FR2949585A1 - METHOD FOR ORGANIZING VARIABLES IN A DATABASE - Google Patents

Abstract

The method aims at organizing a database (4) comprising variables, such as indicators (l, l, l), relating to a multi-state object, to each corresponding variable of the values associated with the respective states. In the method: - automated means (2) identify correlations between at least some of the variables; the means (2) form groups each consisting of one of the variables (I) and others (l, l) of the variables correlated with the latter and sufficient to deduce the latter; and the means (2) associate, in a database (4), with each of the variables of the group, a datum (M) indicating at least one identity of the other variables of the group.

Description

The invention relates to tools for decision support and the organization of variables in a database. For example, we can refer to the telecommunications sector. In the latter, the entire production is implemented through an information system that manages both the flows related to customer communications (voice, SMS, MMS, Internet, etc ...) , flows related to prospecting and marketing, flows related to financial monitoring, flows related to quality of service monitoring, flows related to operational performance, etc. All these flows are listened to in real time at means of computer agents (such as robots) that collect all kinds of data, with granularities more or less fine depending on the needs of analysis (this usually goes from minute to hour). There is usually one agent per measured indicator. These indicators range from the available disk space on a hard drive bay, to the computer throughput on this or that branch of the network, through the CPU load rates of the servers concerned, or even more simply the number of connections of clients on one or another application server, etc ... Thus, the person in charge of the capability analysis (or capacity planning in English) of the company has all the data called learning (the history of the observed complex system) stored in a data warehouse.

Also, when people in charge of the control of works or works need a state of the information system at a given moment, the capability analyst is able to read them. Or even beyond, when a person in charge of business intelligence wants to redefine objectives for activities within the company (which can be called business objectives for business chains) it is this analyst who gives him a possible reading of the indicators directly impacted by these new forecasts. Thus, the capacity analysis activity is similar to a surveillance that provides a reading of the state of the company's health, from sales made in real time within the agencies or via the Internet, to the the set of network connections that must be provided to meet the demand. In addition, the capability analysis makes it possible to establish contingency plans that are decision support tools: if an alert is given as to the operation of an application server, it is desirable to anticipate all the alerts to come and make the right decisions to prevent the crisis from spreading to all of the production.

But so far, it is mainly feedback from experience that allows the capability analyst to consider certain conclusions.

-2- Indeed, the information system is in perpetual evolution and it is difficult for the capability analyst to anticipate the possible evolutions (removal or addition of a server, decrease or increase of a set of connections, variation number of users in the agency, migration to new applications, etc.). Likewise, it is difficult for him to define the new agents that are then necessary for an optimal reading of all the indicators. More generally, we know indicators called key performance indicators (or KPIs for the English Key Performance Indicator). Until now, the KPI repository is a tool whose design is reserved for business intelligence, which relies solely on the nomenclature of the business lines concerned. For its part, the capability analyst must constantly guarantee the support of the complex system according to the planning of the business objectives. Decision-making IT experts unknowingly make choices that influence the information system. For their part, capacity analysts are confronted with the complexity of the information system and poorly apprehend the relevant business chains from the observable technical indicators to the KPI itself. The analyst tends to consider that any remarkable similarity between two indicators implies a cause-and-effect relationship, which considerably distorts the capacity analyzes and the reports of business intelligence. As a result, indicators are often redundant or overloaded in a complex system that has become complicated, poorly observed and costly, thus severely reducing the return on investment. In addition, among the many factors that degrade data quality in a data warehouse is data migration, breakage of referential integrity, and extremely long wait times for clients of the observed complex system. In all cases, it is the stability and reliability of the data field of the indicators that are questioned. And the common attribute of data quality that is being challenged is the integrity of the metrics repository so that data from one table in relation to another is not erased or inadvertently changed. An object of the invention is therefore to improve the quality of decisions based on variables such as indicators. For this purpose, there is provided, according to the invention, a method for organizing a database comprising variables, such as indicators, relating to a multi-state object, to each corresponding variable of the values associated with the respective states, method in which: - automated means identify correlations between at least some of the variables;

The means form groups each consisting of one of the variables and others of the variables correlated with the latter and sufficient to deduce the latter; and the means associate, in a database, with each of the variables of the group, a datum indicating at least one identity of the other variables of the group. Thus, the invention proceeds by relying on the truly observable correlations within the data field of the variables relating to the observed complex system. It ensures the correlation and significant codification of key variables within the capability analysis and enables a true mapping of the variables between them, while consolidating the integrity of the data within the data warehouse (authenticity and reliability). traceability). The method makes it possible to organize discrete and chaotic variables into a tree structure showing probable cause-and-effect relationships, from so-called elementary variables, to key variables. The invention allows a better understanding of the information system in real time. It makes it possible to automate contingency plans, monitoring operations and alert management. The invention makes it possible to quickly read the impacts related to forecasts (computer-based decision-making) as well as to crises (on the control of works or works). Better than an impact study, the database obtained with the invention can be updated regularly to take into account the latest developments in the information system. Advantageously, the means construct a graph, such as a Petri net, of the group, for example by means of a rising algorithm. Thus the graph encapsulates the identity of the key variable and the group to which it belongs.

Advantageously, the means code the graph to produce the data. This code makes it possible to find quickly and easily the corresponding graph, and thus the identities of the variables and their relations. This meaningful coding of variables reinforces the quality of data within a data warehouse, in terms of integrity first (authenticity and traceability), but also in terms of completeness. This form of representation as a graph, combined with the significant codification, allows a subsequent processing, for example of hyperspherization or iconography, as well as queue type modeling. There is also provided according to the invention a method for exploiting variables, such as indicators, relating to a multi-state object, to each corresponding variable of the values associated with the respective states, the method in which;

Automated means obtain in a database at least one datum indicating an identity of variables correlated to a predetermined variable and forming with it a group such that the variables of the group, except one, are sufficient to deduce the latter, the means thus identifying the correlated variables; and the means exploit the identities of the identified variables, for example transmit them on a telecommunication network. Preferably, the means identify, from the data, cause-effect relationships between the variables of the group. Advantageously, the means control the mention on a web page identities variables identified. It is also provided according to the invention a computer program which includes code instructions adapted to control the implementation of a method according to the invention when it is executed on a computer. It is also planned to make this program available on a telecommunication network for downloading, as well as a data recording medium comprising this program in recorded form. The invention also provides a device for organizing a database comprising variables, such as indicators, relating to a multi-state object, to each corresponding variable of the values associated with the respective states, the device comprising means capable of: - to identify correlations between at least some of the variables; - to form groups each constituted by one of the variables and others of the variables correlated to the latter and sufficient to deduce the latter; and - associating, in a database, with each of the variables of the group, a data item indicating at least one identity of the other variables of the group. Provision is also made according to the invention for a device for exploiting variables, such as indicators, relating to a multi-state object, to each corresponding variable of the values associated with the respective states, the device, possibly in accordance with the aforementioned device, comprising suitable means; to obtain in a database at least one datum indicating an identity of variables correlated with a predetermined variable and forming with it a group such that the variables of the group, except one, are sufficient to deduce the latter, the means being thus suitable for identify the correlated variables; and - to exploit the identities of the variables identified, for example to transmit them on a telecommunication network. In addition, according to the invention, a database is provided which comprises:

-5- - variables relating to an object taking several states, to each corresponding variable of the values associated with the respective states; at least one datum relating to at least one of the variables and indicating an identity of some of the variables correlated with it and forming with it a group such that the variables of the group, except one, are sufficient to deduce the latter. The invention can be employed with entities having needs in the areas of business intelligence or capability analysis. All industrial sectors are concerned by this invention: nuclear, transport, pharmaceutical, cosmetic, automotive, equipment manufacturers, energy, financial, insurance, etc ... Indeed, whatever the field of application, it does not matter which names are given to the variables, as long as the requirements of the technique are respected and a real-time reading is possible. The invention can thus be applied for example in the following fields: - nuclear: inside temperature of a glove box, temperature of the hot material during machining, lubricant flow, thickness of the handling gloves, time of operation opening of portholes, exposure time of technicians, etc. - pharmaceutical: efficiency of an automated packaging island, counting of non-compliant capsules, counting of non-compliant substrates, rate of introduction under vacuum, counting of deteriorated substrates at installation, etc ... - energy: river flow, water temperature, cooling circuit flow rate, generator power, core temperature, energy demand, power plant consumption, quantity available energy, etc ... - economy: financial and stock indexes such as the CAC 40, volume of shares traded, key rates, interbank rates, credit volume, volatility index, etc. evolution of GDP, evolution of unemployment, corporate morale, consumer morale, etc. The invention will be better understood on reading the description which follows, given solely by way of example and with reference to the drawings. in which: - Figure 1 is a flowchart illustrating the correspondence between a formal language and a family of trades; FIG. 2 presents curves illustrating the superimposed connection between two indicators; FIGS. 3 and 4 are petri nets of a redundant character and an indicator link; FIGS. 5 and 6 are respectively a matrix of connectivity and the stacking of the indicators relating thereto;

FIGS. 7 and 8 illustrate the same elements in the case of parallel stacking; FIG. 9 is the Petri net of a linear stack of elementary indicators within a chain; FIGS. 10 and 11 show matrices in which the indicators are respectively redundant or overload one of the indicators; FIGS. 12 to 14 are matrices respectively illustrating the initialization of the descriptive matrix in the method of the invention, the definition of the elementary zone and finally the general staircase shape; FIGS. 15 to 21 are matrices and Petri nets illustrating respectively a simple redundancy, a duplicate, a multiple redundancy, a link of indicators, an overload of indicators, a redundant overload and finally a situation of general interpretation. ; FIG. 22 illustrates an example of a parallel Petri net; FIG. 23 shows a descriptive matrix and the connections in the case of the parallel Petri net; FIG. 24 illustrates an example of the linear Petri net; - Figure 25 presents the descriptive matrix and the connections in the case of linear Petri net; FIG. 26 illustrates a graph of the links of a KPI chain; - Figure 27 shows the stacking of basic indicators in the KPI chain; - Figure 28 shows the descriptive matrix and the connections within this chain; FIG. 29 shows a Petri net in an exemplary embodiment; and - Figure 30 is a diagram illustrating means for implementing the invention. We will present below examples of implementation of the invention in which the variables are indicators, the invention is not however reduced to this case.

This is a significant coding process for Key Performance Indicators (KPIs). It implements in this case: - correlation calculations of the indicators of an observed complex system (variance-covariance matrix, matrix of mathematical correlations and matrix of cross-correlations); - construction and interpretation of so-called descriptive matrices and connectivity, and

The representation of all the KPI chains modeled in the form of graphs such as Petri nets. The method implements a dedicated graph grammar that automates the modeling of Petri nets from the simple replay of the significant codification of KPIs thus obtained. This codification constitutes the new entry key of a data warehouse (deposit of data of the technical indicators and trades specific to the observed system) and facilitates the setting up of a data base through for example a technology of the groups assisted by computer (or TGAO), dedicated to the capacity analysis activity.

We will first explain how to define, build, and use the data warehouse-specific database. We use a classification of the studied business chains which here designate groups of variables associated with the same activity within the observed system (sales, production, quality etc.). It is a question of quickly finding their codes thanks to the use of a thesaurus in the database. To do this, we build a meaningful codification, figuratively speaking, of these business chains, then associate the result with a chronological coding, all of which constitutes the new input key of the data warehouse. A thesaurus is a hierarchical dictionary, a standard vocabulary based on generic terms and domain-specific terms. It provides only incidental definitions, the relations of the terms and their choice outweighing the meanings. However, when a thesaurus is based on a significant codification, the codification of an object is not only the reference of this one, but carries in addition a semantics specifying the case of employment. A thesaurus is finally a tree of ordered sets of references, a classification being only the simple fact of relating objects to these references. As part of the capability analysis activity, these objects are here the business chains. It is considered here that a codification is a set of rules defining a one-to-one correspondence (bijection) between information and their representation by characters, symbols or signal elements. It can be a so-called significant or chronological codification. For any business chain thus referenced within a classification specific to capability analysis, there is a unique reference for authenticating and tracing it. A figurative coding is a mnemonic method allowing access to data and information specific to a given object. Preferably, this codification only applies to immutable objects in time. In all the other cases, the implementation of the thesaurus becomes more complex, losing also the benefit of the internal coherence of the latter. A grammar is a formalism to define a syntax and thus a formal language, that is to say a set of words on a given alphabet. In other words, a grammar sets the rules for writing non-arbitrary code. There is a similarity between the generation of sentences from symbols (words) respecting semantics related to a given language and the generation of business chains from business or technical indicators, considering cause-and-effect relationships. Fig. 1 thus illustrates this correspondence between a formal language and a business family. 10 We recall below some correlation tools. Let a random vector x to N discrete and chaotic time indicators X1 have different collection steps within the data warehouse. The first step therefore consists in a relevant interpolation of the poorest indicators so that each indicator can have n realizations within the same time range: X1 = (xl1 ... xln) \ XN ù (xN1 .. Once this preparation is completed, the calculations essentially concern the following elements: - the variances-covariance matrix: 2 6X X 20 62 Xk 2 6X NN.N knowing that all the calculations are based on the law of Bravais -Pearson where n 6xy = cov (x, y) = -1 xi ù 7) (yi .Y) = x. y ù x. y n 6), =. jvar (x) with with x = 1 ~ jxi and where n i-1 - the correlation matrix: 1 ù var (x) = ù 1 (xi ù x) 2 = x2μx2 n 1 1 _ NN - the correlation matrix crossed (it is interesting to have the delays between the indicators): 0 _ NN knowing that the set of calculations is based on the cross correlation method where Fxy (r) = E (X (t) Y (tùr) ) Where E denotes the expectation and where y (z) = f X (t) Y * (t -z) dt with Y * denoting the transform of the function Y such that Y * (tùz) = Y (tùz) 6Te (tùr) and STe (tùz) = 1s (t-rükTe), 8Te being the comb of k = ùco Dirac of sampling period Te We detail below the method of implementation of these calculations making it possible to propose the relations of cause and effect within a business chain, and to deduce some form of representation, then significant codification.

When setting up a data warehouse, we start with the complete inventory of the components constituting the generic and unique model, in order to give a faithful representation of the studied object. The building of the base goes through the following steps:

- data inventory of business chains and related indicators;

- construction of the matrix of correlations between indicators two by two;

- coding of business chains from the identified elementary indicators; - classification of codified trades;

- proofreading of the thesaurus;

- validation of the grammar of the graphs used;

- generic modeling of business chains. -9

This construction is done according to a sequential reading of these steps. As for its use, we proceed in the following way: - from the classification within the thesaurus, selection of the code of a trade chain; - since the graph grammar retained, reading the set of cause-and-effect relationships within this business chain; - from the model of this business chain, hyperspherization for a representation that is both intuitive and cognitive. We will see in the second part how we can automate the writing of business chains since the correlation calculations, and thus build the base. A decision process depends directly on the quality of the data stored within the warehouse. For this reason, it is preferable to carry out an inventory of the data quality attributes of indicators. For each of these attributes, we define a definition, build a metric, measure the metric score, and track the progress of the measurements in real time. These attributes are: Consistency, Completeness, Accessibility, Integrity, Accuracy, Validity, and Timeliness. In database management, referential integrity is a set of computer rules that prevents data from being deleted or inadvertently changed from one table to another. In general terms, integrity refers to the state of the data that, during processing, storage or transmission, does not undergo any alteration or destruction, and retains a format for reuse. The concept of data integrity encapsulates two other attributes of data quality: - authenticity: each data has a unique and verifiable identity (proof); - traceability: each data belongs to an easily identifiable chain (path). Concerning authenticity, this attribute is generally processed by MAC algorithms, Message Authentication Code known in themselves. Concerning traceability, this attribute leads us to the generalization of a universal codification, which must be read and understood by everyone, especially here by the data warehouse. We will now present how graphs and meaningful coding are obtained. Let's look at the particular case of three indicators whose data are supposed to be expressed in the same unit within the International System of Units (SI).

Either a MVL business chain forming a group of three indicators such as MVL _ {I;, I;, Ik1. Figure 2 illustrates an overlap connection between two indicator curves. In the pair (rr, k, çPtk), rp, k denotes the mathematical correlation coefficient between 1k and PPtk denotes the cross-delay of 1k with respect to 1 ;. In the pair (Np ,,), Np, k denotes the mathematical correlation coefficient between Ik and 1 ,, Y ', k denotes the cross-delay of Ik with respect to 1 ;. In the graphic sense, we observe an overlap between the prices of the indicators and 1; We note this connection Lu or L ;;, since we can consider under 1; or 1; under 1 ;. Whatever the delays observed compared to the source indicator courses, the result indicator 1k is always obtained by superimposing the two others while taking into account their respective contribution levels. In addition, we distinguish the level of contribution and the correlation coefficient that do not express the same thing. In the sense of the connection, and 1; are the basic indicators. 1k becomes the induced indicator.

The search for all the graphs allowing the representation of any business chain to be represented first requires the definition of a unique model making it possible to represent all the possible business chains. The following definitions are given: - elementary indicator: all indicators that are not correlated with each other in pairs within a given chain are elementary indicators; Induced indicator: any indicator that is not an elementary indicator is induced; - KPI indicator: an induced indicator becomes a KPI indicator in the sense of the group if and only if it does not allow other indicators to be deduced. A KPI indicator is always placed at the end of the chain at the end of the correlation process; - KPI string: any group, here a string, consisting of elementary indicators, induced and a KPI whose sequences are all known and derived from correlation calculations. There can be multiple KPI strings within a single business chain; - linking of indicators: a link between two elementary or induced indicators always results in the superposition of the prices of these indicators, while taking into account their respective contribution levels, in order to create a new indicator induced within the business chain observed. Beyond two indicators, we say that the indicator binding is overloaded; - redundant character: it appears whether an induced indicator depends only on an elementary or induced indicator; -12- - SI coefficient: coefficient of transformation of a basic indicator, induced or KPI to express it in the units of the international system;

- contribution coefficient: any contribution level, expressed in the SI, from one indicator to another. Example: a variation of the value of 1k by 10 units produces a variation of the value of 1, of the order of -1000 of these same units;

- mathematical correlation: the mathematical correlation coefficient between two indicators is recognized here as soon as its absolute value is greater than or equal to 0.866; since it tends to 0, the two indicators are said to be independent; 2 - covariance of indicators: the covariance of indicators is recognized as valid as soon as its absolute value converges towards O. In this case only, we can affirm that these indicators are independent and that they are never correlated. In this calculation, the convergence threshold towards 0 must be evaluated at the end of the experiment;

- cross-cutting: two interrelated indicators are not likely to be simultaneous. The cross delay makes it possible to quantify this achievement offset in time. We are also talking about phase shift in time;

- cause-effect relationship expressed: experience feedback may be relevant when the calculation alone does not allow to conclude;

- Shannon entropy: When an indicator becomes unstable in the sense of distribution, Shannon's entropy becomes minimal and abruptly approaches O.

Either a group such as a MVL business chain consisting of M indicators, a number of which are elementary indicators. Either a group such as a KPI string JVLkp; consisting of N indicators taken from those of the MVL business chain and of which m of them are basic indicators. We must respect the following inequalities: m <nb <M and m <N <_ M.

We can note the indicators Vi E {1 ... M}. We can note the business chain MVL =

Let XM be the vector consisting of the M indicators present in the MVL business chain; Let AM be the descriptive matrix of MVL such that:

## EQU1 ## - E {1 ... M}, we associate with any valid identified correlation and denoted py the number 7cÿ = 1, or 0 if there is no valid correlation knowing Ti-ii = 1, Life {l. ..M}; AM = [a ;;] 1 a, 7 = u 21-ji = a; ; AM is a square matrix hollow and symmetrical and whose trace is always equal to M. Let Anb be the connectivity matrix of MVL such that: - Anb E V nbxnb V = 10,1}; 5 - E {l ... nb}, we associate with any connection identified and denoted L, 7 the number Su = 1, or 0 if there is no connection knowing that S ;; = 0, Vi E {l ... nb}; - Anb = [a ;;] / a ;; = S = = a ;; ; Anb is a hollow, symmetrical square matrix whose diagonal is always zero. We can note the KPI chain JVLkp; • Let XN be the vector consisting of the N indicators present in the KPI chain JVLkp; Let AN be the descriptive matrix of JVLkp; such as: - AN EUNxN {0,1} - E ... N}, we associate with any valid identified correlation and denoted by rp the number 2cÿ = 1, or 0 if there is no valid correlation knowing that = 1, Life {1 ... N}; - AN = [at] 1a ;; = 21-ÿ = 21-ji = a ;; ; AN is a symmetrical hollow square matrix whose trace is always equal to N. Let Am be the connectivity matrix of JVLkp; such that: - Am EVmxm _ Vi, I {1 ... / v = {0,1}; 1, we associate with any link identified and denoted Lu the number Su = 1, or 20 0 if there is no connection knowing that S ;; = 0, Vi E {1 ... m}; - An, = [a ;;] / a, 7 = Su = S; i = a ;; ; Am is a symmetrical hollow square matrix whose diagonal is always zero. The following representations are in the form of a Petri net: - redundant character: FIG. 3 illustrates the Petri net of a redundant character. 25 with rp ~ E [û1,1] and ç at 0; This formula gives the relation between two redundant indicators with: a; has a contribution coefficient of 1; -14- ai and a; the SI coefficients of the observed indicators and Ctj the contribution coefficient expressed in the SI of 1; on I. - indicator binding: Figure 4 illustrates the Petri net of an indicator link. With p ,, e [û e ~ û hl], that. > _ 0 and that ,. ? ## EQU2 ## where: fnw = fln • the contribution coefficient of Ia over Iw, the end and the coefficients S i of these observed indicators and c, the contribution coefficient expressed in the SI of I, on Iw; Yv .C, nv the contribution coefficient of 1a on Iw, 7 ,, 7 and 7 ,, the SI coefficients of these observed indicators and the contribution coefficient expressed in the SI of 1a on I. We use a simple form of representation and accessible of type network of Petri which, when it is delayed and / or colored, always authorizes any step

Subsequent and complementary hyperspherization or analysis in the form of queues.

The complexity level of the correlation calculation problem increases with the number of indicators constituting the observed business chain. Indeed, the number of overlapping links within the studied business chain: gVL = {I19 ••• 9Inb, ••• 9IM {, 20 depends directly on the number nb of elementary indicators present within the observed business chain (all KPIs aside). The number nb is always greater than or equal to m. This is why we first stop at the particular case of a business chain with a single KPI indicator.

The construction of this chain amounts to stacking linearly (any coefficient of

25 contribution aside) all the elementary indicators through successive overlays. In this case, the business and KPI strings are strictly identical; N = M and nb = m. In a linear stack, the connectivity matrix of JVLkpi = {I1, ..., Im, ..., IN} is as illustrated in Figure 5. Figure 6 illustrates the stacking of the elementary indicators at within MVLkpi and shows what is happening within the studied KPI-chain. From these two representations, we deduce that the number of superimposed bonds present in JVLkp; is m -1. When calculating correlations, it is possible for a business chain to highlight not one KPI, but several. In this case, each KPI string must be treated separately. In the case of a chain having two KPIs, the stacking is necessarily parallel, as shown in Figure 8 which illustrates the stacking of the nb elementary indicators within MVL if there are two KPIs. In this example, the connectivity matrix of MVL takes the form illustrated in Figure 7. We deduce that the general form of the connectivity matrix allows to find the number of KPIs actually present in the trade chain M. In the case presented above, the business chain has two KPI chains: MVLkp ;, and 9VLkpi2. In general, each KPI string to be treated separately, the selected stack is always linear. Thus, the number of superimposed links within the KPI chain JVLkp; is m -1. So we describe the KPI chain JVLkp; (= lhi,, Im, '' 'DINJ as in Figure 9 which illustrates the Petri net of linear stacking of the elementary indicators within JVLkp ;. Let GN be the set of possible Petri nets. , the cardinal of Gy is such that 2 card GN = Cm Pm2 = GAS Am \ 2! m. P ni! m-2 = 21 (m - 2)! (m - 2) '= 2 with: m - C, the number of combinations of 2 elementary indicators taken from m;

- Pm_2, the number of permutations of the remaining m -2 elementary indicators; and

- Am, the number of arrangements of 2 elementary indicators taken from m. The general shape of the Petri net allows us to specify one of the data quality attributes for the studied chain, namely completeness (all necessary data are available in the database). Thus, for a studied KPI chain JVLkp ;, whose general shape of the Petri net is also linear, the completeness is optimal if and only if the number of elementary indicators is such that: N1 bN odd> û1: m = 2 + 1 -16- N VN pair> û2: m = 2 Thus, the card G20 with optimal completeness: 10! 1814400 _ Gard G20 = 2 = 1814400 = G19 In the same way, the card G100 with optimal completeness is written: 50! 15207046600856689021806304083032.1064 card G 100 = 2 = = card G99 Given the complexity of matrix calculations that can be executed during correlation calculations, to stop the final choice of the Petri net exactly describing the KPI string f (JVLkp; = lhi,, Im, '' 'DINJ, we retain the following two criteria: the completeness of the data and the definitive scheduling of the indicators according to the set of calculated cross-delays The number of elementary indicators actually obtained in a KPI chain informs us about the relevance of the choices that are made Suppose that in the first case, the KPI chain is overheated, the indicators tend to become redundant and the descriptive matrix is horizontalised.We can realize savings in measurements and establish mathematical relations in order to computationally deduce the set of redundant indicators from the earlier indicator The matrix is illustrated In this example, the indicators 1 ;, 1k and 1 are redundant. Suppose that in a second case, the KPI string is not listened to enough. The indicators tend to overload certain indicator links and the descriptive matrix becomes vertical. We can complete the initial business chain and add new relevant induced indicators to linearly decompose any overloaded links from the earlier link. The matrix is illustrated in FIG. 11. In this example, the indicators 1 ;, 1k and 1 overload 1 ;.

In both cases, it is the attribute of the quality of the data, the completeness, which must be reinforced, without which the feedback of experience can very soon be necessary by the use of relations of cause and effect. expressed by the expert, what we want to avoid. Preferably, the correlation calculations should not be oriented by expert opinion.

We now present the construction of descriptive matrices and connectivities. Here is what correlation method we can use to explain a business chain.

-17- Let be a business chain M = {119-9 I nb 9 9I M 1. Taking into account the coarsest granularity, we sample all the indicators of this chain so as to retain only n realizations or observations. In some cases it is possible to interpolate missing achievements on indicators whose coarse granularity if retained inevitably causes loss of relevant information at the time of sampling. We initialize AM, the descriptive matrix of MVL, as illustrated in Figure 12. Thanks to the possibilities offered by the principal components analysis (or PCA), we deduce a priori I`YM, the variance-covariance matrix, which we after a few experiments, stop the acceptable threshold of convergence towards 0, then we identify the nb elementary indicators that are finally present within the observed business chain. We update AM by first swapping all the indicators so that the nb elementary indicators are found at the top left of the descriptive matrix, then, diagonally apart, we force all the descriptive coefficients of this elementary zone. at 0. Figure 13 shows the definition of the elementary zone. Thanks to the PCA always, elementary zone aside, we deduce a priori 1-1`YM, the correlation matrix, then we identify all the so-called valid mathematical correlation coefficients, that is to say whose values absolute are greater than or equal to 2 = 0.866. Since they tend towards 0, the concerned indicators are said to be independent, which makes it possible to complete the "elementary zone". We prioritize the indicators through a priori calculation of 1 YM, the cross matrix, which clarifies the crossed delays of indicators correlated between them two by two in the business chain. The scheduling is obtained by means of successive permutations of the rows and columns of the matrix, from the indicators made first. We update AM by forcing all of the descriptive coefficients without any correlation to 0, then, taking into account the crossed delays, we swap the last non-elementary indicators in order to obtain a general form of the descriptive matrix that is as close as possible to its diagonal. Figure 14 shows the general staircase shape. The descriptive matrix of M tells us finally about

-18- genealogy within the observed business chain. And it is the correlation calculations that allow us to get as close as possible to all these filiations. Then, from the interpretation of the descriptive matrix AM thus obtained, we deduce the connectivity matrix Aab. We deduce from the Aäb reading the number of KPIs finally present in the observed business chain. We clearly identify KPI strings. Finally, for each KPI chain, we construct the descriptive matrix AN and the connectivity matrix Am, without redoing the calculations, simply by relying on the results specific to the entire business chain. We can then move on to the construction stage of the Petri net.

The computation of the cross-correlations plays an important role in the organization of the descriptive matrix of M, just like that of JVLkp; Nevertheless, this calculation is not simple a priori and may even be impossible in certain cases, especially if the business chain is too complex. We explain below the descriptive matrix as soon as the so-called valid correlations are obtained, without it being necessary to go through the cross correlation calculations, the scheduling being de facto expressed via the experience feedback, or randomly the case applicable. Here are the different cases that we can encounter in the case of a KPI JVLkp chain; =: - the simple redundant character in figure 15. - the duplicate character in figure 16. - the multiple redundant character in figure 17. - the indicator link in figure 18. - the indicator overload in figure 19. - the redundant overload in figure 20. - the general interpretation in figure 21.

We here automate the writing of Petri nets since knowledge of KPI strings. The Petri net is a classic mathematical tool for describing relationships between conditions and events and for modeling the behavior of dynamic discrete event systems. A Petri net is a kind of oriented tree also called alternating bipartite graph, that is to say that there is alternation of types of nodes. We are then interested in the circulation of marks within this oriented tree. In the representation of a KPI chain, this oriented tree takes the form of a pyramid. Consider two possible processing algorithms. The descending algorithm consists of the construction of the Petri net from the KPI to the supposedly elementary indicators. This algorithm implies random and recursive stacking. During each cycle, the algorithm checks the connections between the supposedly elementary indicators. But it is necessary to wait for the appearance of uncorrelated indicators so that the algorithm discards this proposition of the result before starting a new random and recursive cycle again. This method of treatment is therefore not very advantageous. The upstream algorithm takes into account, from the set of indicators present within the KPI chain, filiations and therefore the genealogy resulting from the calculation of correlations and the interpretation of the descriptive matrix. If the ordering of the indicators is mastered, which implies that the set of cross-correlations is calculated, and if the completeness of the data is verified, which implies that the KPI chain is exhaustive to the point of avoiding indicator overloads and multiple redundant characters, the upstream algorithm then allows two types of Petri net: - f the parallel Petri net. Let be the ordered KPI string JVLkp; {11,12,13,14,15,16,17,18,19,110}, and shown in FIG. 22 as an example of a parallel Petri net. Figure 23 illustrates the descriptive matrix and the connections in the case of the parallel Petri net. - the linear Petri net. Let be the ordered KPI string JVLkp; f = {11,12,13,14,15,16,17,18,19}, and shown in FIG. 24. This is an example of a linear Petri net. Figure 25 shows the descriptive matrix and the connections in the case of the linear Petri net. In these two examples, the connectivity matrix is identical for a different number of indicators. In both cases, it is a linear stack. We present here the theorem of the rising algorithm. In general, to proceed with the generation of the Petri net, the upstream algorithm must operate by successive iterations t - t + 1, from the threshold represented by the set of elementary indicators, on which the possible redundant characters have been applied. , by combining all the elementary or induced indicators already available, in order to find all the induced indicators and missing KPIs resulting from the superposition of elementary indicators. At each iteration, the upstream algorithm must ensure that the integrity rules specific to the redundancy or overlay operations are respected. The process continues until the final KPI is obtained. It should be noted that, at each iteration t, the upstream algorithm must preserve the integrity of the indicators already obtained at the iteration t-1. To clarify the rules of the upstream algorithm, let us now introduce the notion of a link, knowing that a KPI chain is a complete link including all the observed indicators, including the KPI. The principle of the upstream algorithm therefore consists of finding, from the threshold represented by all the elementary indicators, the set of missing links until the final KPI is obtained. Let be a link v of the considered KPI chain. This link gives us two pieces of information: a set of data represented in the form of an ordered triplet comprising: elementary indicators; - indicator links; 10 - redundant characters. a connectivity matrix denoted U ,, such that: UX E v _ {0,1}; - Vi, j E {1 ... x}, we associate with any identified link and denoted Lu the number, or 0 if there is no connection knowing that 8u = 0, Vi E {1 ... x}; UX [u, i] iU; i = Su = Sji = u1; U ,, is a symmetrical hollow square matrix whose diagonal is always zero. To complete our step of regulating the rising algorithm, we must consider at least three links in the KPI chain. Also, there are two other links `i% and 0, respectively having for matrices of connectivity: Vl, and WZ. We now consider the two possible operations within the Petri net. Let the redundancy operation v = Cari: - rule r1: 25 `induced and integrated test (previously realized), or elementary Vl, is connected. - rule r2: l / = V x Cari V U (; 0; (Carj)) - rule r3: v respects the constraints resulting from correlation calculations. Rule r4: U ,, is connected the oriented graph of U ,, is strongly connected. Let the operation of superposition v = [] L, 7 (commutative): 2949585 -21- - rule s1: - `induced and integrated test (previously realized), or elementary Vl, is connected; - West induces and integrates (previously realized), or elementary WZ is connected. - rule s2: 5 `2nW = 0. - rule s3: = [2+! ] ~; ___. Seen W u (0; (Lu W)) - rule s4: v respects the constraints of the correlation calculations. 10 - rule s5: U ,, is connected the oriented graph of U ,, is strongly connected. In order to clarify the rules of the upstream algorithm, here is a simulation built on the basis of a fictitious KPI string. Let the ordered KPI chain JVLkpi = {11, I2, I3, I4, I5, I6,17,18, I9, I1o, I11, I12}, whose graph of the superimposed bonds can be that illustrated in FIG. 26. In the case of a KPI chain, the stacking of the elementary indicators within gVLkpi. is linear as illustrated in FIG. 27. The descriptive matrix and the connectivities of this KPI chain are illustrated in FIG. 28. From these three representations, we can describe all the links that are necessary for the smooth running of the upstream algorithm. of the generation of the Petri net: - lkpi = ((I1, I2, I3, I4, I5); (L12, L23, L34, L45); (Car6, Car10, Car12)); 4111 ((I1, I2, I3, I4, I5); (L12, L23, L34, L45) (Caro Car10)); 4I10 ((I1, I2, I3); (L12, L23); (Car10)); JYL 119 11912 913); (L12, L23); w) - 418 ((14495); (L45); (Car6)); - M1 = ((I1, I2); (L12); 0); - 9i6 = ((I5) '0' (Car6)) We see that the principle is the same as that of Russian dolls. But it is better to anticipate the computer usage by giving these writes a general form which uses only the identifiers of the KPI string indicators. Here is a more appropriate handwriting for computer operation: = ((I1, I2, I3, I4, I5); (I79I99I119I8); (I69I109I12)); = ((11, 12, 13, 14, 15); ((1,1,12913); (17919); (110)); - 9VLi9 ((I1 9 I2 9 I3); (I7 9 I9); w); J1418 ((14 9 I5), (I8), (I6)); - JVLi7 = ((I1 9 I2); (I7); w); J1416 ((I5), O, (I6)). 10 This list has a total of 7 links and is therefore not sufficient. We need to add to this list 5 additional singleton-type links since they are only elementary indicators: - 94.5 ((I5); o; o) - 9VLi4 ((I4); 0; w); -913 ((I3); 0; 0) -9VLi2 = ((I2); 0; w); - JVLi 1 = ((I i); w; 0). Thus, here is the ordered list, according to the upward algorithm, of the operations making it possible to construct the Petri net of the considered KPI: -JVLi6 = M5xI6 25 - Mill = 9VLi8 + JVLi10 1111; - 9VLi12 = JVLkpi = 9VLi11 x 112. The links of the lines relating to JVLi7 and MVLM8 can be made simultaneously. Finally, we are now rewriting the entire KPI chain, which amounts to completely reconstructing the Russian doll: - Mpi = Jl'Li11 X 112 e - JVLkpi = [9VLi8 + JVLi10 1111 X / 12 e 5 - JVLkpi = [[JVLi4 + 9VLi6] 18 + 9VLi9 X 110 1111 X 112 e - JVLkpi = [[\\ I4 h 0 0) + Ji / t, 5 X 16 1/8 + LJVLi3 + J1417 119 X 110 1111 X 112; - JVLkpi = [[I4); 0; 0) + I5); 0; 0) X16] 18 ... + [\\ I3); 0; 0) + [m 1 + Ji / A2 X 110 1111 x 112; - JVLkpi = [[((14 h 0; 01 + ((I5 h 0; 01 X 16 1/8 ... 10 + [\\ I3); 0; 0) + [\\ '1); 0; 0) + ((i2); 0; o) x1101111 x112. We can further simplify this writing by replacing the singleton-type links by the elementary indicators. Here is the definitive writing or code of the Petri net of the KPI chain observed: - JVLkpi = [[14 + 15X / 6] 18+ [13+ [11 + 12] 17] / 9x 110] 111 X 112. 15 Thus, here are the three successive states by which we passed during the processing of correlations within the considered KPI chain: J4kpi = 111912, 139199159 169179 18 9 19 9 110 911, '12}, - Mpi OI19I29I39I49I5); 79'99'119'8); ('69'109'12)), - JVLkpi = [[I4 + / 5 X / 61/8 + [I3 + [I1 + / 21/71 / 9X / 10 1/11 X / 12. 20 Now let's see how we can simply find the Petri net since knowing the KPI string. The state of a KPI can therefore be modeled by a tree of the Petri net type, each place of which represents an indicator in a given state. In computer science, this tree is encoded as a well-parented chain of symbols, where each symbol represents either an indicator or an operation, and each parenthesis level in the chain represents a particular branch of the Petri net. A well-parented chain is such that any open parenthesis is necessarily closed at another point in the chain. In the case of the KPI of the preceding example, the Petri net for modeling this indicator has a unique code represented by the following string: 2949585 -24- 94kpi = [[14 + 15X 16] 18+ [13 + [11 + l2] 17] 19X 110] 111 X 112. It is noted that the code of the Petri net can evolve over time. To describe this string, we use a formal grammar, also known as a rewriting system (a string of characters that replaces another). For this, we must explain the semantics thus found, and give us rules to describe all the operations performed by the different symbols of the chain during an iteration. The successive application of these rules to an initial symbol produces a state transformation sequence. Thus for each iteration, the present state of the Petri net is represented by a chain of symbols resulting from this sequence. The future state at the next iteration step is calculated by simultaneously transforming all the symbols of the present state using the rules specified by the following grammar: - definition of the symbols specific to the Petri net network: - l space is silent; - denotes an indicator of the KPI chain; 15 - + denotes a superposition operation; - x denotes a redundancy operation; - [denotes the opening of an overlay; -] designates the closure of an overlay; U denotes an operation between two links; - ((...); (...); (...)) denotes a link; - 0 denotes the absence of information in this part of the link. - definition of the ordered rules allowing the evolution at the following iteration step: - rule (a): the elementary indicators present in the chain of Petri network are replaced by the links of type singleton; the elementary indicators are easily identifiable since always placed after the symbols [and +. This rule only applies once at the beginning of treatment; ((Ii); o; o) - rule (b): the processing threshold of the upstream algorithm is updated before each iteration by replacing all the redundant characters applied only on the elementary or honest indicators, by the operations corresponding redundancy. The redundant characters concerned are represented by x l; and are always placed after the symbol), rule (a) having been carried out before rule (b) at the beginning of treatment; X I; u (o; o; (Ii)) 2949585 -25- - rule (c): at each iteration from the processing threshold, we perform all the most encapsulated indicator bindings in the Petri network string, replacing them with the corresponding overlay operations. The relevant indicator links are represented by the well-parented sequence 5 [... + ...] 1 ;, rule (b) having always been performed prior to rule (c); [... + ...] 1; ~ ... u ... u (o; (I.); O) - rule (d): this is the rule of Russian dolls also called simplification of the writing of the links. At the end of each iteration, the redundancy or superposition operations are replaced by the result links. The operations concerned are represented by the sequences of type ((1); (J); (K)) u ((L); (M); (N)) for redundancy or ((1); (J) (K)) u ((L); (M); (N)) u ((o); (P); (Q)) for the superposition; 1); (J); (K)) u ((L); (M); (N)) 1, L); (J, M); (K, N)) Let's apply these graph grammar rules to the Petri net string obtained in the previous simulation: 9lkpi = [[14 + 15X 16] 18+ [13+ [11 + 12] 17] 19X 110] 111 X 112. The successive rewritings are thus the following ones: According to rule (a): [[((14); 0; "_) +); 0; 0) X 16 7] 18 + [((13); "_ (J (y ~ J (] 17 7 (15 y ~ J (;" _ y ~ J () + [((I); 0; y ~ J () + ((12); 0; _)] I9X1101111x112 According to the rules (b) + (d):

y ~ J (y ~ J (y ~ J (7 [[((14); y "_) + ((I5); J" _ (I6)) 7] 18 + [((13); y ~ J ("_) + [((I l); y ~ J (" _) + ((I2); y ~ J ("_)] 17] 19 I9 X 110] 111 X 112 According to the rules (c) + (d): 7 [((14915); (18); (16)) + [((13); 0; 0) + ((11'12); (I7); o)] 1sx11o] 111X1,2

According to the rules (c) + (d): [((14915); (18); (16)) + ((11,12913); (17919); 0) X110] 111X112

According to the rules (b) + (d): [((14915); (18); (16)) + ((I1,12913); (17919); (110))] 111 X 112

According to the rules (c) + (d): ((II912913914915); (17 9 19 9 111 9 18); (169110)) x112

According to the rules (b) + (d): ((912913914915); (17 9 19 9 111 9 18); (16 9 110 9112 The Petri net corresponding to this result is illustrated in FIG. being able to represent the KPI chains in the form of a Petri net thus has two big advantages: it allows the data quality to be reinforced within the data warehouse and it allows the quantitative analysis of the data. thanks to the technical evolutions that this type of representation authorizes in terms of so-called timed, interpreted, stochastic, colored, continuous and / or hybrid Petri nets 5 Here the understanding of the model of movement of the marks within the network of These marks are the representation of the ordered realizations within the observed system.The values conveyed by these marks allow a reading of the distributions within the information system. one, combined with queuing type tools 10 then finds all its meaning. Within an organization such as a commercial company, the method that has just been presented can be implemented with the means illustrated in FIG. 30. A device 2 such as a server is connected to at least one base data 4 of a data warehouse (the database that can form the latter). The base contains the indicators 15 relating to at least one object such as the organization itself or its activities, this object taking several states (for example at successive dates), with each corresponding indicator of the values associated with the respective states. The device 2 comprises in particular a central unit and a memory forming means capable of identifying, as explained above, correlations between at least some of the indicators. For example, three indicators 11, 12 and 13 will be considered. The means are capable of forming groups such as chains each consisting of an indicator and indicators correlated with it and sufficient to deduce the latter. Here, we assume that h and 12 induce 13. It is therefore the group (1I, 12, 13). The means are capable of constructing the group's Petri net and coding it by means of grammar as indicated above. These means are capable of associating, in the base 4, with each of the indicators 11, 12 and 13 of the group, in a corresponding field, a data item M which is the codification obtained and which indicates an identity of the other indicators of the group and their relations. cause and effect. FIG. 30 also relates to another data item N relating to another group relating to 11 and 12 but not 13. Thus, the database 4 is constituted and then kept up to date. Indeed, when new indicators are created, correlations are sought and the implementation of the process enriches the database. The operation of the base can be done as follows. It is assumed that an operator such as a person consults the device 2 from his computer 6 connected to a telecommunication network 8 such as the Internet or an intranet via a

-27- server 10 of the organization. For example, he wants to know a recent value of the indicator 1l. The device 2 identifies in the base 4 the data M and N indicating an identity of the indicators 12 and 13 correlated with the indicator consulted 11. The device deduces from the codification by means of the grammar the cause-and-effect relationships between the indicators of the group M. It does the same with those of the group N. The device is also able to exploit these identities, for example by transmitting these identities to the device 10 responsible for building and modifying a web page 12 consulted by the operator, so that the device 10 will reveal the identities of the identified indicators and their relationships.

The operator is thus informed, after consulting the indicator 11 on the page, that he should also be attentive to the value of the indicators 12 and 13 which are correlated to him. A method is therefore implemented in which: the means 2 identify correlations between at least some of the indicators; the means 2 form groups each consisting of an indicator and indicators correlated to it and sufficient to deduce the latter; the means associate, in the base 4, with each of the indicators of the group, a data indicating an identity of the other indicators of the group. In the same method: the means identify in the base 4 at least one M and N data indicating an identity of the indicators 12 and 13 correlated to a consulted indicator 11 and forming with it a group such that the indicators of the group, except one, are sufficient to deduce the latter, and - the means exploit the identities of the identified indicators, for example by transmitting them on the network 8. The devices 2 and 10 comprise one or more computer programs comprising code instructions able to control the setting at least some of the steps of the method when executed on a computer. You can put this program on a recording medium such as a DVD disc, a hard disk or a flash memory. This program can be made available on a telecommunication network such as network 8 for download.

Of course, we can bring to the invention many changes without departing from the scope thereof.

Claims (10)

REVENDICATIONS1. A method for organizing a database (4) comprising variables, such as multi-state object-related indicators (1I, 12, 13), to each corresponding variable of respective state-related values, the method being characterized by that: - automated means (2) identify correlations between at least some of the variables; the means (2) form groups each consisting of one of the variables (13) and others (1I, 12) of the variables correlated with the latter and sufficient to deduce the latter; and the means (2) associate, in a database (4), with each of the variables of the group, a datum (M) indicating at least one identity of the other variables of the group. 2. Method according to the preceding claim wherein the means (2) construct a graph, such as a Petri net, of the group, for example by means of a rising algorithm. 3. Method according to the preceding claim wherein the means (2) encode the graph to produce the data (M). 4. A method for exploiting variables, such as multi-state object-related flags (1I, 12, 13), to each corresponding variable of respective state-related values, the method being characterized in that; automated means (2) obtain in a database at least one datum (M) indicating an identity (12, 13) of variables correlated with a predetermined variable (1I) and forming with it a group such that the variables of the group , except one (13), suffice to deduce the latter, the means thus identifying the correlated variables; and the means (2) exploit the identities of the identified variables, for example transmit them on a telecommunication network (8). 5. Method according to the preceding claim wherein the means (2) identify from the data of cause and effect relationships between the variables (1I, 12, 13) of the group. 6. Method according to any one of claims 4 and 5, wherein the means (2) control the mention on a web page (6) identities variables identified. -29- 7. Computer program characterized in that it comprises code instructions adapted to control the implementation of a method according to any one of the preceding claims when it is executed on a computer. 8. Device (2) for organizing a database (4) comprising variables (1I, 12, 13), such as indicators, relating to a multi-state object, to each corresponding variable of the values associated with the respective states, the device comprising means able: - to identify correlations between at least some of the variables (1I, 12, 13); - to form groups each constituted by one (13) variables and other (1I, 12) variables correlated to the latter and sufficient to deduce the latter; and - associating, in a database (4), with each of the variables of the group, a datum (M) indicating at least one identity of the other variables of the group. 9. Device (2) for exploiting variables (1I, 12, 13), such as indicators, relating to a multi-state object, to each corresponding variable of the values associated with the respective states, the device, optionally according to the claim preceding, being characterized in that it comprises suitable means; to obtain in a database (4) at least one datum (M) indicating an identity (12, 13) of variables correlated with a predetermined variable (1I) and forming with it a group such that the variables of the group, except one (13) suffices to deduce the latter, the means being thus able to identify the correlated variables; and - to exploit the identities of the variables identified, for example to transmit them on a telecommunication network (8). 10. Database (4) characterized in that it comprises: variables (1I, 12, 13) relating to a multi-state object, to each corresponding variable of the values associated with the respective states; at least one datum (M) in relation to at least one of the variables and indicating an identity of some of the variables correlated with it and forming with it a group such that the group variables, except for one (13), are sufficient to deduce this dernière.30