A Methodology for Exploiting Oceans of Data within Territorial Dynamic Applications

Jacky Legrand

Université Paris 2 Paris, France

legrand@u-paris2.fr

Francis Rousseaux Université de Reims Champagne-Ardenne

Reims, France francis.rousseaux@univ-reims.fr

Eddie Soulier

Université de Technologie de Troyes Troyes, France

eddie.soulier@utt.fr

Florie Bugeaud Pôle d’innovation par les services Nekoé

Orléans, France florie.bugeaud.2011@utt.fr

Pierre Saurel

Université Paris 4-Sorbonne Paris, France

psaurel@eidetix.it

Houda Neffati

Université Paris Sud & Cabinet Algorithmics Paris, France

neffati.h@gmail.com

Abstract—The current approaches aiming at collective intelligence modelling often rely on traditional methods (ontologies, graphs). Even if those traditional methods may have reached their limitations, fin front of demanding emerging practices. The major conceptual tools enrolled for current and future Web are deeply rooted in the information storage and retrieval practices. The focus is on developing more original technologies for capturing, analyzing, exploiting and visualizing data. The agencements and the arrangements provide the appropriate epistemological context of our contribution. The simplicial complexes are the mathematical support of the methodology. The result is a shift from networks studied towards graph theory to higher dimensional networks structures. The representation is more than graphs, or even hypergraphs. A geometric perspective shows the arrangement as assembling polyhedra of all sizes. Their contacts can form chains of adjacencies. It not only generalized the notion of path graphs but also made available a range of quantitative and qualitative tools on the structure. Thus, the separate parts, more or less strongly linked, and the length of paths to traverse, and even loops or "missing parts", are meaningful metadata representations.

Keywords-agencement; arrangement; dynamic knowledge; emerging knowledge; simplicial complex

I. INTRODUCTION

While the amount of available data is exploding on the Web, several communities (from economics, law, and sociology to political science), using data technologies through a collective intelligence manner, focus on networks.

Networks are often studied via graph theory (the vertices stand for things and the edges stand for binary relations between pairs of them).

Although easy to study, graphs may be of limited use, if not inadequate, for modelling some complex situations. Higher dimensional networks1 structures as hypergraphs or simplicial complexes have been suggested to generalize

1 Even though called "multidimensional networks", network structural

complexity has not to be confounded with dimensionality studies asking about the ability to reduce the features of objects to a smaller fundamental set.

them to relations among N things and to offer new insights into these situations.

The use of simplicial complexes to study human systems in their natural multidimensional structure has been introduced by Ronald Atkin [1], [2], [3], [4]. Based on the Q-analysis (representation and analysis of binary relations) and algebraic topology, this technique it is still considered powerful, thirty years later, in understanding complexity. In recent years intense research efforts [5], [6], [7], [8], [9], [10], [11], [12], [13] argue for multidimensional networks to be the appropriate concept appropriate for the study of both the structure and the interactions of a wide range of complex systems.

While the amount of on-line textual information is becoming a challenge for web searching, all communities (including academia and business), aiming at semantic information storage focus on ontologies to develop more "semantic meaning" to access these collections.

There is neither a single definition2 of what an ontology is, nor widely accepted abstract data types3 for ontologies. Since we have no room here to be baffled by fundamental questions about theory and formal ontologies, there must be a consensus about ontologies used to improve retrieval effectiveness by storing domain knowledge.

Domain knowledge came to be used to cope with emerging intelligent data ranging from E-commerce [15] to E-governance [16] over a wide field of inquiry including Sentiment Analysis [17] or Science Commons [18].

A careful review of past quests of meaning in the syntactical representations demonstrates that the

2 In spite of some disagreements, the Gruber [14] definition of ontology

is widely cited in the literature: "An ontology is an explicit specification of a conceptualization". This definition supports the vocabulary shift, which licenses computer scientists to use "ontology-ontologies" instead of "semantic modeling products based on an ontological approach".

3 In spite of a statistical consensus, naming-centric ontologies remain far from agents-centric ontologies. The first category is close to a user-oriented formalism while the second one faces inference, task, and strategy challenges.

2012 IEEE Second International Workshop on Advanced Information Systems for Enterprises

978-0-7695-4845-6/12 $26.00 © 2012 IEEE

DOI 10.1109/IWAISE.2012.10

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formalisms purport to capture the full spectrum of human knowledge.

While it remains unclear how best to carve the world at its joints4, the specific tasks in mind point out the following assumption: One might have in advance a list of components for the world to study it.

When actors and their relationships emerge simultaneously (controversies, discoveries, social participations) it urges to develop a network visualization technique that achieves a representation getting rid of this assumption.

This is done in two steps. Section 2 introduces, after the barest essentials of the underlying concepts, the necessary definitions for discovering the mathematical tools. Then, Section 3 inspects the potential real world applications of the methodology from a classificatory point of view.

Whereas the theoretical questions are formulated, a case study is introduced in the Section 4. It exhibits the most dedicated features and extensions of multidimensional networks to support participatory territorial governance.

The conclusion is used as a discussion section to highlight the forthcoming endeavours of a work still at a preliminary stage of development.

II. METHODOLOGY

This methodology should not be understood as a usual data analysis. It is a form of additional and rewarding view that does not suffer the same constraints and is not subject to the same axioms.

A. Agencements Our assumption is that the concept of

agencements/arrangements is generic enough to promote the idea that the interaction between social objects does not depend on a metaphysics of unity (territorialized space around a central force of power) or substance (perdurant identity of entities in interaction). Conversely, it depends on a movement, a multiplicity which comprises many heterogeneous terms and which establishes connections, relations between them, through dimensions, which are heterogeneous. This conceptualization synthesizes the works of Foucault, Deleuze and Latour, which we propose to gather under the term “Theory of the Agencements” 5.

It can provide new tools to model, visualize and represent vast amounts of dynamic data because the agencements start from an assumption of radical heterogeneity of their components:

“Structures are linked to conditions of homogeneity, but assemblages are not (…). What is an assemblage? It

4 Plato, Phaedrus [Socrates 265e]: "That of dividing things again by

classes, where the natural joints are, and not trying to break any part, after the manner of a bad carver." (Perseus digital library translation).

5 In [19], Foucault translator proposes to translate « agencement » by « assemblage » in English whereas in [20] the same notion is translated by “arrangement”. But Callon [21] keeps the term “agencement”: An actor, said Callon and Koray, “is made up of human bodies but also of prostheses, tools, equipment, technical devices, algorithms, etc’. – in other words is made up of an agencement”. An agencement is thus an assemblage, arrangement, configuration or layout. We retain the French ‘agencement’ because it does not have a passive connotation the term ‘assemblage’ has in English.

is a multiplicity which is made up of many heterogeneous terms and which establishes liaisons, relations between them (…) Thus, the assemblage’s only unity is that of co-functioning” [19].

Latour pushes these intuitions to the limit by radicalizing the idea that any materials, attributes or types of bonds can belong to an Actor-Network [20] (human and nonhuman). Here, an active entity (an agent or actant) is defined neither by itself (identity, essence) nor by its relations (its network). This is possible through the dynamic “mediation-translation-trials” dynamic (fig. 1).

Latour and Callon give an account of any phenomenon as a progressive aggregation of a plurality of “heterogeneous entities”. This aggregation is able to stabilize itself during a trajectory, thus forming a “whole” of associated heterogeneous elements.

Heterogeneous entities

Hybrid Collective or Network

Society or Envelope

Points without attributes, “empties” entities (or social vacuity state)

Points made up of the intersection of “free floating” qualities “pluggable” with empty entities

Agencement associating attributes, translated and stabilized, appearing to emanate from the (full) entities

Figure 1. The three main steps of mediation-translation.

At the beginning of the situation of analysis (fig. 1, first column), agents are empty. Gradually, their own action and the action of other agents equip them with heterogeneous attributes and not inter-connected attributes (middle column). Through mediations and translations, entities get themselves associated into situations where they are defined by the modifications (translation) they realized on each quality that defines them. Simultaneously, actors are definable only starting from the list of relations or attributes, which are very distant from what we can image actors are (right column). In short, heterogeneous entities agencements should ideally been visualized simultaneously starting from their activity and their relations.

B. Simplicial Complexes In this paragraph we give technical, if not

mathematical, notational conventions for further understanding.

A graph pictures a set of points that are connected by edges representing a list of pairs. The edges are directed to represent a binary relation.

An agencement — different from the binary relations usually described in the graph theory — is defined by a large volume of elements that enter in composition (non-binarity). The heterogeneous entities form a “system” because their links are based on relations of interdependence, which are heterogeneous. We will focus on the technique of the simplicial complexes to follow and show agencements.

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A hypergraph edge no longer connects pairs of points but rather encloses subsets thereof. Geometrically speaking, a hypergraph is visualized as the subsets of vertices enclosed within circular shapes. They may have properties that are not possessed by the previous elements.

Simplicial complexes are derived from algebraic topology. Topology studies spatial relationships and continuous deformations of paths. Combinatorial topology shifts from a topological space seen as a continuum to a finite discrete space. Algebraic topology adds algebraic tools.

Such an algebraic approach is interesting for the representation of collections (structures) of heterogeneous elements (ingredients) and heterogeneous relationships (connections, dependencies), but also the representation of movements and possible pathways (dynamics).

A simplex is an N-dimensional structure made up with N+1 vertices.

The simplices can be represented as vertices, edges, triangles, tetrahedra and higher-dimensional polyhedra. A face of a simplex is any subset of vertices of the simplex.

A simplicial complex is a set of simplices with all the faces (closed under intersection). Its dimension is the largest dimension of its simplices. Figure 3 is a global example of such a simplicial complex.

Two simplices are said to be "near" when they are connected to each other by the sharing of vertices (common faces). A finite sequence of "near" simplices defines a sequence of connectivity. The dimension of the shared faces determines the dimension of the sequence.

The topological notion of connectivity is the keystone of the methodology. Connecting simplices together is where complexes have a crucial advantage over hypergraphs: hypergraphs have no faces ("subedges").

These connections between simplices form a “path of connectedness” or “polygonal chain”.

Q-loops are circular connecting sequence where a simplex is connected to itself via shared faces of dimension q. According to the density of connections, the loop can be contracted into a single simplex. Should it be otherwise, the "contraction" stops with a minimum sequence length. Some missing simplices seem to be an obstacle to a free shrinking; Atkin [3], [4] called them shomotopic q-objects.

This framework may represent multidimensional networks and provides a formalism of spatial representation of knowledge.

Figure 2. Agencement model with the mathematical tools.

Figure 3. Simplicial Complex - Geometrical visualization.

Agencement Complex and paths

Active entities Simplices

Heterogeneous entities

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Its application to agencements allows a representation in a geometric form (Fig. 2 from the bottom to the top): - The ingredients/heterogeneous entities as “vertices”

(parts); - The combination or coordination of these entities

within active entities in a “simplex” (micro wholes); - The combination or coordination of these active

entities in an agencement as a “simplicial complex” (macro wholes);

- The dynamic construction reality as "paths". In our work, each simplex is an active entity emerging

from social, cognitive, mechanical, etc. relationships between the involved elements.

The importance or lack of connection(s) between two simplices can also be viewed as a complex node or a structural hole revealing a lack or a potential opportunity within the studied territorial situation.

Such a graph is built in two stages: the network description (structure/“backcloth” [22]) with vertices and scores, then the description of dynamics (“traffic” [22]) which is specific to that network. The structure remains abstract but the traffic is a computational research6. The topology of the structure and the characteristics of each of its vertices affect the traffic. Johnson's Hypernetworks [22] go further by offering the distinction of different relationships between a given couple of points. This is a key point for the representation of agencements in which relationships are of various kinds.

Johnson's work also provides an interesting look on the inclusion of the time issue in the emergence of such a structure:

“Simplices provide a way of defining multilevel structure. This relates to system time measured by the formation of simplices as system events” [22 p.375]

Thus time can be measured by the formation of simplices as many events in the system. We can therefore consider following the emergence of an agencement and its trajectory step by step.

III. POTENTIAL APPLICATIONS

We aim at a review of the reality which the above formalisms purport to model. We inspect the potential real world applications of the methodology from a classificatory point of view to produce both domain-oriented and item-oriented typologies.

The discovery of particular relations between the elements is an insightful application task, which has nothing to do with abstract formalisms. A typology of applications may help to clearly circumscribe the underlying assumptions, hence highlighting their importance before investigating an area.

Concrete world. When the simplices are instantiated in geography, transport, architecture and urban planning areas, the geometric facet is here fruitful to reason on 2D or 3D spaces. The shomotopic objects have a "physical" significance.

Relational world. The study of people, social ties and activities, including politics, economics, management, mass media and medicine, have always been very

6 Legrand [23] indicates some calculations: measure of the degree of

intersection between alternatives, measure of the similarity between several connected simplices that are involved in the sequence length.

interested in networks. The studies investigate the structural interdependence of actors. The simplices may show what people have in common. The complex is a backcloth for social life modelling. The shomotopic objects have an observable significance studied by the social sciences.

Abstractions and concepts. The simplices may refer to rather abstract contextual objects or to concepts. Risk diagnosis of large-scale systems, multicriterion decision-making tools, artificial intelligence or information retrieval are such subjects where a preliminary formalisation preceded analysis (often during a previous independent professional idiosyncrasy). The shomotopic objects significance invites data to be inspected with yardsticks that may remain to be invented.

The previous typology does not capture the actual semantic choices. For examples, primary entities, with a spatial topology, are related to a set of rather abstract entities; persons belong to the same geographic community.

Generally speaking, the entities may be either persons (patients, farmers, readers, community members) or concepts (social needs, scientific subjects, social events) or things. The things may be either concrete (shopping centres, spatial areas, manufacturing parts, databases) or abstract. The abstract things may be either representations (bungalow plans, routes design in a road system, failures of fault-units) or symbols (geometrical figures).

The attributes are either characteristics of the entities (measures, properties, scale of descriptors) or "comparable" entities (junction in routes, technology requirements for needs, machines, databases hosts, types of retail outlet for shopping, plant species in areas, squares of the chess board, clinical symptoms, diagnostic categories) or the entities themselves (relationships among people, distance between markets).

IV. A CASE STUDY

"Grand Paris" is a project aiming at transforming Paris and its suburbs to place the Ile-de- France area in the leading bunch of the first five world-cities, along with New York, London, Tokyo, Shanghai and Hong Kong.

In relation to the “Grand Paris” project, an Operation of National Interest plans the creation of the “Paris-Saclay” cluster as a territory with high scientific and technological potential. This project will benefit from an exceptional investment of a billion Euros.

Within the political dynamics of "Grand Paris", local politicians from territorial collectivities gather their efforts to promote a territory (between Saclay and Paris) called the “Scientific Valley of the Bièvre” (VSB). This economical context offers the opportunity to study two projects of new territories, both competitive and complementary.

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Figure 4. Table of actants / attributes.

A test of the Theory of the Agencements has been therefore elaborated by using the Google™ search engine and starting from key words related to the projects headings, scientific disciplines, political actors and organizations. The ranking offered by Google™ enable the analyst to identify the multitude of actions (and discourses) which express existing modes that are at the origin of the heterogeneous attributes. These attributes will be able, in a second time, to become the attributes (or list of relations) of the agents involved in the studied agencement.

Figure 5. Simplicial complex of actants / attributes.

In [24], [25], [26], we analyzed in detail and from a comparative point of view the descriptive categories that are mobilized by their concerned promoters to apprehend the on-surface attributes characterizing the two agencements.

The preceding table (Fig. 4) shows the links between attributes (generated by actions) and agents.

All agents, attributes and relations form a simplicial complex (fig. 5).

The modelling of the territorial agencements provides an access to networks of actants and proposals and their effects. But the reading and the analysis of their mathematical representation may appear still abstract to most actors of this kind of project.

Therefore, we proposed to “spatialized” the modelled agencements. These “spatialized agencements” may allow us to propose a more concrete representation. We also have integrated the computational functions of the territorial arrangements with a generalist GIS (Geographical Information System): Quantum (http://www.qgis.org/). We used the resources of the OpenStreetMap project, which aims at creating free license maps (http://www.openstreetmap.org/).

The preceding figure (Fig. 6) shows the spatial projection of geo-localized elements and inferred elements of the territorial agencement of the Cluster Paris-Saclay.

Thus, thanks to the combination of a "territorial intelligence" approach, we deliver a framework of sustainable development, partnerships and citizen involvement in decisions.

V. CONCLUSION

The achievement of networks with simplicial complexes is powerful because multifaceted (algebraic, topological and combinatorial). It reveals joint presences at varying level of dimensionality. Connectivity is not similarity, but contiguity and inter-relation.

To conclude on the role of digital technologies in the exploration and visualization of agencements, we will consider that a deepening of the designation of the entities and attributes intuitu rei (on an involvement basis) is a keystone. Leaving the comfortable situation where agents (or actants) are selected intuitu personae (on a personal basis), how to access the actants turns considerably complex.

Being neither defined by itself nor through its network, the "empty" entity in a state of "social vacuity state" is not less chosen in consideration of something that is substantial and that deserves a more strict semantic interpretation of the simplices.

The work described in this paper is still at a relatively preliminary stage of development.

We hope our contribution will open up some interplay between this branch of mathematics and new scholars in order to undertake a rather ambitious task since it should be time, funds and corpus consuming. Indeed, the number and heterogeneity of documents and available data is likely to explode in applying the methodology.

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Fig. 6. Extract of the territorial agencement of the cluster Paris-Saclay in the GIS Quantum

ACKNOWLEDGMENT

This project has been sponsored by CPER Champagne Ardenne AidCrisis.

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