Action Sequence Matching of Team Managers

Olaf Flak

, Cong Yang

and Marcin Grzegorzek

Faculty of Radio and Television, University of Silesia in Katowice, Katowice, Poland

Pattern Recognition Group, University of Siegen, Siegen, Germany

Faculty of Informatics and Communication, University of Economics in Katowice, Katowice, Poland

cong.yang@uni-siegen.de

Keywords:

Team Managers, Partial Matching, Action Matching.

Abstract:

Traditionally, team managers are analysed and compared based on human perception with data collected from

surveys and questionnaires. These methods normally have low efﬁciency especially in dynamic and complex

environments. In order to improve the accuracy and stability of manager analysis in management science,

in this paper, we propose a novel manager representation method which is general and ﬂexible enough to

cover most types of managers. For manager analysis, we introduce the ﬁrst manager matching algorithm that

calculates the global similarity between managers. The proposed matching algorithm not only returns robust

and stable manager similarities, but also details the matched parts among managerial action sequences. With

this, the proposed methods provide more research possibilities in management science.

1 INTRODUCTION

A team is deﬁned as a social system of two or more

units that are embedded in an organisation (Hoegl and

Parboteeah, 2007). In a team, team members per-

ceive themselves and each other as collaborating on

a common task. For the purpose of improving the

team work ability on more dynamic and complex en-

vironments (Mathieu et al., 2008) today, research on

team work becomes more and more relevant (Shak-

shuki et al., 2003) and has attracted a lot of attention

in the past decades (Mathieu et al., 2008). One com-

mon perception of those researches is that team man-

agers are the spirit of team works (Sohmen, 2013).

A team manager can be deﬁned as a team member

(1) who comprises inﬂuencing actions affecting the

other team members and (2) who chooses objectives

for the team, organizes activities to accomplish the

objectives and (3) who motivates team members to

achieve the objectives and maintains cooperative re-

lationships and teamwork to optimise collective time

of work (Perlow, 2014).

A team and a team manager are the warp and

woof of the dynamic fabric of organisations. They

cannot exist without each other activated by manage-

rial actions as a constellation of speciﬁc objectives,

resources and processes (Sohmen, 2013). Moreover,

in order to ensure a team can achieve the established

goals with clear assumptions, it is crucial to clarify

managerial actions that govern team actions (Sinar

and Paese, 2016). Consequently, it leads to a strong

need for research on managerial action analysis (Hal-

liday and Stacey, 2009). In general, there are two re-

search challenges related to managerial action anal-

ysis. The ﬁrst challenge is how to model the man-

agerial actions in order to fully represent the charac-

teristics of a team manager. The second challenge is

what kind of methods could be employed to distin-

guish team managers and, additionally, to label their

styles of leadership. Traditionally, the ﬁrst challenge

is addressed by the action sequence analysis which

used to track the order of actions over time (Abbott,

1990). Those actions are usually declared by man-

agers and then collected by questionnaires (Barnes,

1980). Based on that, a team manager can be repre-

sented by a data map describing the action features

of, e.g. “what”, “when” and “how” (Beshears and

Gino, 2015). However, this method is not robust be-

cause some managerial actions could be ignored due

to the poor memory and impression of team man-

agers (Flak and Pyszka, 2013). Moreover, this repre-

sentation method is not general and has low ﬂexibility

since different managers may take different types of

managerial actions (Beshears and Gino, 2015).

In order to solve these problems, in this paper,

we propose a general model to represent a manager

by managerial actions and their features. Speciﬁ-

cally, a manager is ﬁrst represented by an action se-

386

Flak, O., Yang, C. and Grzegorzek, M.

Action Sequence Matching of Team Managers.

DOI: 10.5220/0006189203860393

In Proceedings of the 6th International Conference on Pattern Recognition Applications and Methods (ICPRAM 2017), pages 386-393

ISBN: 978-989-758-222-6

quence. After that, each action is modelled by ac-

tion features within different feature groups. Theoret-

ically, the proposed method can preserve both ﬁne-

and coarse-grained information of a manager. The

main reason is that we describe each managerial ac-

tion by several different action features. Moreover,

the proposed method is general enough to cover most

types of managers since the each managerial action

is represented by ﬂexible feature groups. Lastly, the

proposed model can be easily adapted to different on-

line/off-line managerial tools.

For the second challenge, the team managers

are normally distinguished and labelled by human

perception (Whetten and Cameron, 2016) of, e.g.

managerial actions, attitudes and values. However,

there are four main disadvantages of such a method:

Firstly, it cannot accurately measure the similar-

ity/dissimilarity between managers since human per-

ception is highly abstract. Secondly, this method is

not robust due to the instability of human percep-

tion (Yang et al., 2016). Thirdly, this method has

low efﬁciency since the distinguishing and labelling

processes are both applied manually. Lastly, even

if two managers are similar to each other by hu-

man perception, it is hard to point the detailed sim-

ilar/dissimilar parts among their managerial action

sequences. Therefore, we propose a method that

can overcome these disadvantages. Particularly, by

the action matching between managers, the proposed

method not only returns the similar parts among ac-

tion sequences, but also calculates the global sim-

ilarities. In order to do so, the proposed match-

ing method integrates both local and global match-

ing strategies. The local matching strategy allows

an accurate measuring of local similarity between ac-

tion blocks within action sequences while the global

matching strategy calculates the overall similarity be-

tween managers based on the local similarities. In

such a case, the proposed method can automatically

and accurately distinguish team managers. In addi-

tion, this method provides more research possibilities

in management science (Siedlok and Hibbert, 2014).

The main scientiﬁc contributions of this article in-

clude: (1) We apply an interdisciplinary research be-

tween management science and pattern recognition to

deal with the team manager representation and match-

ing. (2) We introduce an effective and general team

manager representation method. (3) We propose the

ﬁrst algorithm that can accurately measure the simi-

larity between team managers.

2 RELATED WORK

The view of a manager has changed many times over

the last hundred years. At the beginning of the sci-

entiﬁc management age, a manager in an organisa-

tion was represented by his/her functions, such as a

reﬂective planner, an organiser, a leader or a con-

troller (Brodie, 2007). However, these approaches

do not have the information of real managerial ac-

tions. Besides many other later approaches, it took 50

years to experience a signiﬁcant change in the view of

manager natures. Particularly, the most dominating

approaches consist of two main concepts: (1) man-

agerial roles that a manager should play (Mintzberg,

1973), and (2) managerial skills that a manager

should have (Beaudry and Francois, 2010). Koontz

and O’Donneil launched a discussion on the meaning

of managerial skills in 1964 (Koontz and O’Donneil,

1964). In 1974 Katz proposed an approach in which

a manager is represented by managerial skills. He

claimed that successful managers are indeed eclectic

and they must possess and be skilled in technical, hu-

man and conceptual areas of organisational life (Katz,

1974). In 1973 Mintzberg concluded that a manager

can be described in terms of 10 roles (Mintzberg,

1973). Due to the deep inﬂuence of these concepts

among scientists and practitioners, in most publica-

tions a manager is represented by managerial skills

and managerial roles (Sinar and Paese, 2016).

Based on the survey and analysis of the published

methods, we draw a conclusion that managerial skills

and managerial roles as traditional theoretical con-

cepts are sufﬁcient to represent a team manager. But

they are still not general and robust enough to describe

most types of managers. The main reason is that the

concepts of managerial skills and managerial roles

only illustrate what competences a manager should

have and should do, respectively. They do not show

what a manager really does. Built on this observation,

in Section 3, we represent a manager by managerial

actions which are the missing point in relations be-

tween managerial skills and managerial roles. With

this, the proposed representation method integrates

managerial skills and managerial roles and turns them

into managerial actions. Therefore, comparing to the

traditional manager representation method, the pro-

posed approach has high distinguish powering and

stability. In addition, this representation method is

suitable for action sequence matching in Section 4.

Moreover, we also observe that most research

projects were conducted by the survey method with

questionnaires as a research tool (Sinar and Paese,

2016). With this method, it is hard to quantitatively

compare the difference between managers. In order

to distinguish different types of managers, the tradi-

tional perception-based methods are not robust since

human perception could be inﬂuenced by many fac-

Action Sequence Matching of Team Managers

387

Thing 1.1

Thing 3.1

Thing 1.2

Event 2.1

Action 1

Action 2

Action 3

Action 4

Event 1.1

Thing 2.1

Event 3.1

Event 1.2

Figure 1: Fundamental structure of actions.

tors such as memory, emotions, etc. These methods

are time-consuming because they are normally carried

out manually (Alexandru and Diana, 2015) or semi-

automatically (Sinar and Paese, 2016). To solve these

problems, we propose an automatic method that can

calculate the similarity between managers based on

their action sequences. In addition, the partial simi-

lar/dissimilar action blocks within sequences can also

be returned. With the proposed method, researchers

can apply a deeper and more accurate analysis of

managers and their actions. In such a case, the pro-

posed method gives more potential research possibili-

ties in management science. Moreover, since the pro-

posed manager representation and matching are fully

automatic methods, they can be adopted to some man-

agement applications (Mithas et al., 2005). For in-

stance, a manager can be guided by action sequence

matching with the knowledge action sequences from

other managers.

3 MANAGER REPRESENTATION

In this section we ﬁrst introduce the relationship be-

tween managers and their actions. After that, we theo-

retically describe the feasibility of manager represen-

tation using actions and their features. Built on this,

a mathematical model for manager representation is

proposed.

3.1 Managers and Actions

In this article, a team manager is denoted as Ω. As

discussed in Section 1 and 2, compared to the tra-

ditional approaches that represent Ω by managerial

roles and managerial skills, we propose to represent

Ω by managerial actions. The rationale behind this

is that a managerial action can be deﬁned as a real

activity which a manager does in order to play a man-

agerial role and have a certain managerial skill (Pavett

and Lau, 1982). In such a case, a managerial action is

the connection between a managerial role and a man-

agerial skill. Consequently, the proposed representa-

tion method has higher description power.

To represent each managerial action, it is impor-

tant to discuss and analyse its ontological concept:

The system of organisational terms (SOT). SOT is

an original theoretical construct in which the organ-

isation performance is tracked and recorded. In or-

der to do so, observation techniques are used along

with the on-line management tools (Flak, 2015). The

philosophical foundation of SOT is based on Wittgen-

stein’s philosophy: Facts (the only beings in the

world) and their “states of facts” (Brink and Rewitzky,

2002). We extend this concept and propose that man-

agerial actions can be organised by events and things.

Speciﬁcally, as shown in Figure 1, each event and

thing have the label I.J, in which I and J represent

a number and a version of a thing, respectively. Event

1.1 causes thing 1.1, which in turn releases event 2.1

that creates thing 2.1. Thing 2.1 starts event 3.1 which

creates thing 3.1. Then, thing 3.1 generates a new ver-

sion of the ﬁrst event, i.e. event 1.2. In such a way,

a new version of the ﬁrst thing is created, which is

called thing 1.2.

According to events and things, a managerial ac-

tion can be represented by time domain features and

content domain features, respectively (Brinkerhoff,

1985). In this article, we employ the time domain fea-

tures since such features can be easily captured and

quantised. In contrast, the content domain features

involve words, sentences, expressions, characters and

ﬁgures, etc. which are hard to be quantised by exist-

ing models (Alnajjar and Flak, 2016).

3.2 Representation Model

As a manager is organised by several actions, we rep-

resent it by features of each action. Speciﬁcally, as

shown in Figure 2, a manager Ω is composed by M

actions:

Ω = {a

,··· ,a

} . (1)

For a single action a

, it can be represented by a

T -dimensional feature vector:

= [ f

,··· , f

]

. (2)

where f denotes a single feature value, i =

1,2,··· ,M. As discussed in Section 3.1, those fea-

tures can also be classiﬁed into H groups based on

their characteristics, H 6 T . Moreover, the feature

ICPRAM 2017 - 6th International Conference on Pattern Recognition Applications and Methods

388

...

Figure 2: The proposed model to represent a manager Ω.

number in a group G

may be different from others,

u = 1, · · · , H. For example, in Figure 2, G

and G

could have different feature numbers. For notational

simplicity we assume that the features of a

are or-

dered according to the order of their groups. In such

a case, G

= [ f

,·· · , f

i j

], 1 6 t 6 j and t 6 j 6 T .

Consequently, an action a

can also be represented by

feature groups:

= {G

,·· · ,G

} . (3)

Considering all M actions of a manager Ω, it can

be represented by all action features within H feature

groups:

Ω = {G

,·· · ,G

} . (4)

where G

is a M × ( j − t + 1) matrix in which all M

action features within a feature group [ f

, f

] are pre-

served. The proposed representation method in Eq. 4

will be used for action sequence matching in Sec-

tion 4.

It should be noted that the idea of representing

a manager by feature vectors is not new. Such an

idea is also similar to one of the ﬁrst research by

F. and L. Gilbreth in the ﬁeld of scientiﬁc man-

agement at the beginning of 20th century (Karsten,

1996). They investigated human motions at work,

which was the beginning of workforce automation in

industries (Spriegel et al., 1953). Moreover, in lit-

erature we can ﬁnd other representation approaches

used in production (Al-Saleh, 2011), healthcare ser-

vices (Lopetegui et al., 2014), process of physical

workers (Magu et al., 2015), and to some extent, in

managerial work (Tengblad, 2002). However, differ-

ent from these approaches, our method is more ﬂex-

ible to be adapted in different scenarios. In addition,

the proposed representation model in Figure 2 is suit-

able to use in action sequence matching in Section 4.

4 MANAGER MATCHING

In this section, we propose an efﬁcient matching al-

gorithm to ﬁnd partially similar parts among action

sequences from different team managers. Moreover,

it is important to provide a reasonable similarity mea-

sure for tasks such as manager comparison and re-

trieval, etc. Therefore, a manager similarity method

is introduced in the second part of this section.

4.1 Partial Matching

In order to ﬁnd a partial match between two given

managers Ω

and Ω

, their corresponding action se-

quences S

and S

are compared. As introduced

in Section 3.2, each action a

a is described by a T -

dimensional feature vector. Therefore, the action se-

quences S

and S

can be represented by feature ma-

trices with size M × T and N ×T , respectively. M and

N are the number of actions. For notational simplicity

we assume that M 6 N.

Figure 3: An illustration of the general idea of partial

matching. B

and B

are two r × T sized action blocks se-

lected from the action sequences S

and S

, respectively.

D(s,m, r) denotes the dissimilarity between B

and B

The aim of manager matching is to identify parts

of the two action sequences that are similar to each

other. In terms of comparing the two descriptor ma-

trices, as shown in Figure 3, it equals to ﬁnd r × T

sized feature blocks B

and B

, starting at the action

in S

and a

in S

which yield a small dissimi-

larity value d(B

). r is the number of actions in

the matching blocks B

and B

. s and m denote the

index of start actions in S

and S

, respectively. As il-

lustrated in Eq. 4, each manager Ω can be represented

by H feature groups. Since B

and B

have the same

dimensional features and feature groups as Ω, they

can also be represented by:

= {G

,·· · ,G

}

= {G

,·· · ,G

}

(5)

Action Sequence Matching of Team Managers

389

where G

and G

are the r × ( j − t + 1) feature

group matrices, u = 1, · · · , H. This is because a fea-

ture group G

contains r number of actions. More-

over, as shown in Eq. 4 and Figure 2, the feature num-

ber in a feature group is indicated by ( j − t + 1).

Based on Eq. 5, in this article, d(B

)

is calculated by the integrated Bhattacharyya dis-

tance (Dubuisson, 2010) from H feature groups:

d(B

) =

∑

u=1

) (6)

where τ is the weight for fusing H feature groups

and D

) denotes the Bhattacharyya distance

between two feature groups. In practice, τ can be

searched using the heuristic method of Gradient Hill

Climbing integrated with Simulated Annealing (Yang

et al., 2015). Otherwise, it can be set to one for all

feature groups. Speciﬁcally, the Gradient Hill Climb-

ing (Russell and Norvig, 2009) method starts with

randomly selected parameters. Then it changes sin-

gle parameters iteratively to ﬁnd a better set of pa-

rameters. A ﬁtness function then evaluates whether

the new set of parameters performs better or worse.

The Simulated Annealing strategy (Kirkpatrick et al.,

1983) impacts the degree of the changes. In later it-

erations, the changes to the parameters are becoming

smaller. Consequently, with a small part of testing

data in the preliminary experiments, τ

,·· · ,τ

can be

properly assigned.

Furthermore, the Bhattacharyya distance

) is calculated by:

) =

ln(

(

+ 2)) +

(

(µ

− µ

)

+ σ

) (7)

where σ and µ are the variance and mean of a features

within a group G

, respectively. With Eq. 7, the Bhat-

tacharyya distance among all feature groups can be

calculated and then the global dissimilarity d(B

)

between two feature blocks B

and B

is generated

using Eq. 6.

As introduced above, d(B

) is built on the

combination {s, m, r}: Start action in S

(that is s),

start action in S

(that is m) and action number in a

matching block B (that is r). Therefore, to ﬁnd similar

blocks among S

and S

all different matching pos-

sibilities and chain lengths r have to be considered

and the brute-force method (Bellman, 1954) becomes

inefﬁcient for larger number of actions. Therefore,

different authors as e.g. (Osada et al., 2002) proposed

approximations where for example only every n-th ac-

tion is considered as the starting action.

Inspired by (Donoser et al., 2009), we propose an

algorithmic optimisation to overcome the limitations

of the brute-force approach (Osada et al., 2002). The

proposed method is based on a modiﬁed Summed-

Area-Table (SAT) approach (Hensley et al., 2005) to

calculate all the dissimilarity values d(B

) among

different combinations of {s, m, r}. The SAT concept

was originally proposed for texture mapping (Crow,

1984) and then brought back to the community of

computer vision by Viola et al. (Viola and Jones,

2001) as integral image. The integral image concept

allows to calculate rectangle image features like the

sum of all pixel values for any scale and any loca-

tion in constant time (Donoser et al., 2009). How-

ever, different from the method (Donoser et al., 2009)

in which N integral images are generated for triples

{s,m,r} searching, the proposed method only uses M

integral images to speed up the matching process.

Particularly, in order to calculate the dissimilarity

value d(B

) for all possible conﬁguration triplets

{s,m,r} in the most efﬁcient way, M integral images

Int

,·· · ,Int

are built based on Eq. 6 for the

block length r from 1 to M. In such a case, each inte-

gral image Int

is the (M − r) × (N − r) matrix. The

main reason is that we need to consider all possible

matches from action blocks in S

and action blocks in

. Based on these M integral images the dissimilar-

ity values d(B

) can be calculated for every block

of any length starting at any action in constant time.

Finally, all matching triples {s, m, r} which pro-

vide a dissimilarity value d(B

) below a ﬁxed

threshold are returned as the ﬁnal matched parts

among two action sequences S

and S

. As discussed

in (Donoser et al., 2009), the detected matches may

overlap. Therefore, the ﬁnal result is obtained by

merging the different returned matches.

4.2 Manager Similarity

To calculate the global similarity between two man-

agers Ω

and Ω

, a combination of descriptor differ-

ence (Yang et al., 2014) and the bending energy of

an estimated transformation (Torsello and Hancock,

2004) is commonly used. However, these methods

normally only focus on the coarse-grained differences

among action sequences S

and S

and the property of

ﬁne-grained similar and dissimilar blocks are not fully

used. Moreover, in Section 4.1 we already collect the

partial dissimilarities with all possible block lengths.

With this in mind, we adapt a measure described by

Bronstein et al. (Bronstein et al., 2009) and Donoser

et al. (Donoser et al., 2009) to calculate the global

similarity between managers.

Speciﬁcally, we use a Pareto-framework for quan-

titative interpretation of partial similarity. In or-

der to do so, two quantities are deﬁned: partial-

ity λ(B

), which describes the block lengths (the

ICPRAM 2017 - 6th International Conference on Pattern Recognition Applications and Methods

390

higher the value, the smaller the part) and dissimi-

larity d(B

), which measures the dissimilarity be-

tween the blocks, where B

and B

are two action se-

quence blocks. In this paper, partiality λ(B

) is

calculated by 1/r, where r is the block length ( Sec-

tion 4.1). Here we describe a pair of partiality and

dissimilarity values (λ(B

),d(B

)) as Pareto

optimum Φ(B

) (Donoser et al., 2009), that is

Φ(B

) = (λ(B

),d(B

)). With Φ(B

it is possible for us to observe the lowest dissimi-

larity for the given partiality. As described in Sec-

tion 4.1, the proposed partial matching algorithm au-

tomatically evaluates all possible matches for all pos-

sible block lengths, we can easily collect all Pareto

optimums Φ(B

) by focusing on the minimum

dissimilarity values in M integral images.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

(Partiality)

(Dissimilarity)

Salukwadze Distance

Figure 4: The proposed approach for calculating similarity

between managers using the Salukwadze distance.

Finally, to get the global similarity D

(Ω

,Ω

) be-

tween mangers Ω

and Ω

, as shown in Figure 4, all

Pareto optimums are visualised as a curve, referred

to as the set-valued Pareto frontier and the so-called

Salukwadze distance (Bronstein et al., 2009) is em-

ployed based on the collected Pareto frontier by

(Ω

,Ω

) = inf

|Φ(B

(8)

where | · · · |

is the L1-norm of the vector which con-

tains all pairs of partiality and dissimilarity. Conse-

quently, D

(Ω

,Ω

) measures the minimum distance

from the origin (0,0) to the point on the Pareto op-

timum. The Salukwadze distance is then returned as

the similarity value of managers Ω

and Ω

5 EXPERIMENT

In this section, we evaluate the performance of the

proposed manager matching method in an applica-

tion. In order to do so, we designed an on-line ex-

perimental tool, transistorshead.com, to collect man-

agerial actions from different managers. Then, based

on the proposed manager representation model in

Section 3.2, this platform represents each manage-

rial action by different action features within differ-

ent groups. Built on the represented manager, we ap-

ply the manager matching experiment and compare

the matching results to the ground truths. Finally,

the computational complexity of the proposed man-

ager representation and matching methods are anal-

ysed and discussed.

5.1 Experimental Environment

In this paper, we developed a special tool: transis-

torshead.com, to record and represent managerial ac-

tions. This tool was designed based on the main idea

in Section 3.1 and the following principles: (1) Ev-

ery on-line management tool tracks and records man-

agerial actions according to the idea of Unit of Be-

haviours (Curtis et al., 1992). (2) Using a manage-

ment tool by a team manager is equal to an event

occurring in an organisational environment which re-

sults in a thing (Flak, 2013). (3) Every on-line man-

agement tool is useful for describing managerial ac-

tions. With this tool, we record each managerial ac-

tion and describe it with a 24-dimensional feature vec-

tor. Those features are grouped into 7 feature groups.

It is interesting to point out that this tool can also be

extended to represent managerial actions by content

domain features. The detailed information is intro-

duced in (Alnajjar and Flak, 2016).

With this tool, we have collected and built our

dataset: PG-Manager. Speciﬁcally, in order to collect

the managerial actions, 150 volunteers had been in-

volved in our experiment over 15 months. The partic-

ipants worked in small groups from different regions.

Each group consists of a team manager and multi-

ple members. Consequently, PG-Manager contains

56 managers and each manager contains 200 to 400

managerial actions. As introduced above, each ac-

tion is represented by a 24-dimensional feature vector.

This dataset is used to evaluate the proposed manager

representation and matching methods in Section 5.2.

5.2 Manager Matching

In order to evaluate the proposed manager match-

ing algorithm, we perform the managerial action se-

quence matching experiments on the PG-Manager

dataset. Speciﬁcally, our evaluation is built on a re-

trieval framework where managers in the dataset are

ranked based on their similarity to a query. Based on

the ranked results and similarity values, we can dis-

tinguish different managers and also group them into

Action Sequence Matching of Team Managers

391

Table 1: Similarities between similar managers.

Manager1 Manager2 Manager3 Manager4 Manager5 Manager6 Manager7 Manager8

Manager1 1 0.9919 0.9932 0.9797 0.9878 0.9702 0.9925 0.9706

Manager2 0.9919 1 0.9869 0.9868 0.9946 0.9769 0.9940 0.9704

Manager3 0.9932 0.9869 1 0.9702 0.9871 0.9708 0.9866 0.9766

Manager4 0.9797 0.9868 0.9702 1 0.9821 0.9749 0.9896 0.9705

Manager5 0.9878 0.9946 0.9871 0.9821 1 0.9702 0.9906 0.9721

Manager6 0.9702 0.9769 0.9708 0.9749 0.9702 1 0.9701 0.9724

Manager7 0.9925 0.9940 0.9866 0.9896 0.9906 0.9701 1 0.9703

Manager8 0.9706 0.9704 0.9766 0.9705 0.9721 0.9724 0.9703 1

different classes.

Table 1 illustrates the similarities between 8 man-

agers. Those similarities are selected since they are

above the threshold σ = 0.97. Considering the ground

truth, these managers are similar to each other and

belong to the same group. Therefore, the proposed

method can correctly distinguish different managers.

Moreover, compared to the ground truth in which only

similar or dissimilar information is available, the pro-

posed method not only provides such information, but

also gives more accurate similarity scores. In such a

case, scientists and practitioners can apply a deeper

exploration in management science.

5.3 Computational Complexity

(1) For manager representation, the proposed method

in Section 3.2 generally includes two parts: manage-

rial actions and action features. For managerial ac-

tions, the time complexity is O(M) since a manager

Ω is composed by M actions. For a single action a

since it can be represented by a T -dimensional fea-

ture vector, the time complexity is O(T ). Therefore,

the total complexity is O(MT ). Recalling that in prac-

tice there are many more managerial actions than the

number features (M >> T ), the total complexity for

manager representation is bounded by O(M). (2) For

manager matching, an exhaustive search over all pos-

sible matches for all possible block sizes has a com-

plexity of O(2

), where N

and N

are the num-

ber of actions within the two input managers. Our

proposed approach based on integral image analysis

enables matching in O(N

) time. We implemented

our method in Matlab, which enables manager match-

ing on a Laptop within seconds.

6 CONCLUSION

In this paper, we propose a novel manager representa-

tion and matching algorithm based on managerial ac-

tions and their features. For manager representation,

we ﬁrstly represent a manager by a action sequences

collected by existing or the proposed tools. After that,

each action is described by multiple time domain fea-

tures within ﬂexible feature groups. In such a case,

the proposed representation method is ﬂexible and

general enough to cover most types of managers. For

manager matching, based on the action sequences of

managers, we ﬁrst apply a partial matching method to

search the matched blocks within action sequences.

Then, the global similarities between managers are

calculated built on their matched sequence blocks. In

the future, we will extend our manager representation

method by adding more types of managerial action

and action features. In addition, we will try to imple-

ment the proposed algorithms for manager labelling

based on the deep learning approaches.

ACKNOWLEDGEMENTS

Research activities leading to this work have been

supported by the Chinese Scholarship Council (CSC)

and the German Research Foundation (DFG) within

the Research Training Group 1564 (GRK 1564). We

greatly thank Frederic Li from University of Siegen

for his signiﬁcant help in our experiments.

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