Locally-iterative Distributed (Δ + 1)-coloring and Applications

We consider graph coloring and related problems in the distributed message-passing model. Locally-iterative algorithms are especially important in this setting. These are algorithms in which each vertex decides about its next color only as a function of the current colors in its 1-hop-neighborhood . In STOC’93 Szegedy and Vishwanathan showed that any locally-iterative Δ + 1-coloring algorithm requires Ω (Δ log Δ + log * n ) rounds, unless there exists “a very special type of coloring that can be very efficiently reduced” [ 44 ]. No such special coloring has been found since then. This led researchers to believe that Szegedy-Vishwanathan barrier is an inherent limitation for locally-iterative algorithms and to explore other approaches to the coloring problem [ 2 , 3 , 19 , 32 ]. The latter gave rise to faster algorithms, but their heavy machinery that is of non-locally-iterative nature made them far less suitable to various settings. In this article, we obtain the aforementioned special type of coloring. Specifically, we devise a locally-iterative Δ + 1-coloring algorithm with running time O (Δ + log * n ), i.e., below Szegedy-Vishwanathan barrier. This demonstrates that this barrier is not an inherent limitation for locally-iterative algorithms. As a result, we also achieve significant improvements for dynamic, self-stabilizing, and bandwidth-restricted settings. This includes the following results: We obtain self-stabilizing distributed algorithms for Δ + 1-vertex-coloring, (2Δ - 1)-edge-coloring, maximal independent set, and maximal matching with O (Δ + log * n ) time. This significantly improves previously known results that have O(n) or larger running times [ 23 ]. We devise a (2Δ - 1)-edge-coloring algorithm in the CONGEST model with O (Δ + log * n ) time and O (Δ)-edge-coloring in the Bit-Round model with O (Δ + log n ) time. The factors of log * n and log n are unavoidable in the CONGEST and Bit-Round models, respectively. Previously known algorithms had superlinear dependency on Δ for (2Δ - 1)-edge-coloring in these models. We obtain an arbdefective coloring algorithm with running time O (√ Δ + log * n ). Such a coloring is not necessarily proper, but has certain helpful properties. We employ it to compute a proper (1 + ε)Δ-coloring within O (√ Δ + log * n ) time and Δ + 1-coloring within O (√ Δ log Δ log * Δ + log * n ) time. This improves the recent state-of-the-art bounds of Barenboim from PODC’15 [ 2 ] and Fraigniaud et al. from FOCS’16 [ 19 ] by polylogarithmic factors. Our algorithms are applicable to the SET-LOCAL model [ 25 ] (also known as the weak LOCAL model). In this model a relatively strong lower bound of Ω (Δ 1/3 ) is known for Δ + 1-coloring. However, most of the coloring algorithms do not work in this model. (In Reference [ 25 ] only Linial’s O (Δ 2 )-time algorithm and Kuhn-Wattenhofer O (Δ log Δ)-time algorithms are shown to work in it.) We obtain the first linear-in-Δ Δ + 1-coloring algorithms that work also in this model.

Reinforced Neighborhood Selection Guided Multi-Relational Graph Neural Networks

Graph Neural Networks (GNNs) have been widely used for the representation learning of various structured graph data, typically through message passing among nodes by aggregating their neighborhood information via different operations. While promising, most existing GNNs oversimplify the complexity and diversity of the edges in the graph and thus are inefficient to cope with ubiquitous heterogeneous graphs, which are typically in the form of multi-relational graph representations. In this article, we propose RioGNN , a novel Reinforced, recursive, and flexible neighborhood selection guided multi-relational Graph Neural Network architecture, to navigate complexity of neural network structures whilst maintaining relation-dependent representations. We first construct a multi-relational graph, according to the practical task, to reflect the heterogeneity of nodes, edges, attributes, and labels. To avoid the embedding over-assimilation among different types of nodes, we employ a label-aware neural similarity measure to ascertain the most similar neighbors based on node attributes. A reinforced relation-aware neighbor selection mechanism is developed to choose the most similar neighbors of a targeting node within a relation before aggregating all neighborhood information from different relations to obtain the eventual node embedding. Particularly, to improve the efficiency of neighbor selecting, we propose a new recursive and scalable reinforcement learning framework with estimable depth and width for different scales of multi-relational graphs. RioGNN can learn more discriminative node embedding with enhanced explainability due to the recognition of individual importance of each relation via the filtering threshold mechanism. Comprehensive experiments on real-world graph data and practical tasks demonstrate the advancements of effectiveness, efficiency, and the model explainability, as opposed to other comparative GNN models.

Combining Graph Convolutional Neural Networks and Label Propagation

Label Propagation Algorithm (LPA) and Graph Convolutional Neural Networks (GCN) are both message passing algorithms on graphs. Both solve the task of node classification, but LPA propagates node label information across the edges of the graph, while GCN propagates and transforms node feature information. However, while conceptually similar, theoretical relationship between LPA and GCN has not yet been systematically investigated. Moreover, it is unclear how LPA and GCN can be combined under a unified framework to improve the performance. Here we study the relationship between LPA and GCN in terms of feature/label influence , in which we characterize how much the initial feature/label of one node influences the final feature/label of another node in GCN/LPA. Based on our theoretical analysis, we propose an end-to-end model that combines GCN and LPA. In our unified model, edge weights are learnable, and the LPA serves as regularization to assist the GCN in learning proper edge weights that lead to improved performance. Our model can also be seen as learning the weights of edges based on node labels, which is more direct and efficient than existing feature-based attention models or topology-based diffusion models. In a number of experiments for semi-supervised node classification and knowledge-graph-aware recommendation, our model shows superiority over state-of-the-art baselines.

HyperSoRec: Exploiting Hyperbolic User and Item Representations with Multiple Aspects for Social-aware Recommendation

Social recommendation has achieved great success in many domains including e-commerce and location-based social networks. Existing methods usually explore the user-item interactions or user-user connections to predict users’ preference behaviors. However, they usually learn both user and item representations in Euclidean space, which has large limitations for exploring the latent hierarchical property in the data. In this article, we study a novel problem of hyperbolic social recommendation, where we aim to learn the compact but strong representations for both users and items. Meanwhile, this work also addresses two critical domain-issues, which are under-explored. First, users often make trade-offs with multiple underlying aspect factors to make decisions during their interactions with items. Second, users generally build connections with others in terms of different aspects, which produces different influences with aspects in social network. To this end, we propose a novel graph neural network (GNN) framework with multiple aspect learning, namely, HyperSoRec. Specifically, we first embed all users, items, and aspects into hyperbolic space with superior representations to ensure their hierarchical properties. Then, we adapt a GNN with novel multi-aspect message-passing-receiving mechanism to capture different influences among users. Next, to characterize the multi-aspect interactions of users on items, we propose an adaptive hyperbolic metric learning method by introducing learnable interactive relations among different aspects. Finally, we utilize the hyperbolic translational distance to measure the plausibility in each user-item pair for recommendation. Experimental results on two public datasets clearly demonstrate that our HyperSoRec not only achieves significant improvement for recommendation performance but also shows better representation ability in hyperbolic space with strong robustness and reliability.

Refined UNet V4: End-to-End Patch-Wise Network for Cloud and Shadow Segmentation with Bilateral Grid

Remote sensing images are usually contaminated by cloud and corresponding shadow regions, making cloud and shadow detection one of the essential prerequisites for processing and translation of remote sensing images. Edge-precise cloud and shadow segmentation remains challenging due to the inherent high-level semantic acquisition of current neural segmentation fashions. We, therefore, introduce the Refined UNet series to partially achieve edge-precise cloud and shadow detection, including two-stage Refined UNet, v2 with a potentially efficient gray-scale guided Gaussian filter-based CRF, and v3 with an efficient multi-channel guided Gaussian filter-based CRF. However, it is visually demonstrated that the locally linear kernel used in v2 and v3 is not sufficiently sensitive to potential edges in comparison with Refined UNet. Accordingly, we turn back to the investigation of an end-to-end UNet-CRF architecture with a Gaussian-form bilateral kernel and its relatively efficient approximation. In this paper, we present Refined UNet v4, an end-to-end edge-precise segmentation network for cloud and shadow detection, which is capable of retrieving regions of interest with relatively tight edges and potential shadow regions with ambiguous edges. Specifically, we inherit the UNet-CRF architecture exploited in the Refined UNet series, which concatenates a UNet backbone of coarsely locating cloud and shadow regions and an embedded CRF layer of refining edges. In particular, the bilateral grid-based approximation to the Gaussian-form bilateral kernel is applied to the bilateral message-passing step, in order to ensure the delineation of sufficiently tight edges and the retrieval of shadow regions with ambiguous edges. Our TensorFlow implementation of the bilateral approximation is relatively computationally efficient in comparison with Refined UNet, attributed to the straightforward GPU acceleration. Extensive experiments on Landsat 8 OLI dataset illustrate that our v4 can achieve edge-precise cloud and shadow segmentation and improve the retrieval of shadow regions, and also confirm its computational efficiency.

Fast Quaternion Product Units for Learning Disentangled Representations in SO(3)

Real-world 3D structured data like point clouds and skeletons often can be represented as data in a 3D rotation group (denoted as $\mathbb{SO}(3)$). However, most existing neural networks are tailored for the data in the Euclidean space, which makes the 3D rotation data not closed under their algebraic operations and leads to sub-optimal performance in 3D-related learning tasks. To resolve the issues caused by the above mismatching between data and model, we propose a novel non-real neuron model called \textit{quaternion product unit} (QPU) to represent data on 3D rotation groups. The proposed QPU leverages quaternion algebra and the law of the 3D rotation group, representing 3D rotation data as quaternions and merging them via a weighted chain of Hamilton products. We demonstrate that the QPU mathematically maintains the $\mathbb{SO}(3)$ structure of the 3D rotation data during the inference process and disentangles the 3D representations into ``rotation-invariant'' features and ``rotation-equivariant'' features, respectively. Moreover, we design a fast QPU to accelerate the computation of QPU. The fast QPU applies a tree-structured data indexing process, and accordingly, leverages the power of parallel computing, which reduces the computational complexity of QPU in a single thread from $\mathcal{O}(N)$ to $\mathcal {O}(\log N)$. Taking the fast QPU as a basic module, we develop a series of quaternion neural networks (QNNs), including quaternion multi-layer perceptron (QMLP), quaternion message passing (QMP), and so on. In addition, we make the QNNs compatible with conventional real-valued neural networks and applicable for both skeletons and point clouds. Experiments on synthetic and real-world 3D tasks show that the QNNs based on our fast QPUs are superior to state-of-the-art real-valued models, especially in the scenarios requiring the robustness to random rotations.<br>

Fast Quaternion Product Units for Learning Disentangled Representations in SO(3)

Real-world 3D structured data like point clouds and skeletons often can be represented as data in a 3D rotation group (denoted as $\mathbb{SO}(3)$). However, most existing neural networks are tailored for the data in the Euclidean space, which makes the 3D rotation data not closed under their algebraic operations and leads to sub-optimal performance in 3D-related learning tasks. To resolve the issues caused by the above mismatching between data and model, we propose a novel non-real neuron model called \textit{quaternion product unit} (QPU) to represent data on 3D rotation groups. The proposed QPU leverages quaternion algebra and the law of the 3D rotation group, representing 3D rotation data as quaternions and merging them via a weighted chain of Hamilton products. We demonstrate that the QPU mathematically maintains the $\mathbb{SO}(3)$ structure of the 3D rotation data during the inference process and disentangles the 3D representations into ``rotation-invariant'' features and ``rotation-equivariant'' features, respectively. Moreover, we design a fast QPU to accelerate the computation of QPU. The fast QPU applies a tree-structured data indexing process, and accordingly, leverages the power of parallel computing, which reduces the computational complexity of QPU in a single thread from $\mathcal{O}(N)$ to $\mathcal {O}(\log N)$. Taking the fast QPU as a basic module, we develop a series of quaternion neural networks (QNNs), including quaternion multi-layer perceptron (QMLP), quaternion message passing (QMP), and so on. In addition, we make the QNNs compatible with conventional real-valued neural networks and applicable for both skeletons and point clouds. Experiments on synthetic and real-world 3D tasks show that the QNNs based on our fast QPUs are superior to state-of-the-art real-valued models, especially in the scenarios requiring the robustness to random rotations.<br>

Programming big data analysis: principles and solutions

In the age of the Internet of Things and social media platforms, huge amounts of digital data are generated by and collected from many sources, including sensors, mobile devices, wearable trackers and security cameras. This data, commonly referred to as Big Data, is challenging current storage, processing, and analysis capabilities. New models, languages, systems and algorithms continue to be developed to effectively collect, store, analyze and learn from Big Data. Most of the recent surveys provide a global analysis of the tools that are used in the main phases of Big Data management (generation, acquisition, storage, querying and visualization of data). Differently, this work analyzes and reviews parallel and distributed paradigms, languages and systems used today to analyze and learn from Big Data on scalable computers. In particular, we provide an in-depth analysis of the properties of the main parallel programming paradigms (MapReduce, workflow, BSP, message passing, and SQL-like) and, through programming examples, we describe the most used systems for Big Data analysis (e.g., Hadoop, Spark, and Storm). Furthermore, we discuss and compare the different systems by highlighting the main features of each of them, their diffusion (community of developers and users) and the main advantages and disadvantages of using them to implement Big Data analysis applications. The final goal of this work is to help designers and developers in identifying and selecting the best/appropriate programming solution based on their skills, hardware availability, application domains and purposes, and also considering the support provided by the developer community.

A Residual-Based Message Passing Algorithm for Constraint Satisfaction Problems

Message passing algorithms, whose iterative nature captures well complicated interactions among interconnected variables in complex systems and extracts information from the fixed point of iterated messages, provide a powerful toolkit in tackling hard computational tasks in optimization, inference, and learning problems. In the context of constraint satisfaction problems (CSPs), when a control parameter (such as constraint density) is tuned, multiple threshold phenomena emerge, signaling fundamental structural transitions in their solution space. Finding solutions around these transition points is exceedingly challenging for algorithm design, where message passing algorithms suffer from a large message fluctuation far from convergence. Here we introduce a residual-based updating step into message passing algorithms, in which messages varying large between consecutive steps are given a high priority in updating process. For the specific example of model RB, a typical prototype of random CSPs with growing domains, we show that our algorithm improves the convergence of message updating and increases the success probability in finding solutions around the satisfiability threshold with a low computational cost. Our approach to message passing algorithms should be of value for exploring their power in developing algorithms to find ground-state solutions and understand the detailed structure of solution space of hard optimization problems.