TechRank Anita Mezzetti1 Lo c Mar echal23 Dimitri Percia David4 William Lacube2 S ebastien Gillard56 Michael Tsesmelis2 Thomas Maillart5 and Alain

2025-05-06 0 0 2.75MB 29 页 10玖币
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TechRank
Anita Mezzetti1, Lo¨ıc Mar´echal2,3, Dimitri Percia David4, William Lacube2,
S´ebastien Gillard5,6, Michael Tsesmelis2, Thomas Maillart5, and Alain
Mermoud2
1Credit Suisse
2Cyber-Defence Campus, armasuisse Science and Technology
3University of Lausanne (HEC Lausanne)
4University of Applied Science (HES-SO Valais-Wallis)
5GSEM, University of Geneva
6Military Academy, ETH Zurich
Abstract
We introduce TechRank, a recursive algorithm based on a bi-partite graph with
weighted nodes. We develop TechRank to link companies and technologies based on
the method of reflection. We allow the algorithm to incorporate exogenous variables
that reflect an investor’s preferences. We calibrate the algorithm in the cybersecurity
sector. First, our results help estimate each entity’s influence and explain companies’
and technologies’ ranking. Second, they provide investors with a quantitative optimal
ranking of technologies and thus, help them design their optimal portfolio. We propose
this method as an alternative to traditional portfolio management and, in the case of
private equity investments, as a new way to price assets for which cash flows are not
observable.
JEL classification: C14, C69, G17, G24
Keywords: private equity, bipartite networks, technology monitoring, portfolio optimization
This document is the results of a research project funded by the Cyber-Defence Campus, armasuisse
Science and Technology.
arXiv:2210.07824v1 [q-fin.CP] 14 Oct 2022
1. Introduction
This work investigates the innovation structure and the dynamics underlying the life
cycle of technologies. We fill two research gaps. The first concerns the identification of
future benefits and risks of emerging technologies for the society. The second regards the
valuation or early-stage companies and optimal investment decisions. To fill these gaps,
we introduce the TechRank algorithm. Our methodology assigns a score to each entities,
i.e., technologies and firms, based upon their contribution to the technological ecosystem.
We expect this method to help stakeholders in forming optimal decisions for investment,
procurement, and technology monitoring.
We calibrate our model in the cybersecurity sector, although TechRank could apply to
any sector. The cybersecurity technological landscape represents a particular challenge for
this calibration, given the important share of start-ups and fast innovations it yields.[16].
Moreover, the important number of cyber-attacks and the increasing costs they incur has
boosted cybersecurity investments.1According to Bloomberg, “the global cybersecurity
market size is expected to reach USD 326.4 billion by 2027, registering a compound annual
growth rate of 10.0% from 2020 to 2027”.2
To develop the TechRank algorithm, we first model and map the ecosystem of companies
and technologies from the Crunchbase dataset using a bi-partite network. The bi-partite
network structure accurately describes this complex and heterogeneous system. We evaluate
the relative influence of the network nodes in the ecosystem by adapting a recursive algorithm
that estimates network-centrality.
This methodology should help decision-makers and investors to assess the influence of
entities in the cybersecurity ecosystem, reducing investment uncertainties. In fact, around
90% of startups fail and in 42% of the cases this is due to incorrect evaluation of the market
demand. The second reason (29%) is because they run out of funding and personal money.3
Christensen (1997) highlights that well-managed companies also break down, because they
over-invest in new technologies[8]. Thus, by selecting the right technologies to invest in goes
along with the optimal investment strategy.
Our research takes inspiration from Google’s PageRank algorithm, that ranks web pages
according to readers’ interest[25]. We use a similar approach with bi-partite networks to
assign a score to companies and technologies. Our method is flexible and permits to incor-
porate investors’ preferences such as location or previous funding rounds. TechRank let the
investor select entities’ features that reflect their interests. The algorithm uses their choices
as input, which tweaks the entities’ score to reflect them. This enables investors to select a
personalized portfolio strategy using a quantitative methodology. The evaluation of compa-
nies and new technologies largely depends on investors’ personal choices, which may lead to
misread market demand. This work aims to lead to more methodical decision making for
1The New York Times: “As Cyberattacks Surge, Security Start-Ups Reap the Rewards” by Erin Woo
(July 26, 2021).
Yahoo Finance: “Microsoft Securing its Position with Cybersecurity Investments” by TipRanks (July 20,
2021).
2Bloomberg: “Global Cybersecurity Market Could Exceed $320 Billion in Revenues by 2027” (July 29,
2020).
3Findstack: “The Ultimate List of Startup Statistics for 2021” by Jack Steward.
2
investors.
The remainder of this article proceeds as follows. Section 2 presents the literature review
and hypotheses. Section 3 details the data and the methodology. Section 4 presents the
results. Section 5 concludes.
2. Literature review and hypotheses development
2.1. Centrality measures
In network analysis, the centrality estimates the importance of nodes through ranking.
The most simple centrality estimate is the “degree”, which counts the number of neighbours
of a node. One of its drawbacks is that it does not show which one stands in the center of
the network. Two nodes may share the same degree, while being more or less peripheral.
Thus, the degree is a local centrality measure, which does not capture the influence across
nodes within the graph.
Fig. 1: Central and peripheral nodes
This figure depicts the difference between central (red) and peripheral (brown) nodes in a graph.
Another important centrality measure is the “closeness”, which measures how long it
takes for information to spread from one node to the next. Specifically, closeness is defined
as the reciprocal of the “farness”, i.e. the sum of distances of one node with respect to all
other nodes. The “betweenness centrality” of a node measures how often a node stands in
the shortest path between a pair of other nodes (see, e.g., Bavelas; 1948, Saxena and Iyengar;
2020, and Freeman; 1978)2, 28, 14).
Another strand of research focuses on the top-K shortest path identification in a com-
plex network, a topic less tackled by the literature than centrality. To rank nodes, one
must compute the centrality of all nodes and compare them to extract the rank, which is
not always feasible due to the size of the network. To overcome this problem Saxena and
Iyengar (2017) attempt to estimate the global centrality of a node without analyzing the
whole network[29]. Similarly, Bavelas (1948) develops a structural centrality measure in
the context of social graphs[2]. Other centrality concepts include the eigenvector, Katz, or
PageRank centralities[5, 25, 20]. Finally, Freeman (1978) creates a formal mathematical
framework for centrality, which includes degree, closeness, and betweenness and advocates
for the combination of different kinds of centrality measures[14].
3
2.2. Page Rank
Page, Brin, Motwan, and Winograd (1999) develop the PageRank algorithm[25]. Its pri-
mary goal is to rank web pages objectively, a challenge with the fast-growing web. PageRank
assigns a score to each web page based on its relations with other web pages in the graph.
Other fields have benefited PageRank providing modifications and improvements. Xing and
Ghorbani (2014) extend the algorithm and propose the weighted PageRank (WPR)[32]. This
algorithm assigns larger rank values to more important pages, instead of dividing the rank
evenly among its outlink pages.4Each outlink page gets a value proportional to its popu-
larity, taking into account the links weights. On caveat of PageRank and its variants is that
they do not consider n-partite structures, yet, web pages can all be linked to one another.
Bi-partite networks address this issue and capture this complexity, among other structures.
2.3. Bi-partite networks
Networks are a fundamental tool to capture the relations between entities. Graphs (G)
are composed by vertices (V) and edges (E), and we denote G= (V, E). We build links and
mathematically analyze many properties of the whole system and of singular entities. To
graphically represent a real system, we synthesize its information into a simple graph frame-
work. This simplification generates an information loss in the modelling process. Simple
network structures might discard important information about the structure and function
of the original system [23]. As a consequence, the failure of a very small fraction of nodes
in one network may lead to the complete fragmentation of a system[6]. To solve the prob-
lem, extensions to the simple structure G= (V, E) are added and yield graphs with more
powerful features. For instance, in case vertices are connected by relationships of different
kinds, Battiston, Nicosia, and Latora (2014) advocate to work with multiplex networks, i.e.
networks where each node appears in a set of different layers, and each layer describes all the
edges of a given type [1]. When it is possible to distinguish the nature of the edges, multiplex
networks are an effective approach, which starts from embedding the edges in different layers
according to their type. However, even if we have two kinds of nodes, the nature of the edges
is unique. Therefore, a more suitable approach is bi-partite networks. Bi-partite networks
are for instance, a good way to describe the technological and business landscape. In Figure
2, we depict two sets of nodes, companies and technologies, which are interconnected but do
not present edges within the same set.
There are multiple adaptations of the PageRank algorithm to bi-partite structures[3, 12,
31, 21]. In particular, Benzi, Estrada, and Klymko (2015), Donato, Laura, Leonardi, and
Millozzi (2004), and Tu, Jiang, Song, and Zhang (2018) extend the PageRank algorithm
to multiplex networks. They assume that only some clusters of the graph are multiplex
networks and extend the PageRank algorithm only to analyze the sub-graph centrality. Bi-
partite networks are used to transform directed into undirected networks with twice the
number of vertices.
Klein, Maillart, and Chuang (2015) extend PageRank in the Wikipedia editors and ar-
ticles context [21]. The application of this algorithm to the case of interactions between
4Given a web page W, an inlink of W is a link of another web page that includes a link pointing to W.
An outlink of W is a link appearing in W, which points to another web page.
4
c2
c3
t2
t3
1
t
1
c
Companies Technologies
Fig. 2: Bi-partite structure of companies and technologies
The left panel depicts a typical bi-partite structure. The right panel provides an illustration of this
structure with companies (layer 1) and technologies (layer 2).
companies and technologies is straightforward. A major benefit of this approach is that it
starts from an unweighted graph, linking authors and articles. They develop a recursive al-
gorithm in which the two entities contribute to the quality (for articles) or the expertise (for
authors) of each other. They develop a bi-partied random walker by building the adjacency
matrix Me,a that takes value 1 if editor ehas edited article aand 0 otherwise, which tracks
all the editors’ contributions. They obtain Me,a ∈Rne,na, where neand naare the number of
editors and articles. They sort editors by the number of articles’ contributions and assign a
contribution (quality) value to each editor (article) based on their degree. The expertise w0
e
(quality w0
a) is given by the number of articles (editors) they have worked on (have received
modifications).
The second part of the algorithm follows a Markov process in its iterations. The step wn
(wn=wn(α, β)) only depends on information available at wn−1. At each step, the algorithm
incorporates information about the expertise of editors and the quality of articles, within the
bi-partite network structure. The process is a random walker with jumps, whose transition
probability is zero in the case Me,a = 0. Next, the authors define two variables for the
transition probability, Ge,a(β) and Ge,a(α)). Ge,a(β) represents the probability of jumping
from article ato editor eand Ga,e(α) represents the probability to jump from an editor to an
article. Both parameters depend on initial conditions and the selection of optimal parameters
is done through a grid search that maximizes the Spearman rank-correlation between the
rank given by the model and a ground-truth metrics obtained independently. Finally Klein et
al. (2015) observe a “less-is-more” situation since the presence of too many editors working
on an article is detrimental to its quality. Studying different categories of Wikipedia articles
they find αto remain constant, while βvaries significantly across categories.
Estimating the global rank of a node starting from local information and centrality mea-
sures is still an open research question in many sectors [28]. In particular, no research to
our knowledge use this approach for investment’s decision and portfolio optimization. Yet,
this approach could help overcome the limitations of standards financial models in private
equity, in which the network structure is easily obtainable, whereas the cash flow process is
not.
5
摘要：

TechRankAnitaMezzetti1,LocMarechal2,3,DimitriPerciaDavid4,WilliamLacube2,SebastienGillard5,6,MichaelTsesmelis2,ThomasMaillart5,andAlainMermoud21CreditSuisse2Cyber-DefenceCampus,armasuisseScienceandTechnology3UniversityofLausanne(HECLausanne)4UniversityofAppliedScience(HES-SOValais-Wallis)5GSEM,U...

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