Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.

We propose a general modeling and algorithmic framework for discrete structure recovery that can be applied to a wide range of problems. Under this framework, we are able to study the recovery of clustering labels, ranks of players, and signs of regression coefficients from a unified perspective. A simple iterative algorithm is proposed for discrete structure recovery, which generalizes methods including Lloyd's algorithm and the iterative feature matching algorithm. A linear convergence result for the proposed algorithm is established in this paper under appropriate abstract conditions on stochastic errors and initialization. We illustrate our general theory by applying it on three representative problems: clustering in Gaussian mixture model, approximate ranking, and sign recovery in compressed sensing, and show that minimax rate is achieved in each case.

This paper proposes a new method for determining similarity and anomalies between time series, most practically effective in large collections of (likely related) time series, with a particular focus on measuring distances between structural breaks within such a collection. We consolidate and generalise a class of semi-metric distance measures, which we term MJ distances. Experiments on simulated data demonstrate that our proposed family of distances uncover similarity within collections of time series more effectively than measures such as the Hausdorff and Wasserstein metrics. Although our class of distances do not necessarily satisfy the triangle inequality requirement of a metric, we analyse the transitivity properties of respective distance matrices in various contextual scenarios. There, we demonstrate a trade-off between robust performance in the presence of outliers, and the triangle inequality property. We show in experiments using real data that the contrived scenarios that severely violate the transitivity property rarely exhibit themselves in real data; instead, our family of measures satisfies all the properties of a metric most of the time. We illustrate three ways of analysing the distance and similarity matrices, via eigenvalue analysis, hierarchical clustering, and spectral clustering. The results from our hierarchical and spectral clustering experiments on simulated data demonstrate that the Hausdorff and Wasserstein metrics may lead to erroneous inference as to which time series are most similar with respect to their structural breaks, while our semi-metrics provide an improvement.

A main task in data analysis is to organize data points into coherent groups or clusters. The stochastic block model is a probabilistic model for the cluster structure. This model prescribes different probabilities for the presence of edges within a cluster and between different clusters. We assume that the cluster assignments are known for at least one data point in each cluster. In such a partially labeled stochastic block model, clustering amounts to estimating the cluster assignments of the remaining data points. We study total variation minimization as a method for this clustering task. We implement the resulting clustering algorithm as a highly scalable message passing protocol. We also provide a condition on the model parameters such that total variation minimization allows for accurate clustering.

-- Understanding multi-vehicle interactive behaviors with temporal sequential observations is crucial for autonomous vehicles to make appropriate decisions in an uncertain traffic environment. On-demand similarity measures are significant for autonomous vehicles to deal with massive interactive driving behaviors by clustering and classifying diverse scenarios. This paper proposes a general approach for measuring spatiotemporal similarity of interactive behaviors using a multivariate matrix profile technique. The key attractive features of the approach are its superior space and time complexity, real-time online computing for streaming traffic data, and possible capability of leveraging hardware for parallel computation. The proposed approach is validated through automatically discovering similar interactive driving behaviors at intersections from sequential data. One of the biggest challenges for deploying autonomous vehicles (A Vs) in real life is the requirement of the A Vs' capability to interact with surrounding road users. Classifying diverse scenarios and separately designing appropriate decisions using on-hand prior knowledge is unfortunately not realistic [1] because of the diversity of scenarios that are far larger and messier than human beings can cope with [2].

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Understanding urban dynamics, i.e., how the types and intensity of urban residents' activities in the city change along with time, is of urgent demand for building an efficient and livable city. Nonetheless, this is challenging due to the expanding urban population and the complicated spatial distribution of residents. In this paper, to reveal urban dynamics, we propose a novel system UrbanRhythm to reveal the urban dynamics hidden in human mobility data. UrbanRhythm addresses three questions: 1) What mobility feature should be used to present residents' high-dimensional activities in the city? 2) What are basic components of urban dynamics? 3) What are the long-term periodicity and short-term regularity of urban dynamics? In UrbanRhythm, we extract staying, leaving, arriving three attributes of mobility and use a image processing method Saak transform to calculate the mobility distribution feature. For the second question, several city states are identified by hierarchy clustering as the basic components of urban dynamics, such as sleeping states and working states. We further characterize the urban dynamics as the transform of city states along time axis. For the third question, we directly observe the long-term periodicity of urban dynamics from visualization. Then for the short-term regularity, we design a novel motif analysis method to discovery motifs as well as their hierarchy relationships. We evaluate our proposed system on two real-life datesets and validate the results according to App usage records. This study sheds light on urban dynamics hidden in human mobility and can further pave the way for more complicated mobility behavior modeling and deeper urban understanding.

They offer a completely different challenge to a supervised learning problem – there's much more room for experimenting with the data that I have. It's no wonder that the majority of developments and breakthroughs in the machine learning space are happening in the unsupervised learning domain. And one of the most popular techniques in unsupervised learning is clustering. It's a concept we typically learn early on in our machine learning journey and it's simple enough to grasp. I'm sure you've come across or even worked on projects like customer segmentation, market basket analysis, etc.

We address the problem of computing a single linkage dendrogram. A possible approach is to: (i) Form an edge weighted graph $G$ over the data, with edge weights reflecting dissimilarities. (ii) Calculate the MST $T$ of $G$. (iii) Break the longest edge of $T$ thereby splitting it into subtrees $T_L$, $T_R$. (iv) Apply the splitting process recursively to the subtrees. This approach has the attractive feature that Prim's algorithm for MST construction calculates distances as needed, and hence there is no need to ever store the inter-point distance matrix. The recursive partitioning algorithm requires us to determine the vertices (and edges) of $T_L$ and $T_R$. We show how this can be done easily and efficiently using information generated by Prim's algorithm without any additional computational cost.

Based on the online transaction data of COSCO group's centralized procurement platform, this paper studies the clustering method of time series type data. The different methods of similarity calculation, different clustering methods with different K values are analysed, and the best clustering method suitable for centralized purchasing data is determined. The company list under the corresponding cluster is obtained. The time series motif discovery algorithm is used to model the centroid of each cluster. Through ARIMA method, we also made 12 periods of prediction for the centroid of each category. This paper constructs a matrix of "Customer Lifecycle Theory - Five Elements of Marketing ", and puts forward corresponding marketing suggestions for customers at different life cycle stages.