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.

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.

Clustering is a compression task which consists in grouping similar objects into clusters. In real-life applications, the system may have access to several views of the same data and each view may be processed by a specific clustering algorithm: this framework is called multi-view clustering and can benefit from algorithms capable of exchanging information between the different views. In this paper, we consider this type of unsupervised ensemble learning as a compression problem and develop a theoretical framework based on algorithmic theory of information suitable for multi-view clustering and collaborative clustering applications. Using this approach, we propose a new algorithm based on solid theoretical basis, and test it on several real and artificial data sets.

In multi-label learning, each learning instance is associated with multiple class labels simultaneously and the task is to learn a transition from the features space to the labels space. Generally, it is costly and time consuming to get labels for learning samples, especially for the task of multi-label annotation where many class labels must be assigned to the same instance. To overcome this difficulty, semi-supervised multi-label learning aims to exploit unlabeled data readily available to help build a multi-label predictive model. Nevertheless, most semi-supervised solutions for the multi-label learning tasks use a batch method for labeling (e.g., label propagation), and are not suitable for online classification tasks. In this paper, a new online semi-supervised multi-label classifier based on the Growing Neural Gas (GNG) algorithm is presented. Online GNG-based algorithms are already used in several applications, but the existing algorithms are unable to tackle the problem of multi-label classification. There is a real need of online semi-supervised multi-label algorithms. Our main contribution is to propose an online multi-label algorithm based on GNG able to provide on the fly annotation of data without explicit storage of the training instances, i.e, with limited memory usage. The proposed algorithm is experimentally tested on five different data-sets from three different application domains. The performance results of the approach is compared with several state-of-the-art methods. The experiments show that the proposed Semi-Supervised algorithm outperforms the existing multi-label classifiers.

In this work we explore an original strategy for building deep networks, based on stacking layers of Self-Organizing Maps (SOM) with finite weights. We aim to show that our approach, with enough hidden variables, is capable to represents any “soft” distribution over the visible variables, where “soft” means that the distribution does not contain any probabilities of 1 or 0. The algorithm compute the model one layer at a time. The first layer receives the input observations and compute a probability of membership for each observation and each neuron. These probabilities become the input of the second layer, which compute a new set of probabilities and so on. The number of neurons decrease in each layer after the first. The proposed algorithm is experimentally tested on artificial and real data-sets. The effect of the added hidden layers for the representation of data structure is experimentally demonstrated.

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.

Data clustering is a very important and challenging task in Artificial Intelligence (AI) field with many applications such as bio-informatics, medical, enhancing recommendation engines or fraud detection. Among the different families of clustering algorithms, one of the most widely used is the prototype-based clustering, because of its simplicity and reasonable computational time. Prototype-based algorithms compute a compact model of the data structure in the form of a set of prototypes described in the same vectorial space as the data, each prototype representing a cluster. However, in real world applications we often face non-vectorial data that cannot be treated with most prototype-based approaches. Such non-vectorial data are usually represented in the form of relational data, i.e. data defined by their relation to each other (their dissimilarities). In this study, we propose a prototype-based clustering algorithm for relational data based on the Barycentric Coordinates formalism. We compared experimentally the quality of the proposed approach on artificial and real data-sets. The experiments show the high quality of the algorithm in terms of clustering results. We also showed that our approach is a significant improvement in terms of computational and memory complexity compared to the state-of-the-art approaches. We consider that these results are encouraging and pave the road to numerous applications in data clustering.

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.

In this paper, we present a novel method for co-clustering, an unsupervised learning approach that aims at discovering homogeneous groups of data instances and features by grouping them simultaneously. The proposed method uses the entropy regularized optimal transport between empirical measures defined on data instances and features in order to obtain an estimated joint probability density function represented by the optimal coupling matrix. This matrix is further factorized to obtain the induced row and columns partitions using multiscale representations approach. To justify our method theoretically, we show how the solution of the regularized optimal transport can be seen from the variational inference perspective thus motivating its use for co-clustering. The algorithm derived for the proposed method and its kernelized version based on the notion of Gromov-Wasserstein distance are fast, accurate and can determine automatically the number of both row and column clusters. These features are vividly demonstrated through extensive experimental evaluations.

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.

Relational datasets are defined by their relations, or their similarities, with each other. In this paper, we present a new autonomous clustering algorithm for relational data. We propose to use the properties of reordering methods in order to produce a one-dimensional signal of pairwise distances. A signal processing method is then applied to this signal to detect peaks of distance that reflect the clusters' separation. The main advantage of this procedure is that there is no parameter to tweak in order to obtain a reasonable clustering. The proposed method is compared with state-of-the-art algorithms to demonstrate it's efficiency.

Multi-source clustering is common data mining task the aim of which is to use several clustering algorithms to analyze different aspects of the same data. Well known applications of multi-source clustering include horizontal collaborative clustering and multi-view clustering, where several algorithms combine their strengths by exchanging information about their finding on local structures with a goal of mutual improvement. However, many of these proposed algorithms and statistical models lack the capability to detect weak collaborations that may prove detrimental to the global clustering process. In this article, we propose a weighing optimization method that will help detecting which algorithms should exchange their information based on the diversity between the different algorithms' solutions.

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.

In this paper, we propose to improve the classical lifting-based wavelet transforms by defining three classes of pixels which will be predicted differently. More specifically, the proposed idea is inspired by the Essentially Non-Oscillatory (ENO) transform and consists in shifting the stencil used for prediction in order to reduce the error near image singularities. Moreover, the different filters associated with these classes will be optimized in order to design a multiresolution representation well adapted to image characteristics. Our simulations show that the resulting multiscale representation leads to much lower amplitudes of the detail coefficients and improves the linear approximation properties.

The aim of this paper is to construct a new nonlinear and nonseparable multiscale representation of piecewise continuous bidimensional functions. This representation is based on the definition of a linear projection and a nonlinear prediction operator, which locally adapts to the function to be represented. This adaptivity of the prediction operator proves to be very interesting for image encoding in that it enables a considerable reduction in the number of significant coefficients compared with other representations. Applications of this new nonlinear multiscale representation to image compression and super-resolution conclude this paper.

We introduce nonlinear edge-adapted multiresolution transforms for image processing. These transforms have the same structure as wavelet basis decompositions, but incorporate a specific geometric treatment of edges, which results in sparser representations of piecewise smooth images and in turn better compression properties. We also observe visual improvements over classical wavelets for the compression of real images.

We introduce new multiscale representations for images which incorporate a specific geometric treatment of edges. The associated transforms are inherently nonlinear and nontensor product, in contrast to classical wavelet basis decompositions over which they exhibit visual improvement in terms of compression. This approach can be viewed as a bridge between edge detection and the nonlinear multiresolution representations of Ami Harten (see Journal of Applied Numerical Mathematics, vol.12, p.153-93, 1993).