Domain adaptation arises as an important problem in statistical learning theory, arising when the data-generating processes differ between the training and test samples, respectively called source and target domains. Recent theoretical advances have demonstrated that the success of domain adaptation algorithms heavily relies on their ability to minimize the divergence between the probability distributions of the source and target domains. However, minimizing this divergence cannot be achieved independently of other key ingredients, such as the source risk or the combined error of the ideal joint hypothesis. The trade-off between these terms is often ensured through algorithmic solutions that remain implicit and are not directly reflected by the theoretical guarantees. To get to the bottom of this issue, we propose in this paper a new theoretical framework for domain adaptation through hierarchical optimal transport. This framework provides more explicit generalization bounds and enables us to consider the natural hierarchical organization of samples in both domains into structures, i.e. classes or clusters. Additionally, we provide a new divergence measure between the source and target domains called Hierarchical Wasserstein distance that indicates under mild assumptions, which structures need to be aligned to achieve successful adaptation.

Traditional domain adaptation algorithms often struggle when faced with significant divergence between source and target domains. Gradual domain adaptation addresses this problem by enabling sequential adaptation across intermediate domains—composed of unlabeled data—ensuring a smooth transition from the source to the target. This process follows a divide-and-conquer scheme, breaking down adaptation into smaller, more manageable steps. However, its applicability is often constrained by the limited availability of such intermediate data in real-world scenarios. In this paper, we explore an alternative approach that constructs a sequence of intermediate domains using McCann’s interpolation, a method that defines a geodesic path in Wasserstein space, ensuring an optimal transition between probability measures. The generated sequence of intermediate domains can be directly incorporated into any gradual domain adaptation algorithm. Through evaluations on benchmark datasets, we show that the proposed approach achieves adaptation performance comparable to that of manually predefined domain sequences.

This work addresses the problem of multi-source domain adaptation using the Wasserstein barycenter through a hierarchical data representation. Most current approaches tackle this problem by treating each source domain as a probability measure whose support comprises its data points. In this paper, we offer a new perspective: we conceptualize a source domain as a probability measure whose support includes its classes, with each class treated as a separate probability measure, and its support is formed by the points belonging to it. Our method, called Wasserstein Barycenter for Hierarchical Representation (WBHR), aims at constructing an auxiliary source domain formed by aggregated classes sharing the same label within different domains, using the Wasserstein barycenter, thereby transforming the problem into a standard single-source adaptation task, which is addressed through hierarchical optimal transport. We discuss the theoretical aspects of the method and propose a conceptually simple algorithm. Empirical evaluations demonstrate that our WBHR model outperforms existing multi-source domain adaptation techniques across two benchmark datasets, underscoring its efficacy for practical applications.

1Human Activity Recognition (HAR) is a field of study that focuses on identifying and classifying human activities. Skeleton-based Human Activity Recognition has received much attention in recent years, where Graph Convolutional Network (GCN) based method is widely used and has achieved remarkable results. However, the representation of skeleton data and the issue of over-smoothing in GCN still need to be studied. 1). Compared to central nodes, edge nodes can only aggregate limited neighbor information, and different edge nodes of the human body are always structurally related. However, the information from edge nodes is crucial for fine-grained activity recognition. 2). The Graph Convolutional Network suffers from a significant over-smoothing issue, causing nodes to become increasingly similar as the number of network layers increases. Based on these two ideas, we propose a two-stream graph convolution method called Spatial-Structural GCN (SpSt-GCN). Spatial GCN performs information aggregation based on the topological structure of the human body, and structural GCN performs differentiation based on the similarity of edge node sequences. The spatial connection is fixed, and the human skeleton naturally maintains this topology regardless of the actions performed by humans. However, the structural connection is dynamic and depends on the type of movement the human body is performing. Based on this idea, we also propose an entirely data-driven structural connection, which greatly increases flexibility. We evaluate our method on two large-scale datasets, i.e., NTU RGB+D and NTU RGB+D 120. The proposed method achieves good results while being efficient.

Domain adaptation is a subfield of statistical learning theory that takes into account the shift between the distribution of training and test data, typically known as source and target domains, respectively. In this context, this paper presents an incremental approach to tackle the intricate challenge of unsupervised domain adaptation, where labeled data within the target domain is unavailable. The proposed approach, OTP-DA, endeavors to learn a sequence of joint subspaces from both the source and target domains using Linear Discriminant Analysis (LDA), such that the projected data into these subspaces are domain-invariant and well-separated. Nonetheless, the necessity of labeled data for LDA to derive the projection matrix presents a substantial impediment, given the absence of labels within the target domain in the setting of unsupervised domain adaptation. To circumvent this limitation, we introduce a selective label propagation technique grounded on optimal transport (OTP), to generate pseudo-labels for target data, which serve as surrogates for the unknown labels. We anticipate that the process of inferring labels for target data will be substantially streamlined within the acquired latent subspaces, thereby facilitating a self-training mechanism. Furthermore, our paper provides a rigorous theoretical analysis of OTP-DA, underpinned by the concept of weak domain adaptation learners, thereby elucidating the requisite conditions for the proposed approach to solve the problem of unsupervised domain adaptation efficiently. Experimentation across a spectrum of visual domain adaptation problems suggests that OTP-DA exhibits promising efficacy and robustness, positioning it favorably compared to several state-of-the-art methods.

In this paper, we address the problem of unsupervised domain adaptation where we ask to infer a low target risk classifier, while labeled data are only available from the source domain. Our proposed approach, called DA-OTP, aims to learn a gradual subspace alignment of the source and target domains through Supervised Locality Preserving Projection, so that projected data in the joint low-dimensional latent subspace can be domain-invariant and easily separable. However, this objective can be rather challenging to achieve because of the absence of labeled data in the target domain. To overcome this conundrum, we use an incremental label propagation technique based on optimal transport, which performs selective pseudo-labeling in the target domain. The selected pseudo-labeled target samples are then combined with labeled source samples to learn in a self-training fashion a robust classifier after the incremental subspace alignment. Experiments show the competitiveness of the proposed approach across contemporary state-of-the-art methods over a range of domain adaptation problems. We make our code publicly available.11Code is available at: https://github.com/DA-OTP/DA-OTP

Non-negative matrix factorization (NMF) is an unsupervised algorithm for clustering where a non-negative data matrix is factorized into (usually) two matrices with the property that all the matrices have no negative elements. This factorization raises the problem of instability, which means whenever we run NMF for the same dataset, we get different factorization. In order to solve the problem of non-uniqueness and to have a more stable solution, we propose a new approach that consists on collaborating different NMF models followed by a consensus. The proposed approach was validated on several datasets and the experimental results showed the effectiveness of our approach which is based on the reducing of standard reconstruction error in NMF model.

In this paper, we tackle the transductive semi-supervised learning problem that aims to obtain label predictions for the given unlabeled data points according to Vapnik's principle. Our proposed approach is based on optimal transport, a mathematical theory that has been successfully used to address various machine learning problems, and is starting to attract renewed interest in semi-supervised learning community. The proposed approach, Optimal Transport Propagation (OTP), performs in an incremental process, label propagation through the edges of a complete bipartite edge-weighted graph, whose affinity matrix is constructed from the optimal transport plan between empirical measures defined on labeled and unlabeled data. OTP ensures a high degree of predictions certitude by controlling the propagation process using a certainty score based on Shannon's entropy. We also provide a convergence analysis of our algorithm. Experiments task show the superiority of the proposed approach over the state-of-the-art. We make our code publicly available.11Code is available at: https://github.com/MouradElHamri/OTP

Graph clustering techniques are very useful for detecting densely connected groups in large graphs. Many existing graph clustering methods mainly focus on the topological structure, but ignore the vertex properties. Existing graph clustering methods have been recently extended to deal with nodes attribute. In this paper we propose a new method which uses the nodes attributes information along with the topological structure of the network in the clustering process. In order to use the information about the attributes nodes, the collaborative clustering can be employed in the model. The aim of collaborative clustering is to reveal the common underlying structure of data spread across multiple sites by applying different clustering algorithms and therefore improve the final clustering result. The purpose of this article is to introduce a new attributed collaborative multi-view networks based on community detection in networks and topological collaborative learning. The idea consists in modifying databases by adding virtual points which convey clustering information, to change the position of centers of the clustering solution. Experimental results demonstrate the effectiveness of the proposed method through comparisons with the state-of-the-art graph clustering methods on synthetic and real datasets.

Multiplex network model has been recently proposed as a mean to capture high level complexity in real-world interaction networks. This model, in spite of its simplicity, allows handling multi-relationnal, heterogeneous, dynamic and even attributed networks. However, it requiers redefining and adapting almost all basic metrics and algorithms generally used to analyse complex networks. In this work we present MUNA: a MUltiplex Network Analysis library that we have developed in both R and Python on top of igraph network analysis package. In its current version, MUNA provides primitives to build, edit and modify multiplex networks. It also provides a bunch of functions computing basic metrics on multiplex networks. However, the most interesting functionality provided by MUNA is probably the wide variety of available community detection algorithms. Actually, the library implements different approaches for community detection including: partition aggregation approaches, layer aggregation approaches and direct multiplex approaches such as the GenLouvain and MuxLicod algorithms. It also offers an extended list of multiplex community evaluation indexes.