Vassilis N. Ioannidis

Kernel-Based Reconstruction of Space-Time Functions on Dynamic Graphs

Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the attributes of a set of vertices given those of another subset at possibly diffe-rent time instants. Leveraging spatiotemporal dynamics can drastically reduce the number of observed vertices, and hence the sampling cost. Alleviating the limited flexibility of the existing approaches, the present paper broadens the kernel-based graph function estimation framework to reconstruct time-evolving functions over possibly time-evolving topologies. This approach inherits the versatility and generality of kernel-based methods, for which no knowledge on distributions or second-order statistics is required. Systematic guidelines are provided to construct two families of space-time kernels with complementary strengths: the first facilitates judicious control of regularization on a space-time frequency plane, whereas the second accommodates time-varying topologies. Batch and online estimators are also put forth. The latter comprise a novel kernel Kalman filter, developed to reconstruct space-time functions at affordable computational cost. Numerical tests with real datasets corroborate the merits of the proposed methods relative to competing alternatives.

Coupled graph tensor factorization

Factorization of a single matrix or tensor has been used widely to reveal interpretable factors or predict missing data. However, in many cases side information may be available, such as social network activities and user demographic data together with Netflix data. In these situations, coupled matrix tensor factorization (CMTF) can be employed to account for additional sources of information. When the side information comes in the form of item-correlation matrices of certain modes, existing CMTF algorithms do not apply. Instead, a novel approach to model the correlation matrices is proposed here, using symmetric nonnegative matrix factorization. The multiple sources of information are fused by fitting outer-product models for the tensor and the correlation matrices in a coupled manner. The proposed model has the potential to overcome practical challenges, such as missing slabs from the tensor and/or missing rows/columns from the correlation matrices.

Kernel-based reconstruction of space-time functions via extended graphs

Signals evolving over graphs emerge naturally in a number of applications related to network science. A frequently encountered challenge pertains to reconstructing such signals given their values on subsets of vertices at possibly different time instants. Spatiotemporal dynamics can be leveraged so that a small number of vertices suffices to achieve accurate reconstruction. The present paper broadens the existing kernel-based graph-function reconstruction framework to handle time-evolving functions over (possibly dynamic) graphs. The proposed approach introduces the novel notion of graph extension to enable kernel-based estimators over time and space. Numerical tests with real data corroborate that judiciously capturing time-space dynamics markedly improves reconstruction performance.

Inference of spatiotemporal processes over graphs via kernel kriged Kalman filtering

Inference of space-time signals evolving over graphs emerges naturally in a number of network science related applications. A frequently encountered challenge pertains to reconstructing such dynamic processes given their values over a subset of vertices and time instants. The present paper develops a graph-aware kernel-based kriged Kalman filtering approach that leverages the spatio-temporal dynamics to allow for efficient online reconstruction, while also coping with dynamically evolving network topologies. Laplacian kernels are employed to perform kriging over the graph when spatial second-order statistics are unknown, as is often the case. Numerical tests with synthetic and real data illustrate the superior reconstruction performance of the proposed approach.

Kernel-Based Inference of Functions Over Graphs

Abstract The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting—and prevalent in several fields of study—problem is that of inferring a function defined over the nodes of a network. This work presents a versatile kernel-based framework for tackling this inference problem that naturally subsumes and generalizes the reconstruction approaches put forth recently for the signal processing by the community studying graphs. Both the static and the dynamic settings are considered along with effective modeling approaches for addressing real-world problems. The analytical discussion herein is complemented with a set of numerical examples, which showcase the effectiveness of the presented techniques, as well as their merits related to state-of-the-art methods.