Riemannian symmetric spaces (RSS) such as hyperbolic spaces and symmetric positive definite (SPD) manifolds have become popular spaces for representation learning. In this paper, we propose a novel approach for building discriminative neural networks on Siegel spaces, a family of RSS that is largely unexplored in machine learning tasks. For classification applications, one focus of recent works is the construction of multiclass logistic regression (MLR) and fully-connected (FC) layers for hyperbolic and SPD neural networks. Here we show how to build such layers for Siegel neural networks. Our approach relies on the quotient structure of those spaces and the notation of vector-valued distance on RSS. We demonstrate the relevance of our approach on two applications, i.e., radar signal classification and node classification. Our results successfully demonstrate state-of-the-art performance across all datasets.

In this article, we present an innovative clustering framework designed for large datasets and real-time data streams which uses a sliding window and histogram model to address the challenge of memory congestion while reducing computational complexity and improving cluster quality for both static and dynamic clustering. The framework provides a simple way to characterize the probability distribution of cluster distributions through histogram models, regardless of their distribution type. This advantage allows for efficient use with various conventional clustering algorithms . To facilitate effective clustering across windows, we use a statistical measure that allows the comparison and merging of different clusters based on the calculation of the Wasserstein distance between histograms.

Unsupervised learning, particularly clustering, involves systematically categorizing objects based on inherent similarities. As a popular research field of clustering, multi-view data analysis enriches clustering by considering diverse perspectives. Persistent challenges in dynamic multi-view clustering focus on optimizing speed and maintaining quality with an increasing number of views. Motivated by the success of recent researches, we propose in this article an advanced framework of incremental multi-view clustering based on barycentric coordinates representation (IMBC). This framework refines object representation of each view and saves only the first m views as base kernels, then learns a consensus kernel. Updated m base kernels can be obtained via the combination of previous m base kernels and the representation of a new view. The proposed approach also offers the feasibility of incremental multi-modal clustering: its versatility extends to various data types and modalities, enhancing its applicability in diverse scenarios. Through the implementation of various standard clustering algorithms on the consensus kernel, our proposed approaches demonstrate efficient computational processing, achieving comparable clustering performance to existing approaches while incurring lower computational time.

Data is increasingly being collected from multiple sources and described by multiple views. These multi-view data provide richer information than traditional single-view data. Fusing the former for specific tasks is an essential component of multi-view clustering. Since the goal of multi-view clustering algorithms is to discover the common latent structure shared by multiple views, the majority of proposed solutions overlook the advantages of incorporating knowledge derived from horizontal collaboration between multi-view data and the final consensus. To fill this gap, we propose the Joint Multi-View Collaborative Clustering (JMVCC) solution, which involves the generation of basic partitions using Non-negative Matrix Factorization (NMF) and the horizontal collaboration principle, followed by the fusion of these local partitions using ensemble clustering. Furthermore, we propose a weighting method to reduce the risk of negative collaboration (i.e., views with low quality) during the generation and fusion of local partitions. The experimental results, which were obtained using a variety of data sets, demonstrate that JMVCC outperforms other multi-view clustering algorithms and is robust to noisy views.

We consider clustering issues where the available attributes can be divided into various independent groups that frequently offer complimentary information. We concentrate on real-world applications in this paper where a single instance can be represented by a number of heterogeneous features. As was performed successfully in the prior work of clustering on a single view dataset by using barycentric coordinate(BC) representation, and also a recent KMeans-based multi-view clustering RMKMC which proposed that the weights of views can be auto-updated by introducing a hyperparameter γ, we further propose a novel approach of multi-view clustering BCmvlearn by combining these two approaches to reduce complexity without sacrificing clustering quality. In addition, the vector form of the original dataset not being absolutely necessary due to the distance-based property of the BC representation, a variant application of multi-modal clustering is also achievable.

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.

Recently, more researchers are interested in the domain of quantum machine learning as it can manipulate and classify large numbers of vectors in high dimensional space in reasonable time. In this paper, we propose a new approach called Quantum Collaborative K-means which is based on combining several clustering models based on quantum K-means. This collaboration consists of exchanging the information of each algorithm locally in order to find a common underlying structure for clustering. Comparing the classical version of collaborative clustering to our approach, we notice that we have an exponential speed up: while the classical version takes O(K×L×M×N), the quantum version takes only O(K×L×log(M×N)). And comparing to the quantum version of K-means, we get a better solution in terms of the criteria of validation which means in terms of clustering. The empirical evaluations validate the benefits of the proposed approach.

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.

Collaborative clustering is a recent learning paradigm concerned with the unsupervised analysis of complex multi-view data using several algorithms working together. Well known applications of collaborative clustering include multi-view clustering and distributed data clustering, where several algorithms exchange information in order to mutually improve each others based on the diversity of their models or their view of the data. However, many of the proposed algorithms and statistical models in these fields lack the capability to properly detect noisy views and sub-optimal collaborators. As a result, these weak collaborators and noisy views often go undetected during the collaborative process, and end up deteriorating the results of all other algorithms. In this article, we propose a weighting optimization method for the collaborative version of the SOM algorithm that will help detect whether local self-organizing maps should or should not exchange their information based on the diversity between their topologies. This method can further be used to detect noisy views and discard them in unsupervised collaborative and multi-view processes.

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 collaborative topological clustering approach based on Self-Organizing Maps (SOM) with more flexible structure. The main drawback of the previously proposed collaborative methods is they require a strong condition to carry out the collaboration, i.e. all the map related to each site must be learned with the same number of neurones. An alternative approach to overcome the problem of this dimensionality has been proposed in the case of k-means. The idea consists in modifying databases by adding virtual points which convey clustering information, to change the position of centers of the clustering solution. This approach seems promising because it is very flexible. In this paper we propose a method called VP2SOM (Virtual Points to SOM) which uses virtual points to realize the collaboration between SOM maps with different sizes. We have tested the proposed approach on several datasets and the early results seem promising.

This paper introduces a new topological clustering approach to cluster high dimensional datasets based on t-SNE (Stochastic Neighbor Embedding) dimensionality reduction method and spectral clustering. Spectral clustering method needs to construct an adjacency matrix and calculate the eigen-decomposition of the corresponding Laplacian matrix [1] which are computational expensive and is not easy to apply on large-scale data sets. One of the issue of this problem is to reduce the dimensionality before to cluster the dataset. The t-SNE method which performs good results for visualization allows a projection of the dataset in low dimensional spaces that make it easy to use for very large datasets. Using t-SNE during the learning process will allow to reduce the dimensionality and to preserve the topology of the dataset by increasing the clustering accuracy. We illustrate the power of this method with several real datasets. The results show a good quality of clustering results and a higher speed.

Unsupervised machine learning approaches involving several clustering algorithms working together to tackle difficult data sets are a recent area of research with a large number of applications such as clustering of distributed data, multi-expert clustering, multi-scale clustering analysis or multi-view clustering. Most of these frameworks can be regrouped under the umbrella of collaborative clustering, the aim of which is to reveal the common underlying structures found by the different algorithms while analyzing the data. Within this context, the purpose of this article is to propose a collaborative framework lifting the limitations of many of the previously proposed methods: Our proposed collaborative learning method makes possible for a wide range of clustering algorithms from different families to work together based solely on their clustering solutions, thus lifting previous limitation requiring identical prototypes between the different collaborators. Our proposed framework uses a variational EM as its theoretical basis for the collaboration process and can be applied to any of the previously mentioned collaborative contexts. In this article, we give the main ideas and theoretical foundations of our method, and we demonstrate its effectiveness in a series of experiments on real data sets as well as data sets from the literature.

Recent studies have shown that the use of a priori knowledge can significantly improve the results of unsupervised classification. However, capturing and formatting such knowledge as constraints is not only very expensive requiring the sustained involvement of an expert but it is also very difficult because some valuable information can be lost when it cannot be encoded as constraints. In this paper, we propose a new constraint-based clustering approach based on ontology reasoning for automatically generating constraints and bridging the semantic gap in satellite image labeling. The use of ontology as a priori knowledge has many advantages that we leverage in the context of satellite image interpretation. The experiments we conduct have shown that our proposed approach can deal with incomplete knowledge while completely exploiting the available one.

In this paper we introduce a new learning approach, which provides automated topological co-clustering based on Self-Organizing Map. The proposed approach (wd-TCoC) is computationally simple, learns a different feature's weights vector for each prototype (relevance vector) and estimate the data density distribution on the map to produce an automatic clustering. The feature's weights are computed for each observation during the learning process in order to attempt a clustering of both features and observations simultaneously. After the learning phase, a selection method with weight vectors is used to characterize features for each cluster. Compared to classical co-clustering algorithm, the features clustering in the proposed method is a fuzzy clustering, which allows a feature to belongs to different clusters and in this way to be able to eliminate the noisy features. The originality of the proposed method consists of 2 points: i) the co-clustering is made automatically, i.e. there is no parameter to fix to cluster the data and the features and ii) the features are fuzzy clustered. We illustrate the performance of the proposed approach using different data sets.

The aim of collaborative clustering is to reveal the common underlying structures found by different algorithms while analyzing data. The fundamental concept of collaboration is that the clustering algorithms operate locally but collaborate by exchanging information about the local structures found by each algorithm. In this framework, the one purpose of this article is to introduce a new method which allows to reinforce the clustering process by exchanging information between several results acquired by different clustering algorithms. The originality of our proposed approach is that the collaboration step can use clustering results obtained from any type of algorithm during the local phase. This article gives the theoretical foundations of our approach as well as some experimental results. The proposed approach has been validated on several data sets and the results have shown to be very competitive.

The aim of collaborative clustering is to reveal the common structure of data which are distributed on different sites. The topological collaborative clustering, based on Self-Organizing Maps (SOM) is an unsupervised learning method which is able to use the output of other SOMs from other sites during the learning. This paper investigates the impact of the diversity between collaborators on the collaboration's quality and presents a study of different diversity indexes for collaborative clustering. Based on experiments on artificial and real datasets, we demonstrated that the quality and the diversity of the collaboration can have an important impact on the quality of the collaboration and that not all diversity indexes are relevant for this task.

Opinion Mining is the field of computational study of peopel's emotional behavior expressed in text. The purpose of this article is to introduce a new framework for emotion (opinion) mining based on topological unsupervised learning and hierarchical clustering. In contrast to supervised learning, the problem of clustering characterization in the context of opinion mining based on unsupervised learning is challenging, because label information is not available or not used to guide the learning algorithm. The algorithm described in this paper provides topological clustering of the opionon issued from the tweets, each cluster being associated to a prototype and a weight vector, reflecting the relevance of the data belonging to each clsuter. The proposed framework requires simple computational techniques and are based on the double local weighting self-organizing map (dlw-SOM) model and Hierarchical Clustering. The proposed framework has been used on a real dataset issued from the tweets collected during the 2012 French election compaign.

The purpose of this article is to introduce a new collaborative multi-view clustering approach based on a probabilistic model. The aim of collaborative clustering is to reveal the common underlying structure of data spread across multiple data sites by applying clustering techniques. The strength of the collaboration between each pair of data repositories is determined by a fixed parameter. Previous works considered deterministic techniques such as Fuzzy C-Means (FCM) and Self-Organizing Maps (SOM). In this paper, we present a new approach for the collaborative clustering using a generative model, which is the Generative Topographic Mappings (GTM). Maps representing different sites could collaborate without recourse to the original data, preserving their privacy. We present the approach for multi-view collaboration using GTM, where data sets have the same observations but presented in different feature space; i.e. different dimensions. The proposed approach has been validated on several data sets, and experimental results have shown very promising performance.

A common phenomenon in biological experiments is that it is not possible to obtain complete measurements for all the samples. Note that some microarrays are very informative, but very expensive to have them for all the samples. However, we can use publicly available background knowledge about the potential links between the components of different microarrays (known, also, as genes). As a result, we shall translate all the selected genes in the terms of other genes. In line with the most fundamental principles of the incremental learning, those secondary genes are to be included in the regression models automatically to give the learning processes the right initial directions. The proposed method was tested online during the e-LICO data-mining Contest, where we had achieved second best score.

In this paper, we propose a study on the use of weighted topological learning and matrix factorization methods to transform the representation space of a sparse dataset in order to increase the quality of learning, and adapt it to the case of transfer learning. The matrix factorization allows us to find latent variables, weighted topological learning is used to detect the most relevant among them. New data representation is based on their projections on the weighted topological model. Each object in the dataset is described by a new representation consisting of the distances of this object to all components of the topological model (prototypes). For transfer learning, we propose a new method where the representation of data is done in the same way as in the first phase, but using a pruned topological model. This pruning is performed after labeling the units of the topological model using the labels available for transfer. The experiments are presented as a part of an International Challenge [1] where we have obtained promising results (5th rank).

The aim of collaborative clustering is to reveal the common structure of data distributed on different sites. In this paper, we present a formalism of topological collaborative clustering using prototype-based clustering techniques; in particular we formulate our approach using Kohonen's Self-Organizing Maps. Maps representing different sites could collaborate without recourse to the original data, preserving their privacy. We present two different approaches of collaborative clustering: horizontal and vertical. The strength of collaboration (confidence exchange) between each pair of datasets is determined by a parameter, we call coefficient of collaboration, to be estimated iteratively during the collaboration phase using a gradient-based optimization, for both the approaches. The proposed approaches have been validated on several datasets and experimental results have shown very promising performance.

The aim of collaborative clustering is to reveal the common structure of data which are distributed on different sites. The topological collaborative clustering (based on Kohonen Self-Organizing Maps) allows to take into account other maps without recourse to the data in an unsupervised learning. In this paper, the approach is presented in the case of SOM and it is valid for all prototypes based classifications methods. The strength of the collaboration between each pair of datasets is determined by a fixed parameter for the both, vertical and horizontal topological collaborative clustering. In this study, learning the confidence exchange is presented for the both topological collaborative clustering approaches by using the topological knowledge. The gradient based optimization is used to set the value of the confidence parameter for each collaboration. The paper presents the formalism of the approach and its validation. The proposed approach has been validated on several datasets and experimental results have shown very promising performance.

This paper addresses the problem of cluster characterization by selecting a subset of the most relevant features for each cluster from a categorical dataset in an autonomous way. The proposed autonomous model is based on the Relational Topological Clustering (RTC) associated with a statistical test which allows to detect the most important variables in an automatic way without setting any parameters. The RTC approach is used to build a prototypes matrix which contains continuous variables, where each prototype vector represents correlated categorical data. Thereafter, the statistical ScreeTest is used to detect relevant and correlated features (or modalities) for each prototype. The proposed method requires simple computational techniques and the RTC topology technique is based on the principle of the self-organizing map (SOM) model. This method allows the dimensionality reduction, visualization and cluster characterization simultaneously. Empirical results based on real datasets from the UCI repository, are given and discussed.

This paper introduces a new topological clustering formalism, dedicated to categorical data arising in the form of a binary matrix or a sum of binary matrices. The proposed approach is based on the principle of the Kohonen's model (conservation of topological order) and uses the Relational Analysis formalism by optimizing a cost function defined as a Condorcet criterion. We propose an hybrid algorithm, which deals linearly with large datasets, provides a natural clusters identification and allows a visualization of the clustering result on a two dimensional grid while preserving the a priori topological order of the data. The proposed approach called RTC was validated on several datasets and the experimental results showed very promising performances.

This paper introduces a relational topological map model, dedicated to multidimensional categorial data (or qualitative data) arising in the form of a binary matrix or a sum of binary matrices. This approach is based on the principle of Kohonen's model (conservation of topological order) and uses the Relational Analysis formalism by maximizing a modified Condorcet criterion. This proposed method is developed from the classical Relational Analysis approach by adding a neighborhood constraint to the Condorcet criterion. We propose a hybrid algorithm, which deals linearly with large data sets, provides a natural clusters identification and allows a visualization of the clustering result on a two-dimensional grid while preserving the a priori topological order of this data. The proposed approach called Relational Topological Map (RTM) was validated on several databases and the experimental results showed very promising performances.

This paper presents a new learning strategy for the clustering algorithms based on Self-Organizing Map. Our contribution relies on the competitive phase of this unsupervised learning algorithm and proposes a new strategy for choosing the most active cell/neuron. This new strategy is to choose the most active neuron taking into account its historical activations, learned in a voting matrix from the dataset. Indeed, the use of this historic neighbourhood, allows introducing of topological constraints in the final geometry of the map. This new unsupervised learning approach allows discovering of data structure with a better quality (lower topographic error and better clustering purity). The proposed approach was validated on multiple datasets of different sizes and complexities, and the experimental validation shows promising results.

We introduce a new learning approach, which provides simultaneously self-organizing map (SOM) and local weight vector for each cluster. The proposed approach is computationally simple, and learns a different features vector weights for each cell (relevance vector). Based on the self-organizing map approach, we present two new simultaneously clustering and weighting algorithms: local weighting observation lwo-SOM and local weighting distance lwd-SOM. Both algorithms achieve the same goal by minimizing different cost functions. After learning phase, a selection method with weight vectors is used to prune the irrelevant variables and thus we can characterize the clusters. We illustrate the performance of the proposed approach using different data sets. A number of synthetic and real data are experimented on to show the benefits of the proposed local weighting using self-organizing models.