Method for clustering nodes of a textual network taking into account textual content, computer-readable storage device and system implementing said method

A computer-implemented method for clustering nodes i, j which can jointly generate a set of documents or datasets, said communications network comprising a number M of nodes, nodes i, j being associated with edges Aij of an adjacency matrix A,

• a document edge Wij of text data by edge Aij, the document edge Wij being a vector Wij=(Wij1, . . . , Wijd, . . . , WijDij) of size Dij the number of documents shared by or resulting of the interaction between the node i and the node j, where Wijd is the text of the dth document shared by or resulting of the interaction between the node i and the node j, the method comprising steps of:
• 1) a first step of initially clustering all the nodes into a predetermined number Q of clusters, for determining a first estimated clustering Y=Y1, Y2, . . . , YM), M being the number of nodes;
• 2) a second step of inference of a generative model, wherein edges Aij are modeled with a Stochastic Block Model (SBM) and, conditionally to the estimated clustering Y, the sets of documents Wijd between and within clusters are modeled according to a generative model of documents,
• the second step of inference comprising the following sub-steps:
• a. for each cluster q, determining from the estimated clustering Y, an estimated proportion ρq of the cluster q, an estimated probability πqr that a node included in the cluster q and a node included in the other cluster r are associated with text data in the network;
• b. determining from the estimated clustering Y, an estimated distribution R(Z,θ), and an estimated probability β, with:
• Zijdn a topic vector indicating a topic of the word n of the text document Wijd, said word corresponding to Wijdn, θqrk an estimated probability of the topic k of text data associated between the cluster q and the cluster r, making for a vector of topic proportions θqr, βkv a probability of each word v of dictionary being used in the topic k;
• the sub-step b) comprising the following sub-steps:
• b1. for each cluster q, aggregating all the messages Wijd of text data associated with all the pair of nodes (i,j) within the cluster q, so as to produce a first aggregate of text data associated with the cluster q, and for each cluster q, aggregating all the messages Wijd of text data associated with all the pair of nodes (i, j), from which one of the nodes i belongs to the cluster q and the other node j belongs to another cluster r, so as to produce at least one second aggregate associated to the pair of clusters (q,r),
• b2. processing the first and second aggregates to determine topics k corresponding to text data of the first and second aggregates, with a predetermined number K of topics being determined, and
• b3. processing the text data of the first and second aggregates to determine the distribution R(Z,θ) and the probability β;
• b4. iteratively repeating sub-step b1, b2 and b3 of second step 2);
• c. calculating a new estimated clustering Y of the nodes into Q clusters, in accordance with calculated probabilities (β, ρ, π and the estimated distribution R(Z,θ) of the sub-steps a and b of the second step, by determining, for each node i of the network, which optimal cluster provides a maximum value of a statistical criterion when said node i is assigned to said cluster, and assigning a node i to the determined optimal cluster;
• 3) a third step in which the second step 2) is repeated, with the new estimated clustering Y calculated in sub-step c and injected in the step 2), until a convergence criterion is fulfilled for determining and outputting a final clustering Y, the final proportion ρq, the final distribution R(Z,θ), the final probabilities πqr, and the final probability βkv.

A non-transitory computer-readable storage device having computer executable instructions stored therein for executing steps of:

• 1) initially clustering all the nodes into clusters, for determining a first estimated clustering Y=(Y1, Y2, . . . , YM), with M the number of nodes;
• 2) a second step of inference of the generative model, wherein edges Aij are modeled with a Stochastic Block Model (SBM) and, conditionally to the estimated latent clustering Y, the sets of documents Wi,jd between and within clusters are modeled according to the generative model,
• the second step of inference comprising the following sub-steps:
• a. for each cluster q, determining from the estimated clustering Y, an estimated proportion ρq of the cluster q, an estimated probability πq, that a node included in the cluster q and a node included in the other cluster r are associated with text data in the network;
• b. determining from the estimated clustering Y, an estimated distribution R(Z,θ), and an estimated probability β, with:
• Zi,jdn a topic vector indicating the topic of the word n of the text Wijd corresponding to Wijdn, θqrk an estimated probability of the topic k of text data associated between the cluster q and the cluster r, βkv a probability of each word v of dictionary being used in the topic k;
• the sub-step b. comprising the following sub-steps:
• b1. in the generative model, for each cluster q, aggregating all the messages Wijd of text data associated with all pairs of nodes (i,j) that are both within the cluster q, so as to produce a first aggregate of text data associated with the cluster q, and for each cluster q, aggregating all the messages Wijd of text data associated with all pairs of nodes (i,j), in which one of the nodes i belongs to the cluster q and the other node j belongs to another cluster r, so as to produce at least one second aggregate associated to the pair of clusters (q,r),
• b2. in the generative model, processing the first and second aggregates to determine topics k corresponding to text data of the first and second aggregates, and
• b3. processing the text data of the first and second aggregates to determine the distribution R(Z,θ) and the probability β;
• b4. iteratively repeating sub-step b1, b2, b3 of the second step 2);
• c. calculating a new estimated clustering Y, in accordance with calculated probabilities β, ρ, π and the estimated distribution R(Z,θ) of the sub-steps a and b of the second step, by determining, for each node i of the network, which optimal cluster provides a maximum value of a statistical criterion when a node i is assigned to a cluster q, and assigning a node i to the determined optimal cluster;
• 3) a third step in which the second step 2) is repeated, with the new estimated clustering Y calculated in sub-step c and injected in the step 2), until a convergence criterion is fulfilled for determining and outputting a final clustering Y, the final proportions ρq, the final distribution R(Z,θ), the final probabilities πqr, and the final probabilities βkv.

A computer system for clustering nodes of a textual network, comprising:

• a first unit that is configured to receive text data from a textual network, and identify pairs of nodes that are associated with message edges of said text data of the network,
• a second unit that is able to calculate an initial clustering of all the nodes into clusters,
• a third unit that is able to aggregate, for each cluster, text data associated with two nodes within the cluster, so as to produce a first aggregate associated with the cluster, and to aggregate, for each cluster, text data associated with a pair of any node of the cluster and any node of another cluster, so as to produce at least one second aggregate associated to the cluster,
• the third unit also being able to process said first and second aggregates in order to determine topics corresponding to the text data in accordance with a generative model of documents,
• in order to determine, from a clustering Y and first and second aggregates and for each topic k, a probability βkv of each word v of dictionary being used in the topic k, and an estimated distribution R(Z,θ), with Zijdn a topic vector indicating the topic of the word n of the text Wijd corresponding to Wijdn, and θqrk an estimated probability of the topic k of text data associated between the cluster q and the cluster r
• a fourth unit that is able to calculate a new clustering Y in accordance with calculated probabilities β, ρ, π and the estimated distribution R(Z,θ) provided by the third unit, by determining, for each node i of the network, which optimal cluster provides a maximum value of a statistical criterion when a node i is assigned to a cluster q, and assigning a node i to the determined optimal cluster.