Similarity learning can be significantly advanced by informative relationships among different samples and features. The current methods try to excavate the multiple correlations in different aspects, but cannot integrate them into a unified framework. In this paper, we provide to consider the multiple correlations from a unified perspective and propose a new method called MetricFormer, which can effectively capture and model the multiple correlations with an elaborate metric transformer. In MetricFormer, the feature decoupling block is adopted to learn an ensemble of distinct and diverse features with different discriminative characteristics. After that, we apply the batch-wise correlation block into the batch dimension of each mini-batch to implicitly explore sample relationships. Finally, the feature-wise correlation block is performed to discover the intrinsic structural pattern of the ensemble of features and obtain the aggregated feature embedding for similarity measuring. With three kinds of transformer blocks, we can learn more representative features through the proposed MetricFormer. Moreover, our proposed method can be flexibly integrated with any metric learning framework. Extensive experiments on three widely-used datasets demonstrate the superiority of our proposed method over state-of-the-art methods.

Graph similarity is critical in graph-related tasks such as graph retrieval, where metrics like maximum common subgraph (MCS) and graph edit distance (GED) are commonly used. However, exact computations of these metrics are known to be NP-Hard. Recent neural network-based approaches approximate the similarity score in embedding spaces to alleviate the computational burden, but they either involve expensive pairwise node comparisons or fail to effectively utilize structural and scale information of graphs. To tackle these issues, we propose a novel geometric-based graph embedding method called Graph2Region (G2R). G2R represents nodes as closed regions and recovers their adjacency patterns within graphs in the embedding space. By incorporating the node features and adjacency patterns of graphs, G2R summarizes graph regions, i.e., graph embeddings, where the shape captures the underlying graph structures and the volume reflects the graph size. Consequently, the overlap between graph regions can serve as an approximation of MCS, signifying similar node regions and adjacency patterns. We further analyze the relationship between MCS and GED and propose using disjoint parts as a proxy for GED similarity. This analysis enables concurrent computation of MCS and GED, incorporating local and global structural information. Experimental evaluation highlights G2R's competitive performance in graph similarity computation. It achieves up to a 60.0\% relative accuracy improvement over state-of-the-art methods in MCS similarity learning, while maintaining efficiency in both training and inference. Moreover, G2R showcases remarkable capability in predicting both MCS and GED similarities simultaneously, providing a holistic assessment of graph similarity. Code available at https://github.com/liuzhouyang/Graph2Region.

--Graph similarity learning, crucial for tasks such as graph classification and similarity search, focuses on measuring the similarity between two graph-structured entities. The core challenge in this field is effectively managing the interactions between graphs. Traditional methods often entail separate, redundant computations for each graph pair, leading to unnecessary complexity. This paper revolutionizes the approach by introducing a parallel graph interaction method called graph fusion. By merging the node sequences of graph pairs into a single large graph, our method leverages a global attention mechanism to facilitate interaction computations and to harvest cross-graph insights. We further assess the similarity between graph pairs at two distinct levels--graph-level and node-level--introducing two innovative, yet straightforward, similarity computation algorithms. Extensive testing across five public datasets shows that our model not only outperforms leading baseline models in graph-to-graph classification and regression tasks but also sets a new benchmark for performance and efficiency. I NTRODUCTION Applications based on graph data structures, such as social network analysis [1], bioinformatics [2], and recommendation systems [3], play a crucial role in both academia and industry. Among them, graph similarity learning is one of the most significant challenges in graph-related machine learning tasks.

Similarity learning can be significantly advanced by informative relationships among different samples and features. The current methods try to excavate the multiple correlations in different aspects, but cannot integrate them into a unified framework. In this paper, we provide to consider the multiple correlations from a unified perspective and propose a new method called MetricFormer, which can effectively capture and model the multiple correlations with an elaborate metric transformer. In MetricFormer, the feature decoupling block is adopted to learn an ensemble of distinct and diverse features with different discriminative characteristics. After that, we apply the batch-wise correlation block into the batch dimension of each mini-batch to implicitly explore sample relationships.

Alzheimer's disease (AD) is a complex neurodegenerative disorder that affects millions of people worldwide. Due to the heterogeneous nature of AD, its diagnosis and treatment pose critical challenges. Consequently, there is a growing research interest in identifying homogeneous AD subtypes that can assist in addressing these challenges in recent years. In this study, we aim to identify subtypes of AD that represent distinctive clinical features and underlying pathology by utilizing unsupervised clustering with graph diffusion and similarity learning. We adopted SIMLR, a multi-kernel similarity learning framework, and graph diffusion to perform clustering on a group of 829 patients with AD and mild cognitive impairment (MCI, a prodromal stage of AD) based on their cortical thickness measurements extracted from magnetic resonance imaging (MRI) scans. Although the clustering approach we utilized has not been explored for the task of AD subtyping before, it demonstrated significantly better performance than several commonly used clustering methods. Specifically, we showed the power of graph diffusion in reducing the effects of noise in the subtype detection. Our results revealed five subtypes that differed remarkably in their biomarkers, cognitive status, and some other clinical features. To evaluate the resultant subtypes further, a genetic association study was carried out and successfully identified potential genetic underpinnings of different AD subtypes. Our source code is available at: https://github.com/PennShenLab/AD-SIMLR.

Understanding and predicting the behavior of complex physical systems is a cornerstone of scientific and engineering endeavors. In fluid mechanics, for instance, accurately simulating real operational conditions is essential for the design and optimization of pipelines, aerospace components, and various industrial processes. However, full-scale simulations of such systems are often prohibitively expensive and time-consuming due to the intricate dynamics and vast parameter spaces involved. This poses a significant challenge for researchers and engineers who seek to explore and optimize these systems efficiently. One promising approach to mitigate these challenges is the identification of scaling similarities and symmetry groups within physical systems. By uncovering the correct scaling relations, we can develop smaller, more manageable models that accurately capture the essential behavior of real-world scenarios. These scaled models not only reduce computational costs but also accelerate the design and testing processes by allowing for efficient exploration of the parameter space. Moreover, understanding these scaling laws deepens our insight into the fundamental principles governing these systems, enabling us to generalize findings from simplified models to full-scale applications with greater confidence. In recent years, the application of machine learning in fluid mechanics has been on the rise, offering innovative tools to address complex problems that are difficult to solve analytically.

Catastrophic forgetting in neural networks during incremental learning remains a challenging problem. Previous research investigated catastrophic forgetting in fully connected networks, with some earlier work exploring activation functions and learning algorithms. Applications of neural networks have been extended to include similarity learning. Understanding how similarity learning loss functions would be affected by catastrophic forgetting is of significant interest. Our research investigates catastrophic forgetting for four well-known similarity-based loss functions during incremental class learning. The loss functions are Angular, Contrastive, Center, and Triplet loss. Our results show that the catastrophic forgetting rate differs across loss functions on multiple datasets. The Angular loss was least affected, followed by Contrastive, Triplet loss, and Center loss with good mining techniques. We implemented three existing incremental learning techniques, iCaRL, EWC, and EBLL. We further proposed a novel technique using Variational Autoencoders (VAEs) to generate representation as exemplars passed through the network's intermediate layers. Our method outperformed three existing state-of-the-art techniques. We show that one does not require stored images (exemplars) for incremental learning with similarity learning. The generated representations from VAEs help preserve regions of the embedding space used by prior knowledge so that new knowledge does not ``overwrite'' it.

Last week Voxel51 hosted the December 2022 Computer Vision Meetup. Our amazing speakers shared insightful presentations, the virtual room was packed, and the Q&A was vibrant! In this blog post we provide the recordings, recap presentation highlights and Q&A, as well as share the upcoming Meetup schedule so that you can join us at a future event. Hope to see you soon! In lieu of swag, we gave Meetup attendees the opportunity to help guide our monthly donation to charitable causes. The charity that received the highest number of votes was Children International.

One of the most fundamental problems in machine learning is to compare examples: Given a pair of objects we want to return a value which indicates degree of (dis)similarity. Similarity is often task specific, and pre-defined distances can perform poorly, leading to work in metric learning. However, being able to learn a similarity-sensitive distance function also presupposes access to a rich, discriminative representation for the objects at hand. In this dissertation we present contributions towards both ends. In the first part of the thesis, assuming good representations for the data, we present a formulation for metric learning that makes a more direct attempt to optimize for the k-NN accuracy as compared to prior work. We also present extensions of this formulation to metric learning for kNN regression, asymmetric similarity learning and discriminative learning of Hamming distance. In the second part, we consider a situation where we are on a limited computational budget i.e. optimizing over a space of possible metrics would be infeasible, but access to a label aware distance metric is still desirable. We present a simple, and computationally inexpensive approach for estimating a well motivated metric that relies only on gradient estimates, discussing theoretical and experimental results. In the final part, we address representational issues, considering group equivariant convolutional neural networks (GCNNs). Equivariance to symmetry transformations is explicitly encoded in GCNNs; a classical CNN being the simplest example. In particular, we present a SO(3)-equivariant neural network architecture for spherical data, that operates entirely in Fourier space, while also providing a formalism for the design of fully Fourier neural networks that are equivariant to the action of any continuous compact group.

Graph similarity learning refers to calculating the similarity score between two graphs, which is required in many realistic applications, such as visual tracking, graph classification, and collaborative filtering. As most of the existing graph neural networks yield effective graph representations of a single graph, little effort has been made for jointly learning two graph representations and calculating their similarity score. In addition, existing unsupervised graph similarity learning methods are mainly clustering-based, which ignores the valuable information embodied in graph pairs. To this end, we propose a contrastive graph matching network (CGMN) for self-supervised graph similarity learning in order to calculate the similarity between any two input graph objects. Specifically, we generate two augmented views for each graph in a pair respectively. Then, we employ two strategies, namely cross-view interaction and cross-graph interaction, for effective node representation learning. The former is resorted to strengthen the consistency of node representations in two views. The latter is utilized to identify node differences between different graphs. Finally, we transform node representations into graph-level representations via pooling operations for graph similarity computation. We have evaluated CGMN on eight real-world datasets, and the experiment results show that the proposed new approach is superior to the state-of-the-art methods in graph similarity learning downstream tasks.