25 research outputs found
Explainable subgraphs with surprising densities : a subgroup discovery approach
The connectivity structure of graphs is typically related to the attributes of the nodes. In social networks for example, the probability of a friendship between any pair of people depends on a range of attributes, such as their age, residence location, workplace, and hobbies. The high-level structure of a graph can thus possibly be described well by means of patterns of the form `the subgroup of all individuals with a certain properties X are often (or rarely) friends with individuals in another subgroup defined by properties Y', in comparison to what is expected. Such rules present potentially actionable and generalizable insight into the graph.
We present a method that finds node subgroup pairs between which the edge density is interestingly high or low, using an information-theoretic definition of interestingness. Additionally, the interestingness is quantified subjectively, to contrast with prior information an analyst may have about the connectivity. This view immediatly enables iterative mining of such patterns. This is the first method aimed at graph connectivity relations between different subgroups. Our method generalizes prior work on dense subgraphs induced by a subgroup description. Although this setting has been studied already, we demonstrate for this special case considerable practical advantages of our subjective interestingness measure with respect to a wide range of (objective) interestingness measures
Subjectively interesting motifs in time series
This paper introduces an approach to find motifs in time series that are \emph{subjectively interesting}. That is, the aim is to find motifs that are surprising given an informative background distribution, which may for example correspond to the prior knowledge of a user of the tool. We quantify this surprisal using information theory, and more particularly the FORSIED framework. The resulting interestingness function according to which motifs are ranked is then subjective in the statistical sense, enabling us to find subsequence patterns (i.e., motifs and outliers) that are more truly interesting. Although finding the best motif appears intractable, we develop relaxations and a branch-and-bound approach that is implemented in a constraint programming solver. As shown in experiments on synthetic data and two real-world data sets this enables us to mine interesting patterns in small or mid-sized time series
SIMIT : subjectively interesting motifs in time series
Numerical time series data are pervasive, originating from sources as diverse as wearable
devices, medical equipment, to sensors in industrial plants. In many cases, time series contain interesting
information in terms of subsequences that recur in approximate form, so-called motifs. Major open
challenges in this area include how one can formalize the interestingness of such motifs and how the most
interesting ones can be found. We introduce a novel approach that tackles these issues. We formalize the
notion of such subsequence patterns in an intuitive manner and present an information-theoretic approach
for quantifying their interestingness with respect to any prior expectation a user may have about the time
series. The resulting interestingness measure is thus a subjective measure, enabling a user to find motifs
that are truly interesting to them. Although finding the best motif appears computationally intractable,
we develop relaxations and a branch-and-bound approach implemented in a constraint programming
solver. As shown in experiments on synthetic data and two real-world datasets, this enables us to mine
interesting patterns in small or mid-sized time series
Explainable subgraphs with surprising densities : a subgroup discovery approach
The connectivity structure of graphs is typically related to the attributes of the nodes. In social networks for example, the probability of a friendship between two people depends on their attributes, such as their age, address, and hobbies. The connectivity of a graph can thus possibly be understood in terms of patterns of the form 'the subgroup of individuals with properties X are often (or rarely) friends with individuals in another subgroup with properties Y'. Such rules present potentially actionable and generalizable insights into the graph. We present a method that finds pairs of node subgroups between which the edge density is interestingly high or low, using an information-theoretic definition of interestingness. This interestingness is quantified subjectively, to contrast with prior information an analyst may have about the graph. This view immediately enables iterative mining of such patterns. Our work generalizes prior work on dense subgraph mining (i.e. subgraphs induced by a single subgroup). Moreover, not only is the proposed method more general, we also demonstrate considerable practical advantages for the single subgroup special case
OSNet & MNetO: Two Types of General Reconstruction Architectures for Linear Computed Tomography in Multi-Scenarios
Recently, linear computed tomography (LCT) systems have actively attracted
attention. To weaken projection truncation and image the region of interest
(ROI) for LCT, the backprojection filtration (BPF) algorithm is an effective
solution. However, in BPF for LCT, it is difficult to achieve stable interior
reconstruction, and for differentiated backprojection (DBP) images of LCT,
multiple rotation-finite inversion of Hilbert transform (Hilbert
filtering)-inverse rotation operations will blur the image. To satisfy multiple
reconstruction scenarios for LCT, including interior ROI, complete object, and
exterior region beyond field-of-view (FOV), and avoid the rotation operations
of Hilbert filtering, we propose two types of reconstruction architectures. The
first overlays multiple DBP images to obtain a complete DBP image, then uses a
network to learn the overlying Hilbert filtering function, referred to as the
Overlay-Single Network (OSNet). The second uses multiple networks to train
different directional Hilbert filtering models for DBP images of multiple
linear scannings, respectively, and then overlays the reconstructed results,
i.e., Multiple Networks Overlaying (MNetO). In two architectures, we introduce
a Swin Transformer (ST) block to the generator of pix2pixGAN to extract both
local and global features from DBP images at the same time. We investigate two
architectures from different networks, FOV sizes, pixel sizes, number of
projections, geometric magnification, and processing time. Experimental results
show that two architectures can both recover images. OSNet outperforms BPF in
various scenarios. For the different networks, ST-pix2pixGAN is superior to
pix2pixGAN and CycleGAN. MNetO exhibits a few artifacts due to the differences
among the multiple models, but any one of its models is suitable for imaging
the exterior edge in a certain direction.Comment: 13 pages, 13 figure
GLOBAL CLASSICAL SOLUTIONS TO THE 3-D ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH GENERAL INITIAL ENERGY
National Natural Science Foundation of China [11001090]; Fundamental Research Funds for the Central Universities [11QZR16]We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the 3-D compressible Navier-Stokes equations under the assumption that the initial density parallel to rho(0)parallel to(L infinity) is appropriate small and 1 < gamma < 6/5. Here the initial density could have vacuum and we do not require that the initial energy is small