examine 1 a, b, d, e, h thoroughly, c = examine 2 a, d, c, e, g casually, d = check ticket, After executing h, the case ends in the desired final marking 3 with just a token in a, c, d, e, f, b, d, e, g e = decide, f = reinitiate place end. Similarly, it can request, be checked g = that pay the other five traces 4 shown in Table 1.2 a, d, b, e, h are also possible in the model compensation, and that alland of these h = reject traces result 5 in the marking with a, c, d, e, f, d, c, e, f, c, d, e, h just a token in place end. request be a good balance between 6 a, c, d, e, g dequately captured by the net. When comparing the event log and the model, there seems to overfitting and underfitting.
28 Overfitting and Underfitting One of the challenges of process mining is to balance between overfitting (the model is too specific and only allows for the accidental behavior observed) and underfitting (the model is too general and allows for behavior unrelated to the behavior observed). 28
29 Discussion The Petri net shown also allows for traces not in the log. For example, other possible traces are <a, d, c, e, f, b, d, e, g> and <a, c, d, e, f, c, d, e, f, c, d, e, f, c, d, e, f, b, d, e, g> This is a desired phenomenon as the goal is not to represent just the particular set of example traces in the event log. Process mining algorithms need to generalize the behavior contained in the log to show the most likely underlying model that is not invalidated by the next set of observations 29
30 Mining Other Models We used Petri nets to represent the discovered process models, because Petri nets are a succinct way of representing processes and have unambiguous but intuitive semantics. However, some mining techniques are independent of the 1.2 Limitations of Modeling 5 desired representation. Fig. 1.2 The same process modeled in terms of BPMN 30
31 Another Discovery 14 1 Introduction Table 1.1 (Continued) Example Case id Event id Properties 1.4 Analyzing an Example Log 15 Timestamp Activity Resource Cost :15.02 Register request Mike :16.06 Examine casually Ellen :16.22 Check ticket Mike :16.52 Decide Sara :11.47 Pay compensation Mike Table 1.2 A more compact Fig. 1.6 The process model representation discovered byofthe logαalgorithm shown Case based id on Cases 1 and 4, i.e., Trace the set of traces { a, b, d, e, h, a, d, b, ine, Table h } 1.1: a = register request, b = examine 1 a, b, d, e, h thoroughly, c = examine 2 a, d, c, e, g The Petri net shown incasually, Fig. 1.5 d = also check allows ticket, for traces 3 not present in Table a, 1.2. c, d, For e, f, b, d, e, g e = decide, f = reinitiate example, the traces a, d, request, c, e, f, g = b, pay d, e, g and a, 4 c, d, e, f, c, d, e, f, c, a, d, d, e, b, f, e, c, h d, e, f, b, d, e, g are also compensation, possible. and This h = is reject a desired 5 phenomenon as the a, c, goal d, e, is f, d, c, e, f, c, d, e, h not to represent just the request particular set of example 6 traces in the event log. a, Process c, d, e, g mining algorithms need to generalize the behavior... contained in the log to. show.. the most likely underlying model that is not invalidated by the next set of observations. 31 One of the challenges of process mining is to balance between overfitting (the
32 14 1 Introduction Table 1.1 (Continued) Case id Event id Properties Conformance Example Timestamp Activity Resource Cost :15.02 Register request Mike :16.06 Examine casually Ellen :16.22 Check ticket Mike :16.52 Decide Sara :11.47 Pay compensation Mike Analyzing an Example Log Table 1.2 A more compact representation of log shown Case id Trace in Table 1.1: a = register request, b = examine 1 a, b, d, e, h thoroughly, c = examine 2 a, d, c, e, g casually, d = check ticket, Table 1.3 Another event log: 3 a, c, d, e, f, b, d, e, g e = decide, f = reinitiate request, g = pay 4 Cases 7, 8, and a, 10 d, b, are e, h not compensation, Fig. 1.6 The process and h = model rejectdiscovered 5 possible by the αalgorithm according based a, onc, Cases d, to e, f, 1Fig. and d, c, 4, e, i.e., 1.5 f, c, the d, set e, h of request traces { a, b, d, e, h, a, d, b, e, 6 h } a, c, d, e, g 16 1 Introduction The Petri net shown in Fig. 1.5 also allows for traces not present in Table 1.2. For example, the traces a, d, c, e, f, b, d, e, g and a, c, d, e, f, c, d, e, f, c, d, e, f, c, d, e, f, b, d, e, g are also possible. This is a desired phenomenon as the goal is not to represent just the particular set of example traces in the event log. Process mining algorithms need to generalize the behavior contained in the log to show the most likely underlying model that is not invalidated by the next set of observations. One of the challenges of process mining is to balance between overfitting (the model is too specific and only allows for the accidental behavior observed) and underfitting (the model is too general and allows for behavior unrelated to the behavior observed). When comparing the event log and the model, there seems to be a good balance between overfitting and underfitting. All cases start with a and end with either g or h. Every e is preceded by d and one of the examination activities (b or c). Moreover, e is followed by f, g, or h. The repeated execution of b or c, d, and e suggests the presence of a loop. These characteristics are adequately captured by Fig. 1.5 The process model discovered by the αalgorithm [103] based on the set of traces the net of Fig { a, b, d, e, h, a, d, c, e, g, a, c, d, e, f, b, d, e, g, a, d, b, e, h, a, c, d, e, f, d, c, e, f, c, d, e, h, Let a, usc, now d, e, g } consider an event log consisting of only two traces a, b, d, e, h and a, d, b, e, h, i.e., Cases 1 and 4 of the original log. For this log, the αalgorithm constructs the Petri net shown in Fig This model only allows for two traces After and these executing are exactly h, the the case ones ends in the in the small desired eventfinal log. bmarking and d are with modeled just a token as being Case id 32 Trace 1 a, b, d, e, h 2 a, d, c, e, g 3 a, c, d, e, f, b, d, e, g 4 a, d, b, e, h 5 a, c, d, e, f, d, c, e, f, c, d, e, h 6 a, c, d, e, g 7 a, b, e, g 8 a, b, d, e 9 a, d, c, e, f, d, c, e, f, b, d, e, h 10 a, c, d, e, f, b, d, g
33 Process Discovery: αalgorithm 33
34 Process Discovery Process discovery is the activity that combines Discovery with the Controlflow Perspective. The general problem: A process discovery algorithm is a function that maps an event log L onto a process model M such that the model M is representative for the behavior seen in the event log L. We focus on simple event logs and Petri net models (possibly sound workflow nets). 34
35 etri net that can replay event log L 1. Ideally, the Petri net is a sound WFnet efined in Sect Based on these choices, we reformulate the process discove roblem and make it more concrete. Simple Event Log efinition 5.2 (Specific process discovery problem) A process discovery algorith s a function γ that maps a log L B(A ) onto Fnet 1 discovered for L 1 =[ a, b, c, d 3 a marked Petri, a, c, b, d 2 net γ (L) = (N, M deally, N is a sound WFnet and all traces in L correspond, a, to e, possible d ] firing s uences of (N, M). Let A be a set of activities. make things more concrete, we define the target to be a Petri ne A simple trace over A is a finite sequence of activities. Function γ defines a socalled Playin technique as described in Chap. 1. Base, nwe L 1, ause process a simple discovery event algorithm log as γ could input discover (cf. Definition the WFnet shown 4.4). in AFig. simp 5..e., γ (L 1 A ) = simple (N 1, [start]). event Each log trace over ina Lis 1 corresponds a multiset to of atraces. possible firing s uence of WFnet N 1 shown in Fig Therefore, it is easy to see that the WFn an indeed replay all traces [ in the event log. In fact, each of the three L 1 = a, b, c, d 3, a, c, b, d 2 ] possible firin equences of WFnet N 1 appears in L 1., a, e, d Let us now consider another event log: multiset of traces over some set of activities A, i.e., L B(A ple log describing the history of six cases. The goal is now to di L 2 = [ a, b, c, d 3, a, c, b, d 4, a, b, c, e, f, b, c, d 2, a, b, c, e, f, c, b, d, a, c, b, e, f, b, c, d 2, a, c, b, e, f, b, c, e, f, c, b, d ] hat can replay event log L 1. Ideally, the Petri net is a sound W Sect Based on these choices, we reformulate the process d nd make it more concrete is a simple event log consisting of 13 cases represented by 6 different trace
36 Challenges 5.4 Challenges 151 Simple structure Other behaviours allowed No completely unrelated behaviour Fig Balancing the four quality dimensions: fitness, simplicity, precision, and generalization made. For example: What is the penalty if 36 a step needs to be skipped and what is the penalty if tokens remain in the WFnet after replay? Later, we will give concrete
37 Appropriateness 5.4 Challenges Fig Balancing the four quality dimensions: fitness, simplicity, precision, and gen 37 made. For example: What is the penalty if a step needs to be skipped an the penalty if tokens remain in the WFnet after replay? Later, we will giv definitions for fitness. In Sect , we defined performance measures like error, accurac fprate, precision, recall, and F1 score. Recall, also known as the tprate, the proportion of positive instances indeed classified as positive (tp/p). T in the log are positive instances. When such an instance can be replay model, then the instance is indeed classified as positive. Hence, the variou of fitness can be seen as variants of the recall measure. Most of the notion in Sect cannot be used because there are no negative examples, i.e. are unknown (see Fig. 3.14). Since the event log does not contain informa events that could not happen at a particular point in time, other notations ar The simplicity dimension refers to Occam s Razor. This principle wa discussed in Sect In the context of process discovery, this mean simplest model that can explain the behavior seen in the log, is the be The complexity of the model could be defined by the number of nodes in the underlying graph. Also more sophisticated metrics can be used, e.g that take the structuredness or entropy of the model into account. Se an empirical evaluation of the model complexity metrics defined in lite Sect , we also mentioned that this principle can be operationalized
38 αalgorithm The αalgorithm was one of the first process discovery algorithms that could adequately deal with concurrency. It has several limitations, but it provides a good introduction into the topic: The αalgorithm is simple and many of its ideas have been embedded in more complex and robust techniques. The αalgorithm scans the event log for particular patterns, called logbased ordering relations, to create a footprint of the log. 38
39 (c, d), (e, d) d # L1 L1 b L1 # L1 L1 L1 # L1 c L1 L1 # L1 L1 # L1 Logbased Ordering d # L1 L1 L1 # L1 L1 e L1 # L1 # L1 L1 # L1 Relations Definition 5.3 (Logbased ordering relations) L L B(A B(A ). Let a, ). b Let A : a, b A : Let L be an event log over A, i.e., a, a> L b, b if c, and d. onlyhowever, if there is a trace d σ = t 1,t 2,t 3,...,t n and i {1,...,n 1} such that σ L and t i = a and t i+1 = b L1 c because c never hea log. such L b if and that L1 onlyσ contains if a> L band ball t i L = pairs a a andoft i+1 activities = b in a # L b if and only if a L b and b L a a a L b if and L b if and only if a> only if a> L b and b> L a L b and b L a Consider for instance L 1 =[ a, b, c, d 3, a, c, b, d 2, a, e, d ] again. For this and a sometimes event log, the L b if and only the other if a> way following logbased ordering L b and around. b> relations can be found L b a# L1 e > L1 = { (a, b), (a, c), (a, e), (b, c), (c, b), (b, d), (c, d), (e, d) } L1 = { (a, b), (a, c), (a, e), (b, d), (c, d), (e, d) } e L1 # L1, (c, c), (c, e), (d, a), (d, d), (e, b), (e, c), (e, e) } Definition 5.3 (Logbased ordering relations) tivities in a directly follows relation. c> L1 d Let L b a> L b if and only if there is a trace σ = t 1,t 2,t 3,.. d because sometimes d directly follows c and d and a # L d b if L1 and c). only b L1 if ac because L b andb> b L1L ac and Consider for instance L 1 =[ a, b, c, d 3, a, c, b, d A : x L y, y L x, x # L y, or x L y, event log, the following logbased ordering relations ca holds 39 # L1 = { for any pair of activities. Therefore, the (a, a), (a, d), (b, b), (b, e), (c, c), (c, e), (d, a), (d, d), (e, b), (e, c), (e, e) }
40 , b A : c L1 L1 # L1 L1 # L1 e L1 # L1 # L1 L1 # L1 d # L1 L1 L1 # L1 L1 Logbased e L1 # L1 # L1 Ordering L1 # L1 nly if there is a trace σ = t 1,t 2,t 3,...,t n and i {1,..., Definition 5.3 (Logbased ordering ordering relations) relations) L Let a, b A : Land B(At i = ). Let a and a, b ta i+1 : = b Let L be an event log over A, i.e., Relations: Example a> L b if and only if there is a trace σ = t 1,t 2,t 3,...,t n and i {1,...,n 1} such that σ L and t i = a and t i+1 = b a L b if and only if a> L b and b L a a # L b if and only if a L b and b L a a L b if and only if a> L b and b> L a nly if a> L b and b L a > L1 = { (a, b), (a, c), (a, e), (b, c), (c, b), (b, d), (c, d), (e, d) } L1 = { (a, b), (a, c), (a, e), (b, d), (c, d), (e, d) } # L1 = { (a, a), (a, d), (b, b), (b, e), (c, c), (c, e), (d, a), (d, d), (e, b), (e, c), (e, e) } L1 = { (b, c), (c, b) } Relation > L1 contains all pairs of activities in a directly follows relation. c> L1 d because d directly follows c in trace a, b, c, d. However, d L1 c because c never directly follows d in any trace in the log. L1 contains all pairs of activities in a causality relation, e.g., c L1 d because sometimes d directly follows c and never the other way around (c > L1 d and d L1 c). b L1 c because b> L1 c and c> L1 b, i.e., sometimes c follows b and sometimes the other way around. b # L1 e, d), because (b, b L1 b), e and(b, e L1 b. e), (c, c), (c, e), (d, a), (d, d), (e, b), (e, c), For any log L over A and x, y A : x L y, y L x, x # L y, or x L y, 40 i.e., } precisely one of these relations holds for any pair of activities. Therefore, the footprint of a log can be captured in a matrix as shown in Table 5.1. Let L be an event log over A, i.e., a> L b if and only if there is a trace σ = t 1,t 2,t 3,...,t n and i {1,...,n 1} lysuch if athat σ L b Land t i b= a and L at i+1 = b a L b if and only if a> L b and b L a ly if a> a # Consider L b if and L b and b> for instance only Lif 1 =[ a, a L b, b L a c, d and 3, a, bc, b, L d a 2, a, e, d ] again. For this a event L log, b ifthe and following onlylogbased if a> ordering L b and relations b> can L abe found stance L 1 =[ a, b, c, d 3, a, c, b, d 2, a, e, d ] again. F Consider for instance L 1 =[ a, b, c, d 3, a, c, b, d 2, a, e, d ] again. For this event wing log, logbased the followingordering logbased ordering relations relations can canbe found > L1 = { (a, b), (a, c), (a, e), (b, c), (c, b), (b, d), (c, d), (e, d) }, c), (a, e), (b, c), (c, b), (b, d), (c, d), (e, d) } L1 = { (a, b), (a, c), (a, e), (b, d), (c, d), (e, d) }, c), (a, e), (b, d), (c, d), (e, d) } # L1 = { (a, a), (a, d), (b, b), (b, e), (c, c), (c, e), (d, a), (d, d), (e, b), (e, c), (e, e) } L1 = { (b, c), (c, b) } Relation > L1 contains all pairs of activities in a directly follows relation. c> L1 d
Methods for the specification and verification of business processes MPB (6 cfu, 295AA)
Methods for the specification and verification of business processes MPB (6 cfu, 295AA) Roberto Bruni http://www.di.unipi.it/~bruni 24  Process Mining 1 Object We overview the key principles of process
More informationChapter 5 Process Discovery: An Introduction
Chapter 5 Process Discovery: An Introduction Process discovery is one of the most challenging process mining tasks. Based on an event log, a process model is constructed thus capturing the behavior seen
More informationData Science. Research Theme: Process Mining
Data Science Research Theme: Process Mining Process mining is a relatively young research discipline that sits between computational intelligence and data mining on the one hand and process modeling and
More informationUsing Process Mining to Bridge the Gap between BI and BPM
Using Process Mining to Bridge the Gap between BI and BPM Wil van der alst Eindhoven University of Technology, The Netherlands Process mining techniques enable processcentric analytics through automated
More informationChapter 1 Introduction
Chapter 1 Introduction prof.dr.ir. Wil van der Aalst www.processmining.org Overview Chapter 1 Introduction Part I: Preliminaries Chapter 2 Process Modeling and Analysis Chapter 3 Data Mining Part II: From
More informationSummary and Outlook. Business Process Intelligence Course Lecture 8. prof.dr.ir. Wil van der Aalst. www.processmining.org
Business Process Intelligence Course Lecture 8 Summary and Outlook prof.dr.ir. Wil van der Aalst www.processmining.org Overview Chapter 1 Introduction Part I: Preliminaries Chapter 2 Process Modeling and
More informationProcess Mining. ^J Springer. Discovery, Conformance and Enhancement of Business Processes. Wil M.R van der Aalst Q UNIVERS1TAT.
Wil M.R van der Aalst Process Mining Discovery, Conformance and Enhancement of Business Processes Q UNIVERS1TAT m LIECHTENSTEIN Bibliothek ^J Springer Contents 1 Introduction I 1.1 Data Explosion I 1.2
More informationProcess Mining: Making Knowledge Discovery Process Centric
Process Mining: Making Knowledge Discovery Process Centric Wil van der alst Department of Mathematics and Computer Science Eindhoven University of Technology PO Box 513, 5600 MB, Eindhoven, The Netherlands
More informationMaster Thesis September 2010 ALGORITHMS FOR PROCESS CONFORMANCE AND PROCESS REFINEMENT
Master in Computing Llenguatges i Sistemes Informàtics Master Thesis September 2010 ALGORITHMS FOR PROCESS CONFORMANCE AND PROCESS REFINEMENT Student: Advisor/Director: Jorge MuñozGama Josep Carmona Vargas
More informationImplementing Heuristic Miner for Different Types of Event Logs
Implementing Heuristic Miner for Different Types of Event Logs Angelina Prima Kurniati 1, GunturPrabawa Kusuma 2, GedeAgungAry Wisudiawan 3 1,3 School of Compuing, Telkom University, Indonesia. 2 School
More informationProcess Modelling from Insurance Event Log
Process Modelling from Insurance Event Log P.V. Kumaraguru Research scholar, Dr.M.G.R Educational and Research Institute University Chennai 600 095 India Dr. S.P. Rajagopalan Professor Emeritus, Dr. M.G.R
More informationProcess Mining and Visual Analytics: Breathing Life into Business Process Models
Process Mining and Visual Analytics: Breathing Life into Business Process Models Wil M.P. van der Aalst 1, Massimiliano de Leoni 1, and Arthur H.M. ter Hofstede 1,2 1 Eindhoven University of Technology,
More informationLluis Belanche + Alfredo Vellido. Intelligent Data Analysis and Data Mining. Data Analysis and Knowledge Discovery
Lluis Belanche + Alfredo Vellido Intelligent Data Analysis and Data Mining or Data Analysis and Knowledge Discovery a.k.a. Data Mining II An insider s view Geoff Holmes: WEKA founder Process Mining
More informationDiscovering process models from empirical data
Discovering process models from empirical data Laura Măruşter (l.maruster@tm.tue.nl), Ton Weijters (a.j.m.m.weijters@tm.tue.nl) and Wil van der Aalst (w.m.p.aalst@tm.tue.nl) Eindhoven University of Technology,
More informationProcess Mining Data Science in Action
Process Mining Data Science in Action Wil van der Aalst Scientific director of the DSC/e Dutch Data Science Summit, Eindhoven, 452014. Process Mining Data Science in Action https://www.coursera.org/course/procmin
More informationProM 6 Exercises. J.C.A.M. (Joos) Buijs and J.J.C.L. (Jan) Vogelaar {j.c.a.m.buijs,j.j.c.l.vogelaar}@tue.nl. August 2010
ProM 6 Exercises J.C.A.M. (Joos) Buijs and J.J.C.L. (Jan) Vogelaar {j.c.a.m.buijs,j.j.c.l.vogelaar}@tue.nl August 2010 The exercises provided in this section are meant to become more familiar with ProM
More informationUsing Trace Clustering for Configurable Process Discovery Explained by Event Log Data
Master of Business Information Systems, Department of Mathematics and Computer Science Using Trace Clustering for Configurable Process Discovery Explained by Event Log Data Master Thesis Author: ing. Y.P.J.M.
More informationProcess Mining Using BPMN: Relating Event Logs and Process Models
Noname manuscript No. (will be inserted by the editor) Process Mining Using BPMN: Relating Event Logs and Process Models Anna A. Kalenkova W. M. P. van der Aalst Irina A. Lomazova Vladimir A. Rubin Received:
More informationBusiness Intelligence and Process Modelling
Business Intelligence and Process Modelling F.W. Takes Universiteit Leiden Lecture 7: Network Analytics & Process Modelling Introduction BIPM Lecture 7: Network Analytics & Process Modelling Introduction
More informationCategorical Data Visualization and Clustering Using Subjective Factors
Categorical Data Visualization and Clustering Using Subjective Factors ChiaHui Chang and ZhiKai Ding Department of Computer Science and Information Engineering, National Central University, ChungLi,
More informationCHAPTER 1 INTRODUCTION
CHAPTER 1 INTRODUCTION 1.1 Research Motivation In today s modern digital environment with or without our notice we are leaving our digital footprints in various data repositories through our daily activities,
More informationProcess Mining. Data science in action
Process Mining. Data science in action Julia Rudnitckaia Brno, University of Technology, Faculty of Information Technology, irudnickaia@fit.vutbr.cz 1 Abstract. At last decades people have to accumulate
More informationConstructing Probabilistic Process Models based on Hidden Markov Models for Resource Allocation
Constructing Probabilistic Process Models based on Hidden Markov Models for Resource Allocation Berny Carrera and JaeYoon Jung Dept. of Industrial and Management Systems Engineering, Kyung Hee University
More informationMining Process Models with NonFreeChoice Constructs
Mining Process Models with NonFreehoice onstructs Lijie Wen 1, Wil M.P. van der alst 2, Jianmin Wang 1, and Jiaguang Sun 1 1 School of Software, Tsinghua University, 100084, eijing, hina wenlj00@mails.tsinghua.edu.cn,{jimwang,sunjg}@tsinghua.edu.cn
More informationBusiness Process Modeling
Business Process Concepts Process Mining Kelly Rosa Braghetto Instituto de Matemática e Estatística Universidade de São Paulo kellyrb@ime.usp.br January 30, 2009 1 / 41 Business Process Concepts Process
More informationProcess Mining: A TwoStep Approach using Transition Systems and Regions
Process Mining: TwoStep pproach using Transition Systems and Regions Wil M.P. van der alst 1, V. Rubin 2,1,.F. van ongen 1,. Kindler 2, and.w. Günther 1 1 indhoven University of Technology, indhoven,
More informationProM Framework Tutorial
ProM Framework Tutorial Authors: Ana Karla Alves de Medeiros (a.k.medeiros@.tue.nl) A.J.M.M. (Ton) Weijters (a.j.m.m.weijters@tue.nl) Technische Universiteit Eindhoven Eindhoven, The Netherlands February
More informationAnalysis of Service Level Agreements using Process Mining techniques
Analysis of Service Level Agreements using Process Mining techniques CHRISTIAN MAGER University of Applied Sciences WuerzburgSchweinfurt Process Mining offers powerful methods to extract knowledge from
More informationInformation Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay
Information Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay Lecture  17 ShannonFanoElias Coding and Introduction to Arithmetic Coding
More informationBusiness Process Quality Metrics: Logbased Complexity of Workflow Patterns
Business Process Quality Metrics: Logbased Complexity of Workflow Patterns Jorge Cardoso Department of Mathematics and Engineering, University of Madeira, Funchal, Portugal jcardoso@uma.pt Abstract. We
More informationBIS 3106: Business Process Management. Lecture Two: Modelling the Controlflow Perspective
BIS 3106: Business Process Management Lecture Two: Modelling the Controlflow Perspective Makerere University School of Computing and Informatics Technology Department of Computer Science SEM I 2015/2016
More informationGenetic Process Mining: An Experimental Evaluation
Genetic Process Mining: An Experimental Evaluation A.K. Alves de Medeiros, A.J.M.M. Weijters and W.M.P. van der Aalst Department of Technology Management, Eindhoven University of Technology P.O. Box 513,
More informationCompact Representations and Approximations for Compuation in Games
Compact Representations and Approximations for Compuation in Games Kevin Swersky April 23, 2008 Abstract Compact representations have recently been developed as a way of both encoding the strategic interactions
More informationData Extraction Guide
1 Data Extraction Guide One of the big advantages of process mining is that it starts with the data that is already there, and usually it starts very simple. There is no need to first set up a data collection
More informationCost Model: Work, Span and Parallelism. 1 The RAM model for sequential computation:
CSE341T 08/31/2015 Lecture 3 Cost Model: Work, Span and Parallelism In this lecture, we will look at how one analyze a parallel program written using Cilk Plus. When we analyze the cost of an algorithm
More informationService Discovery from Observed Behavior While Guaranteeing Deadlock Freedom in Collaborations
Service Discovery from Observed Behavior While Guaranteeing Deadlock Freedom in Collaborations Richard Müller 1,2, Christian Stahl 2, Wil M.P. van der Aalst 2,3, and Michael Westergaard 2,3 1 Institut
More informationA Capability Model for Business Analytics: Part 2 Assessing Analytic Capabilities
A Capability Model for Business Analytics: Part 2 Assessing Analytic Capabilities The first article of this series presented the capability model for business analytics that is illustrated in Figure One.
More informationEnhanced data mining analysis in higher educational system using rough set theory
African Journal of Mathematics and Computer Science Research Vol. 2(9), pp. 184188, October, 2009 Available online at http://www.academicjournals.org/ajmcsr ISSN 20069731 2009 Academic Journals Review
More informationProcess Mining and Fraud Detection
Process Mining and Fraud Detection A case study on the theoretical and practical value of using process mining for the detection of fraudulent behavior in the procurement process Masters of Science Thesis
More informationWHAT ARE MATHEMATICAL PROOFS AND WHY THEY ARE IMPORTANT?
WHAT ARE MATHEMATICAL PROOFS AND WHY THEY ARE IMPORTANT? introduction Many students seem to have trouble with the notion of a mathematical proof. People that come to a course like Math 216, who certainly
More informationChapter 4 Getting the Data
Chapter 4 Getting the Data prof.dr.ir. Wil van der Aalst www.processmining.org Overview Chapter 1 Introduction Part I: Preliminaries Chapter 2 Process Modeling and Analysis Chapter 3 Data Mining Part II:
More informationModel Discovery from Motor Claim Process Using Process Mining Technique
International Journal of Scientific and Research Publications, Volume 3, Issue 1, January 2013 1 Model Discovery from Motor Claim Process Using Process Mining Technique P.V.Kumaraguru *, Dr.S.P.Rajagopalan
More informationMathematics for Computer Science/Software Engineering. Notes for the course MSM1F3 Dr. R. A. Wilson
Mathematics for Computer Science/Software Engineering Notes for the course MSM1F3 Dr. R. A. Wilson October 1996 Chapter 1 Logic Lecture no. 1. We introduce the concept of a proposition, which is a statement
More informationDecember 4, 2013 MATH 171 BASIC LINEAR ALGEBRA B. KITCHENS
December 4, 2013 MATH 171 BASIC LINEAR ALGEBRA B KITCHENS The equation 1 Lines in twodimensional space (1) 2x y = 3 describes a line in twodimensional space The coefficients of x and y in the equation
More information9.2 Summation Notation
9. Summation Notation 66 9. Summation Notation In the previous section, we introduced sequences and now we shall present notation and theorems concerning the sum of terms of a sequence. We begin with a
More informationBUsiness process mining, or process mining in a short
, July 24, 2014, London, U.K. A Process Mining Approach in Software Development and Testing Process: A Case Study Rabia Saylam, Ozgur Koray Sahingoz Abstract Process mining is a relatively new and emerging
More informationMining Configurable Process Models from Collections of Event Logs
Mining Configurable Models from Collections of Event Logs J.C.A.M. Buijs, B.F. van Dongen, and W.M.P. van der Aalst Eindhoven University of Technology, The Netherlands {j.c.a.m.buijs,b.f.v.dongen,w.m.p.v.d.aalst}@tue.nl
More informationThe Goldberg Rao Algorithm for the Maximum Flow Problem
The Goldberg Rao Algorithm for the Maximum Flow Problem COS 528 class notes October 18, 2006 Scribe: Dávid Papp Main idea: use of the blocking flow paradigm to achieve essentially O(min{m 2/3, n 1/2 }
More informationTowards Comprehensive Support for Organizational Mining
Towards Comprehensive Support for Organizational Mining Minseok Song and Wil M.P. van der Aalst Eindhoven University of Technology P.O.Box 513, NL5600 MB, Eindhoven, The Netherlands. {m.s.song, w.m.p.v.d.aalst}@tue.nl
More informationMethods for the specification and verification of business processes MPB (6 cfu, 295AA)
Methods for the specification and verification of business processes MPB (6 cfu, 295AA) Roberto Bruni http://www.di.unipi.it/~bruni 19  Eventdriven process chains 1 Object We overview EPC and the main
More informationRuntime Verification  Monitororiented Programming  Monitorbased Runtime Reflection
Runtime Verification  Monitororiented Programming  Monitorbased Runtime Reflection Martin Leucker Technische Universität München (joint work with Andreas Bauer, Christian Schallhart et. al) FLACOS
More informationNotes on Complexity Theory Last updated: August, 2011. Lecture 1
Notes on Complexity Theory Last updated: August, 2011 Jonathan Katz Lecture 1 1 Turing Machines I assume that most students have encountered Turing machines before. (Students who have not may want to look
More informationFormal Languages and Automata Theory  Regular Expressions and Finite Automata 
Formal Languages and Automata Theory  Regular Expressions and Finite Automata  Samarjit Chakraborty Computer Engineering and Networks Laboratory Swiss Federal Institute of Technology (ETH) Zürich March
More informationDotted Chart and ControlFlow Analysis for a Loan Application Process
Dotted Chart and ControlFlow Analysis for a Loan Application Process Thomas Molka 1,2, Wasif Gilani 1 and XiaoJun Zeng 2 Business Intelligence Practice, SAP Research, Belfast, UK The University of Manchester,
More informationOPRE 6201 : 2. Simplex Method
OPRE 6201 : 2. Simplex Method 1 The Graphical Method: An Example Consider the following linear program: Max 4x 1 +3x 2 Subject to: 2x 1 +3x 2 6 (1) 3x 1 +2x 2 3 (2) 2x 2 5 (3) 2x 1 +x 2 4 (4) x 1, x 2
More informationDATA ANALYSIS II. Matrix Algorithms
DATA ANALYSIS II Matrix Algorithms Similarity Matrix Given a dataset D = {x i }, i=1,..,n consisting of n points in R d, let A denote the n n symmetric similarity matrix between the points, given as where
More informationProtein Protein Interaction Networks
Functional Pattern Mining from Genome Scale Protein Protein Interaction Networks YoungRae Cho, Ph.D. Assistant Professor Department of Computer Science Baylor University it My Definition of Bioinformatics
More informationBusiness process measurement  data mining. enn@cc.ttu.ee
Business process measurement  data mining. enn@cc.ttu.ee Business process measurement Balanced scorecard Process mining  ProM Äriprotsessi konteksti perspektiiv Clear & measurable goals Effective solutions
More informationMeasuring the Performance of an Agent
25 Measuring the Performance of an Agent The rational agent that we are aiming at should be successful in the task it is performing To assess the success we need to have a performance measure What is rational
More informationTowards CrossOrganizational Process Mining in Collections of Process Models and their Executions
Towards CrossOrganizational Process Mining in Collections of Process Models and their Executions J.C.A.M. Buijs, B.F. van Dongen, W.M.P. van der Aalst Department of Mathematics and Computer Science, Eindhoven
More informationPragmatic guidelines for Business Process Modeling
Pragmatic guidelines for Business Process Modeling MorenoMontes de Oca I, Snoeck M. KBI_1509 Pragmatic guidelines for Business Process Modeling Technical Report Isel MorenoMontes de Oca Department of
More informationKnowledge Discovery and Data Mining. Structured vs. NonStructured Data
Knowledge Discovery and Data Mining Unit # 2 1 Structured vs. NonStructured Data Most business databases contain structured data consisting of welldefined fields with numeric or alphanumeric values.
More informationGlobally Optimal Crowdsourcing Quality Management
Globally Optimal Crowdsourcing Quality Management Akash Das Sarma Stanford University akashds@stanford.edu Aditya G. Parameswaran University of Illinois (UIUC) adityagp@illinois.edu Jennifer Widom Stanford
More informationLoad Balancing and Switch Scheduling
EE384Y Project Final Report Load Balancing and Switch Scheduling Xiangheng Liu Department of Electrical Engineering Stanford University, Stanford CA 94305 Email: liuxh@systems.stanford.edu Abstract Load
More information2) Write in detail the issues in the design of code generator.
COMPUTER SCIENCE AND ENGINEERING VI SEM CSE Principles of Compiler Design UnitIV Question and answers UNIT IV CODE GENERATION 9 Issues in the design of code generator The target machine Runtime Storage
More informationProcess Mining The influence of big data (and the internet of things) on the supply chain
September 16, 2015 Process Mining The influence of big data (and the internet of things) on the supply chain Wil van der Aalst www.vdaalst.com @wvdaalst www.processmining.org http://www.engineersjournal.ie/factoryofthefuturewillseemergingofvirtualandrealworlds/
More informationMATH10212 Linear Algebra. Systems of Linear Equations. Definition. An ndimensional vector is a row or a column of n numbers (or letters): a 1.
MATH10212 Linear Algebra Textbook: D. Poole, Linear Algebra: A Modern Introduction. Thompson, 2006. ISBN 0534405967. Systems of Linear Equations Definition. An ndimensional vector is a row or a column
More informationDecision Mining in Business Processes
Decision Mining in Business Processes A. Rozinat and W.M.P. van der Aalst Department of Technology Management, Eindhoven University of Technology P.O. Box 513, NL5600 MB, Eindhoven, The Netherlands {a.rozinat,w.m.p.v.d.aalst}@tm.tue.nl
More informationRow Ideals and Fibers of Morphisms
Michigan Math. J. 57 (2008) Row Ideals and Fibers of Morphisms David Eisenbud & Bernd Ulrich Affectionately dedicated to Mel Hochster, who has been an inspiration to us for many years, on the occasion
More informationChapter 6. The stacking ensemble approach
82 This chapter proposes the stacking ensemble approach for combining different data mining classifiers to get better performance. Other combination techniques like voting, bagging etc are also described
More informationContinued Fractions and the Euclidean Algorithm
Continued Fractions and the Euclidean Algorithm Lecture notes prepared for MATH 326, Spring 997 Department of Mathematics and Statistics University at Albany William F Hammond Table of Contents Introduction
More informationnot possible or was possible at a high cost for collecting the data.
Data Mining and Knowledge Discovery Generating knowledge from data Knowledge Discovery Data Mining White Paper Organizations collect a vast amount of data in the process of carrying out their daytoday
More informationCSE8393 Introduction to Bioinformatics Lecture 3: More problems, Global Alignment. DNA sequencing
SE8393 Introduction to Bioinformatics Lecture 3: More problems, Global lignment DN sequencing Recall that in biological experiments only relatively short segments of the DN can be investigated. To investigate
More informationUNIT 2 MATRICES  I 2.0 INTRODUCTION. Structure
UNIT 2 MATRICES  I Matrices  I Structure 2.0 Introduction 2.1 Objectives 2.2 Matrices 2.3 Operation on Matrices 2.4 Invertible Matrices 2.5 Systems of Linear Equations 2.6 Answers to Check Your Progress
More informationIntroduction. A. Bellaachia Page: 1
Introduction 1. Objectives... 3 2. What is Data Mining?... 4 3. Knowledge Discovery Process... 5 4. KD Process Example... 7 5. Typical Data Mining Architecture... 8 6. Database vs. Data Mining... 9 7.
More informationData quality in Accounting Information Systems
Data quality in Accounting Information Systems Comparing Several Data Mining Techniques Erjon Zoto Department of Statistics and Applied Informatics Faculty of Economy, University of Tirana Tirana, Albania
More informationRegular Languages and Finite Automata
Regular Languages and Finite Automata 1 Introduction Hing Leung Department of Computer Science New Mexico State University Sep 16, 2010 In 1943, McCulloch and Pitts [4] published a pioneering work on a
More informationBRIDGING THE GAP BETWEEN BUSINESS MODELS AND WORKFLOW SPECIFICATIONS
International Journal of Cooperative Information Systems c World Scientific Publishing Company BRIDGING THE GAP BETWEEN BUSINESS MODELS WORKFLOW SPECIFICATIONS JULIANE DEHNERT Fraunhofer ISST, Mollstr.
More informationMINITAB ASSISTANT WHITE PAPER
MINITAB ASSISTANT WHITE PAPER This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. OneWay
More informationInvestigating Clinical Care Pathways Correlated with Outcomes
Investigating Clinical Care Pathways Correlated with Outcomes Geetika T. Lakshmanan, Szabolcs Rozsnyai, Fei Wang IBM T. J. Watson Research Center, NY, USA August 2013 Outline Care Pathways Typical Challenges
More informationInformation Management course
Università degli Studi di Milano Master Degree in Computer Science Information Management course Teacher: Alberto Ceselli Lecture 01 : 06/10/2015 Practical informations: Teacher: Alberto Ceselli (alberto.ceselli@unimi.it)
More informationLifeCycle Support for Staff Assignment Rules in ProcessAware Information Systems
LifeCycle Support for Staff Assignment Rules in ProcessAware Information Systems Stefanie RinderleMa 1,2 and Wil M.P. van der Aalst 2 1 Department Databases and Information Systems, Faculty of Engineering
More informationA Second Course in Mathematics Concepts for Elementary Teachers: Theory, Problems, and Solutions
A Second Course in Mathematics Concepts for Elementary Teachers: Theory, Problems, and Solutions Marcel B. Finan Arkansas Tech University c All Rights Reserved First Draft February 8, 2006 1 Contents 25
More information11 Ideals. 11.1 Revisiting Z
11 Ideals The presentation here is somewhat different than the text. In particular, the sections do not match up. We have seen issues with the failure of unique factorization already, e.g., Z[ 5] = O Q(
More informationEDIminer: A Toolset for Process Mining from EDI Messages
EDIminer: A Toolset for Process Mining from EDI Messages Robert Engel 1, R. P. Jagadeesh Chandra Bose 2, Christian Pichler 1, Marco Zapletal 1, and Hannes Werthner 1 1 Vienna University of Technology,
More informationData Mining Algorithms Part 1. Dejan Sarka
Data Mining Algorithms Part 1 Dejan Sarka Join the conversation on Twitter: @DevWeek #DW2015 Instructor Bio Dejan Sarka (dsarka@solidq.com) 30 years of experience SQL Server MVP, MCT, 13 books 7+ courses
More informationKirsten Sinclair SyntheSys Systems Engineers
Kirsten Sinclair SyntheSys Systems Engineers Kirsten Sinclair SyntheSys Systems Engineers Spicingup IBM s Enterprise Architecture tools with Petri Nets On Today s Menu Appetiser: Background Starter: Use
More informationA Labeling Algorithm for the MaximumFlow Network Problem
A Labeling Algorithm for the MaximumFlow Network Problem Appendix C Networkflow problems can be solved by several methods. In Chapter 8 we introduced this topic by exploring the special structure of
More informationPerformance Metrics for Graph Mining Tasks
Performance Metrics for Graph Mining Tasks 1 Outline Introduction to Performance Metrics Supervised Learning Performance Metrics Unsupervised Learning Performance Metrics Optimizing Metrics Statistical
More informationRSA VIA LIFECYCLE AND GOVERNENCE: ROLE MANAGEMENT BEST PRACTICES
RSA VIA LIFECYCLE AND GOVERNENCE: ROLE MANAGEMENT BEST PRACTICES A practitioner s perspective on best practices for Role Management ABSTRACT This white paper provides an overview of the Role Management
More informationSocial Media Mining. Data Mining Essentials
Introduction Data production rate has been increased dramatically (Big Data) and we are able store much more data than before E.g., purchase data, social media data, mobile phone data Businesses and customers
More informationJust the Factors, Ma am
1 Introduction Just the Factors, Ma am The purpose of this note is to find and study a method for determining and counting all the positive integer divisors of a positive integer Let N be a given positive
More informationBuilding a Data Quality Scorecard for Operational Data Governance
Building a Data Quality Scorecard for Operational Data Governance A White Paper by David Loshin WHITE PAPER Table of Contents Introduction.... 1 Establishing Business Objectives.... 1 Business Drivers...
More informationStructural Detection of Deadlocks in Business Process Models
Structural Detection of Deadlocks in Business Process Models Ahmed Awad and Frank Puhlmann Business Process Technology Group Hasso Plattner Institut University of Potsdam, Germany (ahmed.awad,frank.puhlmann)@hpi.unipotsdam.de
More informationSolution to Homework 2
Solution to Homework 2 Olena Bormashenko September 23, 2011 Section 1.4: 1(a)(b)(i)(k), 4, 5, 14; Section 1.5: 1(a)(b)(c)(d)(e)(n), 2(a)(c), 13, 16, 17, 18, 27 Section 1.4 1. Compute the following, if
More informationModule 10. Coding and Testing. Version 2 CSE IIT, Kharagpur
Module 10 Coding and Testing Lesson 23 Code Review Specific Instructional Objectives At the end of this lesson the student would be able to: Identify the necessity of coding standards. Differentiate between
More informationManaging Process Architecture and Requirements in a CMMI based SPI project 1
Managing Process Architecture and Requirements in a CMMI based SPI project 1 Author: Filippo Vitiello Abstract When developing or changing a process, and all its related assets, often the process engineers
More informationNODAL ANALYSIS. Circuits Nodal Analysis 1 M H Miller
NODAL ANALYSIS A branch of an electric circuit is a connection between two points in the circuit. In general a simple wire connection, i.e., a 'shortcircuit', is not considered a branch since it is known
More informationCHAPTER 3 Numbers and Numeral Systems
CHAPTER 3 Numbers and Numeral Systems Numbers play an important role in almost all areas of mathematics, not least in calculus. Virtually all calculus books contain a thorough description of the natural,
More informationChapter 21: The Discounted Utility Model
Chapter 21: The Discounted Utility Model 21.1: Introduction This is an important chapter in that it introduces, and explores the implications of, an empirically relevant utility function representing intertemporal
More information