Social group detection is a crucial aspect of various robotic applications, including robot navigation and human-robot interactions. To date, a range of model-based techniques have been employed to address this challenge, such as the F-formation and trajectory similarity frameworks. However, these approaches often fail to provide reliable results in crowded and dynamic scenarios. Recent advancements in this area have mainly focused on learning-based methods, such as deep neural networks that use visual content or human pose. Although visual content-based methods have demonstrated promising performance on large-scale datasets, their computational complexity poses a significant barrier to their practical use in real-time applications. To address these issues, we propose a simple and efficient framework for social group detection. Our approach explores the impact of motion trajectory on social grouping and utilizes a novel, reliable, and fast data-driven method. We formulate the individuals in a scene as a graph, where the nodes are represented by LSTM-encoded trajectories and the edges are defined by the distances between each pair of tracks. Our framework employs a modified graph transformer module and graph clustering losses to detect social groups. Our experiments on the popular JRDBAct dataset reveal noticeable improvements in performance, with relative improvements ranging from 2% to 11%. Furthermore, our framework is significantly faster, with up to 12x faster inference times compared to state-of-the-art methods under the same computation resources. These results demonstrate that our proposed method is suitable for real-time robotic applications.
Graph-based representations and message-passing modular policies constitute prominent approaches to tackling composable control problems in reinforcement learning (RL). However, as shown by recent graph deep learning literature, such local message-passing operators can create information bottlenecks and hinder global coordination. The issue becomes more serious in tasks requiring high-level planning. In this work, we propose a novel methodology, named Feudal Graph Reinforcement Learning (FGRL), that addresses such challenges by relying on hierarchical RL and a pyramidal message-passing architecture. In particular, FGRL defines a hierarchy of policies where high-level commands are propagated from the top of the hierarchy down through a layered graph structure. The bottom layers mimic the morphology of the physical system, while the upper layers correspond to higher-order sub-modules. The resulting agents are then characterized by a committee of policies where actions at a certain level set goals for the level below, thus implementing a hierarchical decision-making structure that can naturally implement task decomposition. We evaluate the proposed framework on a graph clustering problem and MuJoCo locomotion tasks; simulation results show that FGRL compares favorably against relevant baselines. Furthermore, an in-depth analysis of the command propagation mechanism provides evidence that the introduced message-passing scheme favors learning hierarchical decision-making policies.
Spectral Toolkit of Algorithms for Graphs (STAG) is an open-source library for efficient spectral graph algorithms, and its development starts in September 2022. We have so far finished the component on local graph clustering, and this technical report presents a user's guide to STAG, showcase studies, and several technical considerations behind our development.
The stochastic block model (SBM) is widely studied as a benchmark for graph clustering aka community detection. In practice, graph data often come with node attributes that bear additional information about the communities. Previous works modeled such data by considering that the node attributes are generated from the node community memberships. In this work, motivated by a recent surge of works in signal processing using deep neural networks as priors, we propose to model the communities as being determined by the node attributes rather than the opposite. We define the corresponding model; we call it the neural-prior SBM. We propose an algorithm, stemming from statistical physics, based on a combination of belief propagation and approximate message passing. We analyze the performance of the algorithm as well as the Bayes-optimal performance. We identify detectability and exact recovery phase transitions, as well as an algorithmically hard region. The proposed model and algorithm can be used as a benchmark for both theory and algorithms. To illustrate this, we compare the optimal performances to the performance of simple graph neural networks.
SpectralNet is a graph clustering method that uses neural network to find an embedding that separates the data. So far it was only used with $k$-nn graphs, which are usually constructed using a distance metric (e.g., Euclidean distance). $k$-nn graphs restrict the points to have a fixed number of neighbors regardless of the local statistics around them. We proposed a new SpectralNet similarity metric based on random projection trees (rpTrees). Our experiments revealed that SpectralNet produces better clustering accuracy using rpTree similarity metric compared to $k$-nn graph with a distance metric. Also, we found out that rpTree parameters do not affect the clustering accuracy. These parameters include the leaf size and the selection of projection direction. It is computationally efficient to keep the leaf size in order of $\log(n)$, and project the points onto a random direction instead of trying to find the direction with the maximum dispersion.
Graph-based clustering methods like spectral clustering and SpectralNet are very efficient in detecting clusters of non-convex shapes. Unlike the popular $k$-means, graph-based clustering methods do not assume that each cluster has a single mean. However, these methods need a graph where vertices in the same cluster are connected by edges of large weights. To achieve this goal, many studies have proposed graph reduction methods with parameters. Unfortunately, these parameters have to be tuned for every dataset. We introduce a graph reduction method that does not require any parameters. First, the distances from every point $p$ to its neighbors are filtered using an adaptive threshold to only keep neighbors with similar surrounding density. Second, the similarities with close neighbors are computed and only high similarities are kept. The edges that survive these two filtering steps form the constructed graph that was passed to spectral clustering and SpectralNet. The experiments showed that our method provides a stable alternative, where other methods performance fluctuated according to the setting of their parameters.
Conventional methods for speaker diarization involve windowing an audio file into short segments to extract speaker embeddings, followed by an unsupervised clustering of the embeddings. This multi-step approach generates speaker assignments for each segment. In this paper, we propose a novel Supervised HierArchical gRaph Clustering algorithm (SHARC) for speaker diarization where we introduce a hierarchical structure using Graph Neural Network (GNN) to perform supervised clustering. The supervision allows the model to update the representations and directly improve the clustering performance, thus enabling a single-step approach for diarization. In the proposed work, the input segment embeddings are treated as nodes of a graph with the edge weights corresponding to the similarity scores between the nodes. We also propose an approach to jointly update the embedding extractor and the GNN model to perform end-to-end speaker diarization (E2E-SHARC). During inference, the hierarchical clustering is performed using node densities and edge existence probabilities to merge the segments until convergence. In the diarization experiments, we illustrate that the proposed E2E-SHARC approach achieves 53% and 44% relative improvements over the baseline systems on benchmark datasets like AMI and Voxconverse, respectively.
Approximate spectral clustering (ASC) was developed to overcome heavy computational demands of spectral clustering (SC). It maintains SC ability in predicting non-convex clusters. Since it involves a preprocessing step, ASC defines new similarity measures to assign weights on graph edges. Connectivity matrix (CONN) is an efficient similarity measure to construct graphs for ASC. It defines the weight between two vertices as the number of points assigned to them during vector quantization training. However, this relationship is undirected, where it is not clear which of the vertices is contributing more to that edge. Also, CONN could be tricked by noisy density between clusters. We defined a directed version of CONN, named DCONN, to get insights on vertices contributions to edges. Also, we provided filtering schemes to ensure CONN edges are highlighting potential clusters. Experiments reveal that the proposed filtering was highly efficient when noise cannot be tolerated by CONN.
The recently emerged spectral clustering surpasses conventional clustering methods by detecting clusters of any shape without the convexity assumption. Unfortunately, with a computational complexity of $O(n^3)$, it was infeasible for multiple real applications, where $n$ could be large. This stimulates researchers to propose the approximate spectral clustering (ASC). However, most of ASC methods assumed that the number of clusters $k$ was known. In practice, manual setting of $k$ could be subjective or time consuming. The proposed algorithm has two relevance metrics for estimating $k$ in two vital steps of ASC. One for selecting the eigenvectors spanning the embedding space, and the other to discover the number of clusters in that space. The algorithm used a growing neural gas (GNG) approximation, GNG is superior in preserving input data topology. The experimental setup demonstrates the efficiency of the proposed algorithm and its ability to compete with similar methods where $k$ was set manually.
Spectral clustering became a popular choice for data clustering for its ability of uncovering clusters of different shapes. However, it is not always preferable over other clustering methods due to its computational demands. One of the effective ways to bypass these computational demands is to perform spectral clustering on a subset of points (data representatives) then generalize the clustering outcome, this is known as approximate spectral clustering (ASC). ASC uses sampling or quantization to select data representatives. This makes it vulnerable to 1) performance inconsistency (since these methods have a random step either in initialization or training), 2) local statistics loss (because the pairwise similarities are extracted from data representatives instead of data points). We proposed a refined version of $k$-nearest neighbor graph, in which we keep data points and aggressively reduce number of edges for computational efficiency. Local statistics were exploited to keep the edges that do not violate the intra-cluster distances and nullify all other edges in the $k$-nearest neighbor graph. We also introduced an optional step to automatically select the number of clusters $C$. The proposed method was tested on synthetic and real datasets. Compared to ASC methods, the proposed method delivered a consistent performance despite significant reduction of edges.
Spectral clustering became a popular choice for data clustering for its ability of uncovering clusters of different shapes. However, it is not always preferable over other clustering methods due to its computational demands. One of the effective ways to bypass these computational demands is to perform spectral clustering on a subset of points (data representatives) then generalize the clustering outcome, this is known as approximate spectral clustering (ASC). ASC uses sampling or quantization to select data representatives. This makes it vulnerable to 1) performance inconsistency (since these methods have a random step either in initialization or training), 2) local statistics loss (because the pairwise similarities are extracted from data representatives instead of data points). We proposed a refined version of -nearest neighbor graph, in which we keep data points and aggressively reduce number of edges for computational efficiency. Local statistics were exploited to keep the edges that do not violate the intra-cluster distances and nullify all other edges in the -nearest neighbor graph. We also introduced an optional step to automatically select the number of clusters . The proposed method was tested on synthetic and real datasets. Compared to ASC methods, the proposed method delivered a consistent performance despite significant reduction of edges
We propose a graph clustering formulation based on multicut (a.k.a. weighted correlation clustering) on the complete graph. Our formulation does not need specification of the graph topology as in the original sparse formulation of multicut, making our approach simpler and potentially better performing. In contrast to unweighted correlation clustering we allow for a more expressive weighted cost structure. In dense multicut, the clustering objective is given in a factorized form as inner products of node feature vectors. This allows for an efficient formulation and inference in contrast to multicut/weighted correlation clustering, which has at least quadratic representation and computation complexity when working on the complete graph. We show how to rewrite classical greedy algorithms for multicut in our dense setting and how to modify them for greater efficiency and solution quality. In particular, our algorithms scale to graphs with tens of thousands of nodes. Empirical evidence on instance segmentation on Cityscapes and clustering of ImageNet datasets shows the merits of our approach.
Stock market investment have been an ideal form of investment for many years. Investing capitals smartly in stock market yields high profit returns. But there are many companies available in a market. Currently there are more than $345$ active companies who have stocks in Dhaka Stock Exchange (DSE). Analyzing all these companies is quite impossible. However, many companies tend to move together. This study aims at finding which companies in DSE have a close connection and move alongside each other. By analyzing this relation, the investors and traders will be able to analyze a lot of companies' statistics from a calculating just a handful number of companies. The conducted experiment yielded promising results. It was found that though the system was not given anything other than technical data, it was able to identify companies that show domain specific outcomes. In other words, a relation between technical data and fundamental data was discovered from the conducted experiment.
Benefiting from the intrinsic supervision information exploitation capability, contrastive learning has achieved promising performance in the field of deep graph clustering recently. However, we observe that two drawbacks of the positive and negative sample construction mechanisms limit the performance of existing algorithms from further improvement. 1) The quality of positive samples heavily depends on the carefully designed data augmentations, while inappropriate data augmentations would easily lead to the semantic drift and indiscriminative positive samples. 2) The constructed negative samples are not reliable for ignoring important clustering information. To solve these problems, we propose a Cluster-guided Contrastive deep Graph Clustering network (CCGC) by mining the intrinsic supervision information in the high-confidence clustering results. Specifically, instead of conducting complex node or edge perturbation, we construct two views of the graph by designing special Siamese encoders whose weights are not shared between the sibling sub-networks. Then, guided by the high-confidence clustering information, we carefully select and construct the positive samples from the same high-confidence cluster in two views. Moreover, to construct semantic meaningful negative sample pairs, we regard the centers of different high-confidence clusters as negative samples, thus improving the discriminative capability and reliability of the constructed sample pairs. Lastly, we design an objective function to pull close the samples from the same cluster while pushing away those from other clusters by maximizing and minimizing the cross-view cosine similarity between positive and negative samples. Extensive experimental results on six datasets demonstrate the effectiveness of CCGC compared with the existing state-of-the-art algorithms.
In this paper, we reduce the complexity of approximating the correlation clustering problem from $O(m\times\left( 2+ \alpha (G) \right)+n)$ to $O(m+n)$ for any given value of $\varepsilon$ for a complete signed graph with $n$ vertices and $m$ positive edges where $\alpha(G)$ is the arboricity of the graph. Our approach gives the same output as the original algorithm and makes it possible to implement the algorithm in a full dynamic setting where edge sign flipping and vertex addition/removal are allowed. Constructing this index costs $O(m)$ memory and $O(m\times\alpha(G))$ time. We also studied the structural properties of the non-agreement measure used in the approximation algorithm. The theoretical results are accompanied by a full set of experiments concerning seven real-world graphs. These results shows superiority of our index-based algorithm to the non-index one by a decrease of %34 in time on average.
Graph clustering is a fundamental problem in unsupervised learning, with numerous applications in computer science and in analysing real-world data. In many real-world applications, we find that the clusters have a significant high-level structure. This is often overlooked in the design and analysis of graph clustering algorithms which make strong simplifying assumptions about the structure of the graph. This thesis addresses the natural question of whether the structure of clusters can be learned efficiently and describes four new algorithmic results for learning such structure in graphs and hypergraphs. All of the presented theoretical results are extensively evaluated on both synthetic and real-word datasets of different domains, including image classification and segmentation, migration networks, co-authorship networks, and natural language processing. These experimental results demonstrate that the newly developed algorithms are practical, effective, and immediately applicable for learning the structure of clusters in real-world data.
We study the problem of graph clustering under a broad class of objectives in which the quality of a cluster is defined based on the ratio between the number of edges in the cluster, and the total weight of vertices in the cluster. We show that our definition is closely related to popular clustering measures, namely normalized associations, which is a dual of the normalized cut objective, and normalized modularity. We give a linear time constant-approximate algorithm for our objective, which implies the first constant-factor approximation algorithms for normalized modularity and normalized associations.
Using graph neural networks for large graphs is challenging since there is no clear way of constructing mini-batches. To solve this, previous methods have relied on sampling or graph clustering. While these approaches often lead to good training convergence, they introduce significant overhead due to expensive random data accesses and perform poorly during inference. In this work we instead focus on model behavior during inference. We theoretically model batch construction via maximizing the influence score of nodes on the outputs. This formulation leads to optimal approximation of the output when we do not have knowledge of the trained model. We call the resulting method influence-based mini-batching (IBMB). IBMB accelerates inference by up to 130x compared to previous methods that reach similar accuracy. Remarkably, with adaptive optimization and the right training schedule IBMB can also substantially accelerate training, thanks to precomputed batches and consecutive memory accesses. This results in up to 18x faster training per epoch and up to 17x faster convergence per runtime compared to previous methods.
Contrastive deep graph clustering, which aims to divide nodes into disjoint groups via contrastive mechanisms, is a challenging research spot. Among the recent works, hard sample mining-based algorithms have achieved great attention for their promising performance. However, we find that the existing hard sample mining methods have two problems as follows. 1) In the hardness measurement, the important structural information is overlooked for similarity calculation, degrading the representativeness of the selected hard negative samples. 2) Previous works merely focus on the hard negative sample pairs while neglecting the hard positive sample pairs. Nevertheless, samples within the same cluster but with low similarity should also be carefully learned. To solve the problems, we propose a novel contrastive deep graph clustering method dubbed Hard Sample Aware Network (HSAN) by introducing a comprehensive similarity measure criterion and a general dynamic sample weighing strategy. Concretely, in our algorithm, the similarities between samples are calculated by considering both the attribute embeddings and the structure embeddings, better revealing sample relationships and assisting hardness measurement. Moreover, under the guidance of the carefully collected high-confidence clustering information, our proposed weight modulating function will first recognize the positive and negative samples and then dynamically up-weight the hard sample pairs while down-weighting the easy ones. In this way, our method can mine not only the hard negative samples but also the hard positive sample, thus improving the discriminative capability of the samples further. Extensive experiments and analyses demonstrate the superiority and effectiveness of our proposed method.
We pose video object segmentation as spectral graph clustering in space and time, with one graph node for each pixel and edges forming local space-time neighborhoods. We claim that the strongest cluster in this video graph represents the salient object. We start by introducing a novel and efficient method based on 3D filtering for approximating the spectral solution, as the principal eigenvector of the graph's adjacency matrix, without explicitly building the matrix. This key property allows us to have a fast parallel implementation on GPU, orders of magnitude faster than classical approaches for computing the eigenvector. Our motivation for a spectral space-time clustering approach, unique in video semantic segmentation literature, is that such clustering is dedicated to preserving object consistency over time, which we evaluate using our novel segmentation consistency measure. Further on, we show how to efficiently learn the solution over multiple input feature channels. Finally, we extend the formulation of our approach beyond the segmentation task, into the realm of object tracking. In extensive experiments we show significant improvements over top methods, as well as over powerful ensembles that combine them, achieving state-of-the-art on multiple benchmarks, both for tracking and segmentation.