Method and device for generating a representative map of an N-dimensional data set, and use of said map for analyzing biological drift in a subject

Abstract

Method and device for generating a mapping representative of an N-dimensional data set, and use of said mapping for analyzing biological drift in a subject This method for generating a mapping representative of an N-dimensional data set, each dimension being associated with a given physical or biological parameter of a subject, comprises an acquisition of said N-dimensional data set in the form of P sets of N values, forming coordinates of P points in an N-dimensional subspace, and steps of: calculating (42) a graph representing said P points, each vertex of the graph corresponding to a first point of said subspace, and having a neighborhood comprising second points, k closest neighbors of the first point in the sense of a predetermined metric, k being a chosen positive integer;for each point of said subspace having an associated vertex in said graph, construction (54) of an associated convex hull, encompassing the points corresponding to the vertices of the neighborhood of said associated vertex, said mapping being formed by the union of the convex hulls associated with the points of the subspace. Figure for the abstract: Figure 2;

Description

Title of the invention: Method and device for generating a representative map of an N-dimensional data set, and use of said map for analyzing biological drift in a subject

[0001] The present invention relates to a method and a device for generating a mapping representative of an N-dimensional data set, and an associated computer program.

[0002] The invention also relates to uses of the mapping thus generated for the analysis of the biological drift of at least one of a number N greater than or equal to two of quantitative biological parameters in a subject.

[0003] In many fields of application, for example in the supervision and predictive maintenance of industrial systems or diagnosis based on physiological variables, values ​​of many parameters are measured.

[0004] The exploitation of parameter values, by data analysis methods, in particular for prevention and diagnostic assistance applications, is a rapidly growing field.

[0005] However, most known models are based, explicitly or implicitly, on assumptions of linear modeling of the data space. This is the case, for example, when data analysis uses linear regression.

[0006] However, in many application fields, the data to be analyzed, for example from measurements of various physical or biological parameters, actually belong to a non-linear subspace. In such a case, classical linear models and linear metrics are not applicable, or else provide an inaccurate or even erroneous result.

[0007] In particular, in the field of health, the analysis of biological parameters in a subject is an essential tool to aid in the diagnosis of a pathology.

[0008] Indeed, there are more or less direct links between certain biological parameters and given pathologies, for example between blood sugar and diabetes, iron levels and anemia, blood pressure and hypertension, the presence of a pathogen and an infection linked to this pathogen, sedimentation rate and an infection or inflammation, etc. The measurement of certain biological parameters thus makes it possible to direct or confirm a diagnosis. It also makes it possible to monitor a patient's response to a treatment, by following the evolution of one or more parameters linked to the disease concerned.

[0009] The analysis of a biological parameter generally consists of measuring the value of this biological parameter, and then to determine whether the value obtained is within a range of reference values ​​defined by a minimum reference threshold value and a maximum reference threshold value. Thus, the results of a biological analysis are generally classified into three categories: (i) below the minimum reference threshold value, (ii) between the minimum and maximum reference threshold values ​​or (iii) above the maximum reference threshold value. A value falling within a range of reference threshold values ​​will be considered "normal". The "normality" of a value that is outside a range of reference threshold values ​​is left to the judgment of the practitioner, in particular depending on the deviation of this value from one of the reference threshold values.

[0010] The analysis of biological parameters can also concern several biological parameters. Conventionally, each biological parameter has associated minimum reference threshold values ​​and maximum reference threshold values, and the analysis of several biological parameters is carried out by comparing each of the biological parameters considered to the reference threshold values ​​associated with it. If we consider N biological parameters, the estimation of normality amounts to verifying whether the values ​​of the N biological parameters for a subject belong to the N-dimensional hyper-cube formed from the reference threshold values ​​for each of the parameters. However, such an analysis does not allow for taking into account a possible correlation between the biological parameters considered.

[0011] The invention aims to remedy the aforementioned drawbacks by providing a method and device for modeling an underlying subspace representative of an N-dimensional data set of a subject.

[0012] A particular application is the application to the in vitro analysis of the biological drift of one or more quantitative biological parameters among N quantitative biological parameters considered jointly, to provide more precise biological analysis methods and / or making it possible to detect earlier one or more biological parameters whose values ​​correspond to an abnormal or potentially abnormal state of health.

[0013] For this purpose, the invention relates to a method for generating a mapping representative of an N-dimensional data set, N being an integer greater than or equal to 2, each dimension being associated with a given physical or biological parameter of a subject, the method being implemented by a processor of an electronic computing device, the method comprising an acquisition of said N-dimensional data set in the form of P sets of N values, forming coordinates of P points in an N-dimensional subspace, P being an integer greater than or equal to two. This method further comprises steps, implemented by the computing processor, of: - calculation of a graph representing said P points, the graph comprising vertices and edges, each edge connecting two vertices together, in which for a given vertex, the set of vertices connected to said vertex by an edge forms a neighborhood of said given vertex in the graph, in which each vertex of the graph corresponds to a first point of said subspace, and its neighborhood comprises vertices corresponding to second points of said subspace, the second points being the k closest neighbors of the first point in the sense of a predetermined metric, k being a chosen positive integer; - for each point of said subspace having an associated vertex in said graph, construction of an associated convex hull, encompassing the points corresponding to the vertices of the neighborhood of said associated vertex,

[0014] said mapping being formed by the union of the convex envelopes associated with the points of the subspace.

[0015] According to other advantageous aspects of the invention, the method for generating a mapping representative of an N-dimensional data set comprises one or more of the following characteristics, taken in isolation or in all technically possible combinations.

[0016] The method further comprises a calculation of at least one numerical value associated with each convex hull, the or each numerical value being calculated from an attribute of the convex hull.

[0017] The attribute of the convex hull is representative of a local density of points belonging to said convex hull.

[0018] For a given attribute, the numerical value is a quantile of a value of the attribute in a statistical distribution of the values ​​of said attribute.

[0019] The method comprises an association of a weight with each edge of the graph, as a function of the distance, according to said metric, between the points corresponding to the vertices of the graph connected by said edge.

[0020] The metric is the Euclidean distance in N dimensions.

[0021] The step of calculating the graph comprises a sub-step of connecting non-connected components, each component being a sub-graph, the connection step comprising an addition of an edge between vertices each belonging to a distinct non-connected component, and an addition of a connection neighbor in the neighborhood of the points corresponding to said vertices.

[0022] The graph calculation step includes a sub-step of symmetrization of the neighborhoods associated with the P points.

[0023] The method further comprises an identification and storage of extreme points of the union of the convex envelopes, each extreme point being an external point of a of said convex envelopes and which does not belong to another of the convex envelopes.

[0024] The invention also relates to a device for generating a mapping representative of an N-dimensional data set, N being an integer greater than or equal to 2, each dimension being associated with a given physical or biological parameter of a subject, the device being configured to acquire the N-dimensional data set in the form of P sets of N values, forming coordinates of P points in an N-dimensional subspace, P being an integer greater than or equal to two, the device comprising a calculation processor configured to implement: - a module for calculating a graph representing said P points, the graph comprising vertices and edges, each edge connecting two vertices together, in which for a given vertex, the set of vertices connected to said vertex by an edge forms a neighborhood of said given vertex in the graph, in which each vertex of the graph corresponds to a first point of said subspace,and its neighborhood comprises vertices corresponding to second points of said subspace, the second points being the k closest neighbors of the first point in the sense of a predetermined metric, k being a chosen positive integer; , - a convex hull construction module configured, for each point of said subspace having an associated vertex in said graph, to construct an associated convex hull, encompassing the points corresponding to the vertices of the neighborhood of said associated vertex, - a module for forming said mapping, said mapping being formed by the union of the convex hulls associated with the points of the subspace.

[0025] The invention also relates to a computer program comprising software instructions which, when executed by a computer, implement a method for generating a mapping representative of an N-dimensional data set as defined above.

[0026] According to another aspect, the invention relates to a method for analyzing a biological drift of at least one of a number N greater than or equal to two of quantitative biological parameters in a subject, the method comprising steps, implemented by a calculation processor, of:

[0027] -for a reference population formed of a group of P subjects, obtain values ​​of said N quantitative biological parameters forming an N-dimensional data set,

[0028] -generate a representative map of the N-dimensional data set by a map generation method as briefly described above, said car topography being a reference mapping associated with the reference population, and being represented in the form of the union of convex hulls of the N-dimensional space,

[0029] - obtaining values ​​of the N quantitative biological parameters of said subject,

[0030] -determine whether a point relative to said subject in the N-dimensional space of coordinates equal to the values ​​of the N quantitative biological parameters of said subject is located inside the union of convex envelopes,

[0031] - if said point relative to said subject is not located inside the union of envelopes convex, conclude that the combination of said N biological parameters of the subject is abnormal in view of the combinations of said N parameters observed in the reference subjects.

[0032] According to other advantageous aspects of the invention, each convex hull of said mapping has an associated numerical value, the numerical value being calculated from an attribute of the convex hull, the method for analyzing a biological drift further comprising, if said point relating to said subject is located inside the union of convex hulls, identifying the convex hull(s) containing the point relating to said subject, and deducing therefrom a level of drift as a function of the numerical value(s) associated with the hull(s) containing the point relating to said subject.

[0033] According to other advantageous aspects of the invention, the attribute is representative of a density of points of the convex hull, and a division of the drift levels is carried out according to quantile intervals of said attribute.

[0034] According to another aspect, the invention relates to a device for analyzing a biological drift of at least one of a number N greater than or equal to two of quantitative biological parameters in a subject, the analysis device comprising a calculation processor, configured to implement modules configured to:

[0035] -for a reference population formed of a group of P subjects, obtain values ​​of said N quantitative biological parameters forming an N-dimensional data set,

[0036] -generating a mapping representative of the N-dimensional data set by a mapping generation method as briefly described above, said mapping being a reference mapping associated with the reference population, and being represented in the form of the union of convex hulls of the N-dimensional space,

[0037] - obtaining values ​​of the N quantitative biological parameters of said subject,

[0038] -determine whether a point relative to said subject in the N-dimensional space of coordinates equal to the values ​​of the N quantitative biological parameters of said subject is located inside the union of convex envelopes,

[0039] - if said point relative to said subject is not located inside the union of envelopes convex, conclude that the combination of said N biological parameters of the subject is abnormal in view of the combinations of said N parameters observed in the reference subjects-

[0040] The invention will appear more clearly on reading the description which follows, given solely by way of non-limiting example, and made with reference to the drawings in which:

[0041] [Fig-1] [Fig.l] is a block diagram of a device for generating a map representative of an N-dimensional data set and a device for analyzing biological drift using mapping;

[0042] [Fig.2] [Fig.2] is a flowchart of the main steps of a method for generating a mapping representative of an N-dimensional data set according to one embodiment;

[0043] [Fig.3] [Fig.3] represents an example of data mapping in a two-dimensional subspace;

[0044] [Fig.4] [Fig.4] is a flowchart of the main steps of a method for analyzing a biological drift of at least one of a number N greater than or equal to two of quantitative biological parameters in a subject.

[0045] The invention relates to the generation of representative mapping of an N-dimensional data set, N being an integer greater than or equal to 2, in the context of data representative of physical or biological parameters of a subject, human or animal.

[0046] The term mapping refers to a spatial modeling of the underlying N-dimensional subspace, also called a "manifold" in mathematics or "manifold" in English, by providing an approximation of its shape and boundaries. As will be described in more detail below, the mapping is formed of envelopes associated with points of the N-dimensional subspace.

[0047] In the field of health, the invention finds applications in the in vitro characterization of the biological drift of a subject from at least two quantitative biological parameters.

[0048] In the context of such applications, the invention comprises a phase of generating a mapping representative of N-dimensional data in an N-dimensional subspace, each dimension being associated with a physical or physiological parameter.

[0049] For example, in the field of health, the mapping represents a reference population.

[0050] By "reference population", also called "reference group", we mean a population of individuals (or subjects) in which the biological parameters of interest are measured.

[0051] In a particular embodiment, the reference population is for example made up of healthy individuals, that is to say presenting a good general state of health.

[0052] The reference population comprises a number P of subjects, preferably at least 50 subjects, preferably at least 60 subjects, more preferably at least 70 subjects, at least 80 subjects, at least 90 subjects, more preferably still at least 100 subjects, at least 110 subjects, for example at least 120 subjects.

[0053] By “biological parameter” is meant here any parameter, quantitative or qualitative, allowing, directly or indirectly, the evaluation of the state of health of a subject.

[0054] The biological parameter is preferably selected from the group consisting of a serum parameter, an infectious parameter, a genetic parameter and a non-serum parameter (such as a clinical parameter or a lifestyle parameter).

[0055] Lifestyle-related parameters are preferably qualitative.

[0056] Serum, genetic, clinical, non-serum and infectious parameters can be quantitative or qualitative parameters.

[0057] The biological parameter, in particular the serum, infectious, genetic and certain non-serum parameters, can be measured in a biological sample of a subject.

[0058] The biological sample may be a blood sample, urine sample, cerebrospinal fluid sample, stool sample or a biopsy.

[0059] The biological sample may have undergone one or more pre-treatment steps prior to analysis (such as purification, centrifugation, filtration, precipitation, PCR and / or RT-PCT).

[0060] By "serum parameter" is meant here a biological parameter measured in a blood sample or a sample obtained from a blood sample (for example, in plasma).

[0061] The serum parameter may, for example, be selected from the group consisting of in: - the number, concentration and / or proportion of given blood cells or blood cell populations: for example, the number, concentration and / or proportion of red blood cells, leukocytes, polyneutrophils, polyeosinophils, polybasophils, monocytes, lymphocytes or platelets, - blood count (CBC), - hemoglobin concentration, - hematocrit, i.e. the volume occupied by red blood cells in a given volume of whole blood, - the platelets, - the sedimentation rate, - VGM (Mean Cell Volume), - CGMH (Mean Blood Hemoglobin Concentration), - TCMH (Mean Corpuscular Hemoglobin Content), - the quantity, concentration and / or proportion of a given enzyme, for example lipase, the quantity, concentration and / or proportion of Alkaline Phosphatase, Gamma GT, transaminase TgO or transaminase TgP, - the quantity, concentration and / or proportion of lipids, in particular total cholesterol, HDL cholesterol, LDL cholesterol or triglycerides, - blood sugar, - the quantity, concentration and / or proportion of chlorine, uric acid, urea, or creatinine, - protein electrophoresis, in particular the quantity, concentration and / or proportion of total protein, albumin, alpha 1 globulin, alpha 2 globulin, beta 1 globulin, beta 2 globulin and / or gamma globulin, - the protein profile, in particular the quantity, concentration and / or proportion of serum proteins, such as IgA, IgG, IgM and / or IgE, - an ionogram, in particular the quantity, concentration and / or proportion of one or more ions, such as sodium, potassium, calcium, magnesium, chlorine, and / or bicarbonate, for example in blood plasma, - the quantity, concentration and / or proportion of one or more hormones, or - the blood group (e.g. ABO blood group).

[0062] The inventors noted that when a plurality of quantitative biological parameters are taken into consideration, at least some of the parameters being correlated, the evaluation of normality by analysis of the value taken by each of the biological parameters taken independently, in relation to the associated minimum and maximum reference threshold values, is not satisfactory.

[0063] The generation of a mapping of an N-dimensional data set makes it possible to represent the values ​​of the biological parameters of a reference population and to generalize “normality” by the membership or not of a set of values ​​of the N biological parameters considered of a subject to the mapping represented in the form of a union of convex envelopes.

[0064] [Fig.l] represents a device 2 for generating a mapping representative of an N-dimensional data set and for analyzing a biological drift of a subject.

[0065] The device 2 is a programmable electronic device, for example a computer or a plurality of computers connected to each other.

[0066] The device 2 comprises a user interface 4, comprising an input / output interface 6 and a display screen 8, allowing to present results and receive commands and data from a user.

[0067] Alternatively, the user interface 4 is a touch screen which then combines the input / output interface and display screen functionalities.

[0068] The device 2 further comprises a calculation processor 10, an electronic memory unit 12, and a communication module 16 configured to connect to a communication network using a communication protocol.

[0069] The various elements 4, 10, 12, 16 are configured to communicate with each other via a data communication bus 15.

[0070] The calculation processor 10 is configured to implement:

[0071] - a module 20 for acquiring a set of N-dimensional data forming co ordinates of P points in an N-dimensional subspace,

[0072] - a module 22 for calculating a graph representing the P points,

[0073] - a module 24 for constructing a convex envelope associated with each of the P points,

[0074] - a module 26 for training and representing a map 30 of the game of N-dimensional data, the mapping 30 of the N-dimensional data set being formed by the union of the convex hulls thus constructed;

[0075] -optionally, a module 28 for using the mapping 30 for analyzing the biological drift of a subject.

[0076] A representation of the mapping 30 is stored in the electronic memory unit 12.

[0077] Optionally, the module 26 also performs a calculation and an association of at least one numerical value with each convex hull. Preferably, the numerical values ​​associated with the convex hulls are also stored in the electronic memory unit 12.

[0078] A programmable electronic device 2 comprising a module 28 for using the mapping 30 for analyzing the biological drift of a subject is a device for analyzing the biological drift of at least one of a number N greater than 2 of quantitative biological parameters in a subject.

[0079] In one embodiment, the modules 20, 22, 24, 26 are implemented in the form of software instructions forming a computer program, which, when executed by a programmable electronic device, implements a method for generating a mapping representative of an N-dimensional data set as described.

[0080] In one embodiment, the modules 20, 22, 24, 26, 28 are produced in the form of software instructions forming a computer program, which, when executed by a programmable electronic device, implements a method for analyzing a biological drift of at least one of a number N greater than or equal to two of pa- quantitative biological parameters in a subject as described.

[0081] In a variant not shown, the modules 20, 22, 24, 26, 28 are each produced in the form of programmable logic components, such as FPGAs (Field Programmable Gate Arrays) or microprocessors, GPGPU components (General-purpose processing or graphics processing), or even dedicated integrated circuits, such as ASICs (Application Specific Integrated Circuits).

[0082] The computer program comprising software instructions is further capable of being recorded on a non-transitory, computer-readable information recording medium. This computer-readable medium is, for example, a medium capable of storing electronic instructions and of being coupled to a bus of a computer system. For example, this medium is an optical disk, a magneto-optical disk, a ROM memory, a RAM memory, any type of non-volatile memory (for example EPROM, EEPROM, FLASH, NVRAM), a magnetic card or an optical card.

[0083] With reference to [Fig.2] we describe the main steps of generating a mapping representative of an N-dimensional data set, N being an integer greater than or equal to 2, each dimension being associated with a physical or biological parameter of a subject (human or animal), previously defined according to the intended use.

[0084] The method comprises a step 40 of acquiring P sets of N values, P being an integer greater than or equal to 2.

[0085] For example, P is greater than or equal to 50, each set of N values ​​being representative of the values ​​of the biological parameters considered for a subject of a reference population.

[0086] Each set of N values ​​forms coordinates of a point of the N-dimensional subspace considered, hereinafter called the initial point.

[0087] The method further comprises a step 42 of calculating a graph representing the P initial points.

[0088] A graph is a data structure comprising vertices and edges, each edge connecting two vertices together.

[0089] Step 42 of calculating a graph comprises several sub-steps described below.

[0090] Step 42 comprises a sub-step 44 of initializing the graph, each initial point being associated with a vertex of the graph.

[0091] It also comprises a sub-step 46 of determining, for each initial point, called first point, a neighborhood formed of the k second points, called neighbors or neighboring points, closest to the first point in the sense of a predetermined metric, also called first metric, for example the metric eu Clidean in the RA space, and connected by an edge between the vertex associated with the first point and each vertex associated with a second point in the neighborhood. The number k is a predetermined integer, for example greater than or equal to 1, preferably greater than or equal to 10, k being less than or equal to P.

[0092] In addition, a weight is associated with each edge (step 48), the weight being equal to the distance according to the first metric (eg Euclidean distance) between the two points associated with the vertices connected by the edge.

[0093] A second metric is defined to estimate the distance between points of the N-dimensional subspace, which is a metric associated with the graph: the distance between two points according to this second metric is equal to the smallest sum of the weights associated with the edges connecting the vertices corresponding to the two points in the graph.

[0094] Step 42 then comprises a symmetrization sub-step 50, consisting of adding connecting edges, if necessary, so as to ensure that if a point A is part of the neighborhood of a point B, point B is also part of the neighborhood of point A.

[0095] Thus, where appropriate, one or more additional points are added in the vicinity of a first point given in the symmetrization step.

[0096] For each point, at the end of the symmetrization sub-step 50, the associated neighborhood is stored, this neighborhood comprising the “natural” neighbors (the k nearest neighbors), as well as, where appropriate, the forced neighbors obtained by symmetry.

[0097] Finally, step 42 comprises a step 52 of connecting, where appropriate, subgraphs which are not connected by edges.

[0098] If the obtained graph is composed of C components, each component being a graph of points connected by edges, identifiable by a depth-first traversal algorithm.

[0099] In other words, a component C is a subset of points of the graph such that it is possible to connect any two points of C by a path connecting one or more edges.

[0100] If C is strictly greater than 1, then the graph formed is an unconnected graph, and the following process implemented in the connection step 52 makes it possible to connect the C components by minimizing the sum of the weights of the added edges: • SI- association with each component of an identifier being an integer; • S2-calculation and storage of the distance, according to the first predefined metric (eg the Euclidean distance), of each pair of points located in different components and for each pair of different components, storage of the pair of points with the smallest distance; • S3 - connection of the two components having the minimum distance, via the edge linking the points of the pair of points having the smallest distance; • S4 - update of component identifiers so that both components that have just been connected have the same identifier; • S5 -reiteration of steps 3 and 4 until all components have the same identifier. A total of -Cl iterations are required to obtain a single remaining connected component (i.e. connected graph).

[0101] Thus, at the end of the connection step 52, a fully connected graph is obtained, and some of the neighborhoods are enriched with an additional neighbor called a connecting neighbor.

[0102] In the end, the constructed graph represents the set of P initial points, and each vertex of the graph is connected to all other vertices of the graph by traversing the edges of the graph. In other words, all vertices are connected via one or more edges of the graph.

[0103] In other words, at the end of step 42, each initial point called first point is associated with a first vertex of the graph, and has second neighboring points, the second neighboring points being the initial points associated with second vertices, each second vertex being connected to the first vertex by an edge.

[0104] The neighborhood of a first point, associated with a vertex of the graph, is formed of the second points, whose associated vertices are connected directly (by a single edge) to the first vertex. This neighborhood is stored for each first point.

[0105] The neighborhood of a first given point comprises at least the points which are its k closest neighbors (called natural neighbors), but may also comprise one or more points resulting from the symmetrization (called forced neighbors), and one or more points resulting from the connection step (called connecting neighbors).

[0106] The method then comprises a step 54 of calculating (or constructing), for each initial point having an associated vertex in the graph, an associated convex hull, constructed from the points corresponding to the vertices of the natural neighbors of said associated vertex. The mapping representative of the initial data set is then formed by the union of the calculated convex hulls.

[0107] According to a first variant, the convex envelope is constructed on the natural neighbors.

[0108] According to a second variant, the convex hull is constructed on the natural neighbors and the forced neighbors.

[0109] According to a third variant, the convex hull is constructed on the natural neighbors, the forced neighbors and the connecting neighbors.

[0110] In one embodiment, the calculation of the convex hulls of a set of points P is performed via an implementation of the algorithm known as the “QUICKHULL ALGORITHM”, described in particular in the article “The Quickhull Algorithm for Convex Hulls” by C. Bradford Barber et al, published in ACM Transactions on Mathematical Software, vol. 22, pp 469-483 and available at [YES]

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[0126] following: https: / / dl.acm.org / doi / 10.1145 / 235815.235821. For example, programmed functions for processing convex hulls are used. The method involves, for each convex hull, the memorization of the different faces of the convex hull (which forms a polytope) and the R points, among the points of the neighborhood, located on the surface of the convex hull. As is known, to check whether a point lies inside a convex hull, it is necessary to check whether the given point can be expressed as a linear combination of the S vertices {pl,...,pS} of the convex hull, such that the coefficients of the linear combination are all positive and their sum is equal to one. In other words: the elements belonging to a convex hull whose vertices are a set of S points are the points x which can be written in the form: Where the coefficients X; are positive real numbers such that: ¢ / .= 1 The union of the computed convex hulls forms a mapping of the N-dimensional data space. The method further comprises an identification 56 of the extreme points, that is to say on the surface of the union of the convex envelopes. A point belonging to a convex hull can be located inside it, or on the surface of this convex hull. A point is on the surface of a convex hull if it belongs to one of the faces of this convex hull. A point is extreme, and therefore considered on the surface of the union of convex hulls, if it is on the surface of all the convex hulls to which it belongs. The extreme points are stored, which allows the contour of the calculated map to be characterized. In addition, the method includes a calculation 58 and a storage of at least one numerical value associated with each convex hull. For example, the numeric value is a statistical quantile of an attribute associated with the convex hull in the distribution of that attribute. The attribute is for example the volume of the convex hull, calculated by an algorithm such as "QUICKHULL ALGORITHM" mentioned above. Alternatively, the attribute is the average distance according to the first metric (eg Euclidean distance) between the initial point for which the convex hull was calculated and its k nearest neighbors. Advantageously, these attributes reflect a local density of points.

[0127] In one embodiment, a value of the chosen attribute is calculated for each convex hull.

[0128] The distribution of the values ​​obtained makes it possible to associate a statistical rank with each of them and then a quantile by dividing this rank by the number of values ​​in the distribution. In statistics, the rank q of a statistical sample is equal to the g-th smallest value. The rank of a value relative to a set of values ​​corresponds to its index in an increasingly ordered sequence of these values. Low quantiles of convex hull volume, or of average distances to the k-nearest neighbors will then be associated with a high density and high quantiles with low densities.

[0129] Preferably, following the construction of the mapping, the following are stored: • the set of convex hulls; • the faces constituting each convex envelope; • the vertices of each convex hull; • one or more associated numerical values, i.e. the values ​​of different attributes (volume, distance to nearest neighbor, local point density, surface area of ​​the envelope or any attribute relating to the envelope), • the neighbors of each point: • natural neighbors (k nearest neighbors) • neighbors forced by symmetrization, • connecting neighbors • the nearest neighbor graph as described above: • its vertices • its edges and their associated weights • the set of extreme points, following the calculation of the extreme points. • the distribution and quantiles of the attribute associated with each convex hull.

[0130] With reference to [Fig.3], as a simplified, non-limiting example, a 2-dimensional data map (N=2) is illustrated.

[0131] The points indicated by circles correspond to the initial points of the reference population and form a cloud of points, represented in the two-dimensional space of the parameters "hemoglobin" (in g / L) and "albumin" (in mmol / L). Each of the parameters has associated minimum and maximum reference threshold values, which are illustrated in the figure, namely Vl_m and V 1_M for albumin, and V2_m and V2_M for hemoglobin.

[0132] The resulting Carto mapping is illustrated schematically, delimited by a dotted line outline in [Fig.3]. In addition, three convex hulls EC_1, EC_2, EC_3, associated with respective initial points A, B, C are represented.

[0133] Points SI, S2, S3 are points corresponding to measurements carried out for distinct subjects for which the possible biological drift of the “albumin” and “hemoglobin” parameters is to be estimated.

[0134] Considering the biological parameters independently amounts to deciding that from the moment when the values ​​of the biological parameters of a subject are inside the rectangle corresponding to the respective threshold values ​​associated with these two parameters (rectangle represented in [Fig.3]), the subject is "normal" in view of the reference population.

[0135] Point SI corresponds to an albumin value between Vl_m and V1_M, but a hemoglobin value greater than V2_M.

[0136] Points S2 and S3 both correspond to albumin values ​​between Vl_m and V 1_M and hemoglobin values ​​between V2_m and V2_M.

[0137] According to the independent interpretation of the parameters (i.e. the hemoglobin and albumin parameters taken separately), point SI is not considered “normal”, but points S2 and S3 are normal.

[0138] However, in view of the distribution of the initial points, using the Carto mapping generated by the method described, it will be considered that the point S2 is not “normal”, or in other words is outside the reference threshold values, because the values ​​of the parameters for this subject S2 are outside the union of convex envelopes calculated from the initial points, even if it is located in the admissible range of each of the reference threshold values.

[0139] Point S3 is located inside one of the calculated convex hulls, so it is considered "normal" in view of the union of the convex hulls, therefore of the global mapping representative of the reference population. A drift may nevertheless be observed for point S3, and a drift level calculated according to the numerical value associated with the convex hull to which point S3 belongs, as explained in more detail below.

[0140] It should be noted that thanks to the use of mapping, the representation of the parameters of the reference population is much more precise than when the biological parameters are considered independently.

[0141] A method for analyzing a biological drift of at least one of N quantitative biological parameters in a subject, the number N being greater than or equal to two, is described with reference to [Fig.4].

[0142] The method comprises a step 60 of generating the mapping representation of a reference population for the N quantitative biological parameters considered, in the form of a union of convex envelopes, by implementing the method described above.

[0143] For example, such a mapping is generated during a prior step and stored in a memory of the programmable electronic device implementing the method or in a database stored on a remote server.

[0144] The method also comprises obtaining 62 of the values ​​of the N biological parameters for a subject considered at a given time instant Ti: Vt = {, v / jV} These values ​​are provided to the programmable electronic device.

[0145] Then, it is determined (step 64) whether a point p(V;) of the N-dimensional space of coordinates equal to the values ​​of the N quantitative biological parameters of the subject {v1? ..., viN] lies inside the union of convex envelopes.

[0146] In one embodiment, in step 64 it is checked whether there exists a convex hull which contains the point p(Vi).

[0147] If one or more convex hulls contain the point p(Vi), the point is considered to have normal values.

[0148] Step 64 is then followed by a step 70 during which the convex envelope Cm to which the point p(Vi) belongs is identified and the numerical value Val(Cm) associated with the convex envelope Cm is obtained. If p(Vi) is contained by several convex envelopes, p(Vi) is identified with the smallest value associated with the convex envelopes obtained.

[0149] The numerical value Val(Cm) associated with the point p(Vi) makes it possible to assign it a drift level (step 72).

[0150] The more the point is located in a low density area, the more it is considered to be drifting.

[0151] In one embodiment, a division of the drift levels is carried out according to intervals of quantiles of volumes of convex hulls or of average distance to the k nearest neighbors, two attributes inversely correlated with the density.

[0152] The optimum (or absence of drift) is defined for attribute values ​​associated with a quantile located in a first interval [0; XI], with for example Xl=68.26. A drift (or first level of drift) is defined for attribute values ​​associated with a quantile located in a second interval [XI; X2], with for example X2=95.44. A significant drift (or second level of drift) is defined for attribute values ​​associated with a quantile located in the interval [X2; X3] with X3=99.7. A very significant drift (or third level of drift) is defined for attribute values ​​associated with a quantile located in the interval [X3; 100].

[0153] For example, referring to [Fig.3], assuming that the numerical value of the convex hulls is associated with their volume, if p(Vi) is located in the convex hull of point A, whose convex hull associated with a low volume, and therefore an associated quantile located in the interval [0; 68.26], p(Vi) is considered to be at the optimum (absence of drift).

[0154] If p(Vi) is located in the convex hull of point B whose convex hull associated with a volume whose quantile is in the interval [68.26; 95.44], it is considered to have a first level drift.

[0155] If p(Vi) is located in the convex hull of point C whose convex hull associated with a larger volume (greater than the respective volumes of the convex hulls associated with points A and B) and therefore an associated quantile in the interval [95.44; 99.7]; point p(Vi) is considered to have a significant drift (second level of drift), because the quantile of the volume is very high.

[0156] Thus, when the numerical value associated with each convex hull is representative of the statistical distribution of the points of the reference population, the more the point p(Vi) is located in a dense zone, the more it is considered “normal” (in other words the level of drift is low, or even zero and therefore the point is at the optimum), and the more it is located in a low density zone, the higher the level of drift.

[0157] If none of the convex hulls contains the point p(Vi), then the point is considered abnormal in view of the reference population approximated by the union of the convex hulls, and therefore probably pathological.

[0158] It is then planned to calculate a distance between the point p(Vi) and the union of the convex envelopes and to store this distance (step 66).

[0159] Optionally, an alert is raised (step 68) to indicate the presence of parameter values ​​outside the mapping of the reference population and / or the calculated drift level. The value of the distance calculated in step 66 is optionally transmitted and / or displayed when the alert is raised.

[0160] According to one embodiment, it is envisaged to repeat the method for the same subject in order to follow the evolution over time of the values ​​of the biological parameters considered, or in other words, the trajectory of the successive points whose coordinates are the values ​​of the biological parameters considered for the subject at offset time instants Ti.

[0161] This then makes it possible to add a time dimension, and to calculate a trend over time.

[0162] The use of the mapping of the N biological parameters of a healthy reference population makes it possible to carry out an in vitro diagnosis of a disease according to the membership of the values ​​of the biological parameters considered of a subject, at a time instant or at a succession of shifted time instants, to an N-dimensional subspace representative of the healthy reference population. When a potential drift of the values ​​of the biological parameters considered of the subject is observed, the diagnosis of a disease or of a risk of suffering from a disease associated with the N biological parameters is made.

Claims

Claims

1. Method for generating a mapping representative of an N-dimensional data set, N being an integer greater than or equal to 2, each dimension being associated with a given physical or biological parameter of a subject, the method being implemented by a processor of an electronic computing device, the method comprising an acquisition of said N-dimensional data set in the form of P sets of N values, forming coordinates of P points in an N-dimensional subspace, P being an integer greater than or equal to two, the method being characterized in that it further comprises steps, implemented by the computing processor, of: - calculating (42) a graph representing said P points, the graph comprising vertices and edges, each edge connecting two vertices together, in which for a given vertex, the set of vertices connected to said vertex by an edge forms a neighborhood of said given vertex in the graph,in which each vertex of the graph corresponds to a first point of said subspace, and its neighborhood comprises vertices corresponding to second points of said subspace, the second points being the k closest neighbors of the first point in the sense of a predetermined metric, k being a chosen positive integer; - for each point of said subspace having an associated vertex in said graph, construction (54) of an associated convex hull, encompassing the points corresponding to the vertices of the neighborhood of said associated vertex, said mapping (30) being formed by the union of the convex hulls associated with the points of the subspace.,

2. The method of claim 1, further comprising calculating (58) at least one numerical value associated with each convex hull, the or each numerical value being calculated from an attribute of the convex hull.

3. The method of claim 2, wherein said attribute of the convex hull is representative of a local density of points belonging to said convex hull.

4. A method according to one of claims 2 or 3, wherein, for a given attribute, the numerical value is a quantile of a value of the attribute in a statistical distribution of the values ​​of said attribute.

5. Method according to any one of claims 1 to 4, comprising an association (48) of a weight to each edge of the graph, as a function of the distance, according to said metric, between the points corresponding to the vertices of the graph connected by said edge.

6. A method according to any one of claims 1 to 5, wherein said metric is the Euclidean distance in N dimensions.

7. Method according to any one of claims 1 to 6, in which the step of calculating (42) the graph comprises a sub-step of connecting (52) / unconnected components, each component being a sub-graph, the connecting step (52) comprising an addition of an edge between vertices each belonging to a distinct unconnected component, and an addition of a connecting neighbor in the neighborhood of the points corresponding to said vertices.

8. Method according to one of claims 1 to 7, in which the step of calculating the graph comprises a sub-step of symmetrization (50) of the neighborhoods associated with the P points.

9. Method according to any one of claims 1 to 8, further comprising an identification (56) and storage of extreme points of the union of the convex envelopes, each extreme point being an external point of one of said convex envelopes and which does not belong to another of the convex envelopes.

10. Device for generating a mapping representative of an N-dimensional data set, N being an integer greater than or equal to 2, each dimension being associated with a given physical or biological parameter of a subject, the device being configured to acquire the N-dimensional data set in the form of P sets of N values, forming coordinates of P points in an N-dimensional subspace, P being an integer greater than or equal to two, the device comprising a calculation processor configured to implement: - a module (22) for calculating a graph representing said P points, the graph comprising vertices and edges, each edge connecting two vertices together, in which for a given vertex, the set of vertices connected to said vertex by an edge forms a neighborhood of said given vertex in the graph, in which each vertex of the graph corresponds to a first point of said subspace, and its neighborhood comprises vertices corresponding to second points of said subspace, the second points being the k closest neighbors of the first point in the sense of a predetermined metric, k being a chosen positive integer; - a module (26) for constructing convex hulls configured, for each point of said subspace having an associated vertex in said graph, to construct an associated convex hull, encompassing the points corresponding to the vertices of the neighborhood of said associated vertex, a module (26) for forming said mapping (30), said mapping (30) being formed by the union of the convex hulls associated with the points of the subspace.

11. A computer program comprising software instructions which, when executed by a programmable electronic device, implement a method for generating a mapping representative of an N-dimensional data set according to claims 1 to 9.

12. Method for analyzing a biological drift of at least one of a number N greater than or equal to two of quantitative biological parameters in a subject, the method being characterized in that it comprises steps, implemented by a calculation processor, of: - for a reference population formed of a group of P subjects, obtaining values ​​of said N quantitative biological parameters forming an N-dimensional data set, - generating (60) a mapping representative of the N-dimensional data set by a method according to claims 1 to 9, said mapping being a reference mapping associated with the reference population, and being represented in the form of the union of convex hulls of the N-dimensional space, - obtaining (62) values ​​of the N quantitative biological parameters of said subject, - determining (64) whether a point relating to said subject of the N-dimensional space with coordinates equal to the values ​​of the N biological parameters- quantitative logics of said subject is located inside the union of convex envelopes, - if said point relating to said subject is not located inside the union of convex envelopes, conclude that the combination of said N biological parameters of the subject is abnormal in view of the combinations of said N parameters observed in the reference subjects.

13. A method of analyzing biological drift according to claim 12, wherein each convex hull of said mapping has an associated numerical value, the numerical value being calculated from an attribute of the convex hull, the method further comprising, if said point relating to said subject is located inside the union of convex hulls, identifying (70) the convex hull(s) containing the point relating to said subject, and deducing therefrom (72) a level of drift as a function of the numerical value(s) associated with the hull(s) containing the point relating to said subject.

14. Method for analyzing a biological drift according to claim 13, in which said attribute is representative of a density of points of the convex hull, and in which a division of the drift levels is carried out according to intervals of quantiles of said attribute.

15. Device for analyzing a biological drift of at least one of a number N greater than or equal to two of quantitative biological parameters in a subject, the analysis device comprising a calculation processor, configured to implement modules configured to: - for a reference population formed of a group of P subjects, obtain values ​​of said N quantitative biological parameters forming an N-dimensional data set, - generate a mapping representative of the N-dimensional data set by a method according to claims 1 to 9, said mapping being a reference mapping associated with the reference population, and being represented in the form of the union of convex hulls of the N-dimensional space, - obtain values ​​of the N quantitative biological parameters of said subject,-determine whether a point relative to said subject in the N-dimensional space of coordinates equal to the values ​​of the N quantitative biological parameters of said subject is located inside the union of convex envelopes, - if said point relative to said subject is not located inside the union, convex envelopes, conclude that the combination of said N biological parameters of the subject is abnormal in view of the combinations of said N parameters observed in the reference subjects.

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