Guillaume Santini

Graph abstraction for closed pattern mining in attributed networks

We address the problem of finding patterns in an attributed graph. Our approach consists in extending the standard methodology of frequent closed pattern mining to the case in which the set of objects, in which are found the pattern supports, is the set of vertices of a graph, typically representing a social network. The core idea is then to define graph abstractions as subsets of the vertices satisfying some connectivity property within the corresponding induced subgraphs. Preliminary experiments illustrate the reduction in closed patterns we obtain as well as what kind of abstract knowledge is found via abstract implications rules.

Hybrid Method Inference for the Construction of Cooperative Regulatory Network in Human

Reconstruction of large scale gene regulatory networks (GRNs in the following) is an important step for understanding the complex regulatory mechanisms within the cell. Many modeling approaches have been introduced to find the causal relationship between genes using expression data. However, they have been suffering from high dimensionality-large number of genes but a small number of samples, overfitting, heavy computation time and low interpretability. We have previously proposed an original Data Mining algorithm Licorn, that infers cooperative regulation network from expression datasets. In this work, we present an extension of Licorn to a hybrid inference method h-Licorn that uses search in both discrete and real valued spaces. Licorns algorithm, using the discrete space to find cooperative regulation relationships fitting the target gene expression, has been shown to be powerful in identifying cooperative regulation relationships that are out of the scope of most GRN inference methods. Still, as many of related GRN inference techniques, Licorn suffers from a large number of false positives. We propose here an extension of Licorn with a numerical selection step, expressed as a linear regression problem, that effectively complements the discrete search of Licorn. We evaluate a bootstrapped version of h-Licorn on the in silico Dream5 dataset and show that h-Licorn has significantly higher performance than Licorn, and is competitive or outperforms state of the art GRN inference algorithms, especially when operating on small data sets. We also applied h-Licorn on a real dataset of human bladder cancer and show that it performs better than other methods in finding candidate regulatory interactions. In particular, solely based on gene expression data, h-Licorn is able to identify experimentally validated regulator cooperative relationships involved in cancer.

Automatic classification of protein structures relying on similarities between alignments

BackgroundIdentification of protein structural cores requires isolation of sets of proteins all sharing a same subset of structural motifs. In the context of an ever growing number of available 3D protein structures, standard and automatic clustering algorithms require adaptations so as to allow for efficient identification of such sets of proteins.ResultsWhen considering a pair of 3D structures, they are stated as similar or not according to the local similarities of their matching substructures in a structural alignment. This binary relation can be represented in a graph of similarities where a node represents a 3D protein structure and an edge states that two 3D protein structures are similar. Therefore, classifying proteins into structural families can be viewed as a graph clustering task. Unfortunately, because such a graph encodes only pairwise similarity information, clustering algorithms may include in the same cluster a subset of 3D structures that do not share a common substructure. In order to overcome this drawback we first define a ternary similarity on a triple of 3D structures as a constraint to be satisfied by the graph of similarities. Such a ternary constraint takes into account similarities between pairwise alignments, so as to ensure that the three involved protein structures do have some common substructure. We propose hereunder a modification algorithm that eliminates edges from the original graph of similarities and gives a reduced graph in which no ternary constraints are violated. Our approach is then first to build a graph of similarities, then to reduce the graph according to the modification algorithm, and finally to apply to the reduced graph a standard graph clustering algorithm. Such method was used for classifying ASTRAL-40 non-redundant protein domains, identifying significant pairwise similarities with Yakusa, a program devised for rapid 3D structure alignments.ConclusionsWe show that filtering similarities prior to standard graph based clustering process by applying ternary similarity constraints i) improves the separation of proteins of different classes and consequently ii) improves the classification quality of standard graph based clustering algorithms according to the reference classification SCOP.

VIRTLAB: a virtual molecular biology laboratory.

SUMMARY VIRTLAB is a self-training program based on PBL (Problem-Based-Learning Pathway) built to simulate a molecular biology laboratory. It has been designed to stimulate students in the biological sciences to analyse and solve molecular biology problems using standard laboratory techniques (e.g. restriction enzyme digestions, analytical and preparative agarose gels, DNA cloning and sequencing, etc.) and can thus be viewed as a teaching aid. AVAILABILITY The VIRTLAB package is distributed free of charge to non-profit organisations by the authors (virtlab@biol.dgbm. unina.it). On-line help and tutorials, available now in English, French, Italian, and shortly in German, are provided with the software or at http://biol.dgbm.unina.it:8080/virtlab.html++ +

Self-organizing trees for visualizing protein dataset

Clustering and visualizing multidimensional or structured data are important tasks for data analysis, especially in bioinformatics. Self-organizing models are often used to address both of these issues. In this paper we introduce a hierarchical and topological visualization technique called Self-organizing Trees (SoT) which is able to represent data in hierarchical and topological structure. The experiment is conducted on a real-world protein data set.

Use of ternary similarities in graph based clustering for protein structural family classification

Classification of proteins 3D structures into structural families is reformulated in terms of graph based clustering of objects which are modular as similarities between two 3D structures relies on the local similarities of their matching substructures. Similarities between 3D structures are then represented as edges connecting objects in a graph. Applying clustering algorithms to such a graph results in the following drawback: subsets of more than two 3D structures belonging to the same cluster may share no similar substructure. To overcome this drawback we propose to introduce constraints about ternary similarities, i.e. constraints on triples of objects. The 3D structures graph is first transformed into its line graph, that represents the adjacencies between the graph edges. The ternary constraints are applied on the line graph, and a maximal line graph is then extracted from the modified line graph. The corresponding 3D structures graph now satisfies the above mentioned ternary constraints. In our experiments applying clustering on the new graph results in a more stable classification which is coherent with the expert classification SCOP.

Formal Concept Analysis of Attributed Networks

We consider attribute pattern mining in an attributed graph through recent developments of Formal Concept Analysis. The core idea is to restrain the extensional space, i.e., the space of possible pattern extensions in the vertex set O, to vertex subsets satisfying some topological property. We consider two levels. At the abstract level, we reduce the extension of each pattern in such a way that the corresponding abstract extension induces a subgraph whose nodes satisfy some connectivity property. At the local level a pattern has various extensions each associated with a connected component of the abstract subgraph associated with the pattern. We obtain that way abstract closed patterns and local closed patterns, together with abstract and local implications. Furthermore, working at abstract and local levels leads to proper interestingness measures that evaluate to what extent patterns and implications are related to the topological information. Finally, we relate local concepts to network communities and show that to plainly express such a notion it may be necessary to apply our methodology to a new graph derived from the original network. We consider in particular the detection and ordering of k-communities in subgraphs of an attributed network.

Abstract and Local Rule Learning in Attributed Networks

We address the problem of finding local patterns and related local knowledge, represented as implication rules, in an attributed graph. Our approach consists in extending frequent closed pattern mining to the case in which the set of objects is the set of vertices of a graph, typically representing a social network. We recall the definition of abstract closed patterns, obtained by restricting the support set of an attribute pattern to vertices satisfying some connectivity constraint, and propose a specificity measure of abstract closed patterns together with an informativity measure of the associated abstract implication rules. We define in the same way local closed patterns, i.e. maximal attribute patterns each associated to a connected component of the subgraph induced by the support set of some pattern, and also define specificity of local closed patterns together with informativity of associated local implication rules. We also show how, by considering a derived graph, we may apply the same ideas to the discovery of local patterns and local implication rules in non disjoint parts of a subgraph as k-cliques communities.

Local Knowledge Discovery in Attributed Graphs

We address the problem of finding local patterns and related local knowledge in an attributed graph. Our approach consists in extending the methodology of frequent closed pattern mining to the case in which the set of objects, in which are to be found the patterns support sets, is the set of vertices of a graph, typically representing a social network. We propose an algorithm to enumerate triples (c,e,l) where c is a (global) closed pattern which leads in the region e of the graph to a local closed pattern l and define a basis of implication rules expressing what new attributes l\c appear when focussing in this region. We discuss how to apply this methodology to the detection of frequent k-communities.

Bi-Pattern Mining of Two Mode and Directed Networks.

In two-mode networks there are two kinds of vertices, i.e objects, each being possibly described with a proper attribute set. This means that to select a subnetwork according to vertex descriptions we have to consider a pair of vertex subsets. A common technique is to extract from a network an essential subnetwork, the core subgraph of the network. Formal Concept Analysis and closed pattern mining were previously applied to networks with the purpose of reducing extensions of patterns to be core subgraphs. To apply this methodology to two-mode networks, we need to consider the two vertex subsets of two-mode cores and define accordingly abstract closed bi-patterns. Each component of a bi-pattern is then associated to one mode. We also show that the same methodology applies to hub-authority cores of directed networks in which each vertex subset is associated to a role (in or out). We illustrate the methodology both on a two-mode network of epistemological data and on a directed advice network of lawyers.