Related papers: Representing two-parameter persistence modules via…
Analyzing interconnection structures among underlying entities or objects in a dataset through the use of graph analytics has been shown to provide tremendous value in many application domains. However, graphs are not the primary…
Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution…
Persistent homology is a popular technique in topological data analysis that tracks the lifespans of homological features in a nested sequence of spaces. This data is typically presented in a multi-set called a persistence diagram or a…
Graphs are general and powerful data representations which can model complex real-world phenomena, ranging from chemical compounds to social networks; however, effective feature extraction from graphs is not a trivial task, and much work…
Visualization in the emerging field of topological data analysis has progressed from persistence barcodes and persistence diagrams to display of two-parameter persistent homology. Although persistence barcodes and diagrams have permitted…
In a recent paper, we introduced the simultaneous representation problem (defined for any graph class C) and studied the problem for chordal, comparability and permutation graphs. For interval graphs, the problem is defined as follows. Two…
Can we use machine learning to compress graph data? The absence of ordering in graphs poses a significant challenge to conventional compression algorithms, limiting their attainable gains as well as their ability to discover relevant…
We introduces the umodules, a generalisation of the notion of graph module. The theory we develop captures among others undirected graphs, tournaments, digraphs, and $2-$structures. We show that, under some axioms, a unique decomposition…
Graphs or networks are a very convenient way to represent data with lots of interaction. Recently, Machine Learning on Graph data has gained a lot of traction. In particular, vertex classification and missing edge detection have very…
Recently a variety of methods have been developed to encode graphs into low-dimensional vectors that can be easily exploited by machine learning algorithms. The majority of these methods start by embedding the graph nodes into a…
A storage code is an assignment of symbols to the vertices of a connected graph $G(V,E)$ with the property that the value of each vertex is a function of the values of its neighbors, or more generally, of a certain neighborhood of the…
Compression aims to reduce the size of an input, while maintaining its relevant properties. For multi-parameter persistent homology, compression is a necessary step in any computational pipeline, since standard constructions lead to large…
Patterns stored within pre-trained deep neural networks compose large and powerful descriptive languages that can be used for many different purposes. Typically, deep network representations are implemented within vector embedding spaces,…
Persistent homology is a fundamental tool in Topological Data Analysis. The associated algebraic structure is the persistence module, a sequence of vector spaces connected by linear maps. Persistence modules admit a complete and…
Persistence diagrams (PDs), often characterized as sets of death and birth of homology class, have been known for providing a topological representation of a graph structure, which is often useful in machine learning tasks. Prior works rely…
The barcode of a persistence module serves as a complete combinatorial invariant of its isomorphism class. Barcodes are typically extracted by performing changes of basis on a persistence module until the constituent matrices have a special…
The classical persistence algorithm computes the unique decomposition of a persistence module implicitly given by an input simplicial filtration. Based on matrix reduction, this algorithm is a cornerstone of the emergent area of topological…
Generative models for source code are an interesting structured prediction problem, requiring to reason about both hard syntactic and semantic constraints as well as about natural, likely programs. We present a novel model for this problem…
Graph is an important data representation which appears in a wide diversity of real-world scenarios. Effective graph analytics provides users a deeper understanding of what is behind the data, and thus can benefit a lot of useful…
Graph Neural Networks (GNNs) have demonstrated remarkable performance in a wide range of tasks, such as node classification, link prediction, and graph classification, by exploiting the structural information in graph-structured data.…