Generalised Mutual Information: a Framework for Discriminative Clustering

In the last decade, recent successes in deep clustering majorly involved the Mutual Information (MI) as an unsupervised objective for training neural networks with increasing regularisations. While the quality of the regularisations have been largely discussed for improvements, little attention has been dedicated to the relevance of MI as a clustering objective. In this paper, we first highlight how the maximisation of MI does not lead to satisfying clusters. We identified the Kullback-Leibler divergence as the main reason of this behaviour. Hence, we generalise the mutual information by changing its core distance, introducing the Generalised Mutual Information (GEMINI): a set of metrics for unsupervised neural network training. Unlike MI, some GEMINIs do not require regularisations when training as they are geometry-aware thanks to distances or kernels in the data space. Finally, we highlight that GEMINIs can automatically select a relevant number of clusters, a property that has been little studied in deep discriminative clustering context where the number of clusters is a priori unknown.

The Deep Latent Position Topic Model for Clustering and Representation of Networks with Textual Edges

Numerical interactions leading to users sharing textual content published by others are naturally represented by a network where the individuals are associated with the nodes and the exchanged texts with the edges. To understand those heterogeneous and complex data structures, clustering nodes into homogeneous groups as well as rendering a comprehensible visualisation of the data is mandatory. To address both issues, we introduce Deep-LPTM, a model-based clustering strategy relying on a variational graph auto-encoder approach as well as a probabilistic model to characterise the topics of discussion. Deep-LPTM allows to build a joint representation of the nodes and of the edges in two embeddings spaces. The parameters are inferred using a variational inference algorithm. We also introduce IC2L, a model selection criterion specifically designed to choose models with relevant clustering and visualisation properties. An extensive benchmark study on synthetic data is provided. In particular, we find that Deep-LPTM better recovers the partitions of the nodes than the state-of-the art ETSBM and STBM. Eventually, the emails of the Enron company are analysed and visualisations of the results are presented, with meaningful highlights of the graph structure.

Are labels informative in semi-supervised learning? -- Estimating and leveraging the missing-data mechanism

Semi-supervised learning is a powerful technique for leveraging unlabeled data to improve machine learning models, but it can be affected by the presence of ``informative'' labels, which occur when some classes are more likely to be labeled than others. In the missing data literature, such labels are called missing not at random. In this paper, we propose a novel approach to address this issue by estimating the missing-data mechanism and using inverse propensity weighting to debias any SSL algorithm, including those using data augmentation. We also propose a likelihood ratio test to assess whether or not labels are indeed informative. Finally, we demonstrate the performance of the proposed methods on different datasets, in particular on two medical datasets for which we design pseudo-realistic missing data scenarios.

Sparse GEMINI for Joint Discriminative Clustering and Feature Selection

Feature selection in clustering is a hard task which involves simultaneously the discovery of relevant clusters as well as relevant variables with respect to these clusters. While feature selection algorithms are often model-based through optimised model selection or strong assumptions on $p(\pmb{x})$, we introduce a discriminative clustering model trying to maximise a geometry-aware generalisation of the mutual information called GEMINI with a simple $\ell_1$ penalty: the Sparse GEMINI. This algorithm avoids the burden of combinatorial feature subset exploration and is easily scalable to high-dimensional data and large amounts of samples while only designing a clustering model $p_\theta(y|\pmb{x})$. We demonstrate the performances of Sparse GEMINI on synthetic datasets as well as large-scale datasets. Our results show that Sparse GEMINI is a competitive algorithm and has the ability to select relevant subsets of variables with respect to the clustering without using relevance criteria or prior hypotheses.

Generalised Mutual Information for Discriminative Clustering

In the last decade, recent successes in deep clustering majorly involved the mutual information (MI) as an unsupervised objective for training neural networks with increasing regularisations. While the quality of the regularisations have been largely discussed for improvements, little attention has been dedicated to the relevance of MI as a clustering objective. In this paper, we first highlight how the maximisation of MI does not lead to satisfying clusters. We identified the Kullback-Leibler divergence as the main reason of this behaviour. Hence, we generalise the mutual information by changing its core distance, introducing the generalised mutual information (GEMINI): a set of metrics for unsupervised neural network training. Unlike MI, some GEMINIs do not require regularisations when training. Some of these metrics are geometry-aware thanks to distances or kernels in the data space. Finally, we highlight that GEMINIs can automatically select a relevant number of clusters, a property that has been little studied in deep clustering context where the number of clusters is a priori unknown.

Active Speaker Detection as a Multi-Objective Optimization with Uncertainty-based Multimodal Fusion

It is now well established from a variety of studies that there is a significant benefit from combining video and audio data in detecting active speakers. However, either of the modalities can potentially mislead audiovisual fusion by inducing unreliable or deceptive information. This paper outlines active speaker detection as a multi-objective learning problem to leverage best of each modalities using a novel self-attention, uncertainty-based multimodal fusion scheme. Results obtained show that the proposed multi-objective learning architecture outperforms traditional approaches in improving both mAP and AUC scores. We further demonstrate that our fusion strategy surpasses, in active speaker detection, other modality fusion methods reported in various disciplines. We finally show that the proposed method significantly improves the state-of-the-art on the AVA-ActiveSpeaker dataset.

Unobserved classes and extra variables in high-dimensional discriminant analysis

In supervised classification problems, the test set may contain data points belonging to classes not observed in the learning phase. Moreover, the same units in the test data may be measured on a set of additional variables recorded at a subsequent stage with respect to when the learning sample was collected. In this situation, the classifier built in the learning phase needs to adapt to handle potential unknown classes and the extra dimensions. We introduce a model-based discriminant approach, Dimension-Adaptive Mixture Discriminant Analysis (D-AMDA), which can detect unobserved classes and adapt to the increasing dimensionality. Model estimation is carried out via a full inductive approach based on an EM algorithm. The method is then embedded in a more general framework for adaptive variable selection and classification suitable for data of large dimensions. A simulation study and an artificial experiment related to classification of adulterated honey samples are used to validate the ability of the proposed framework to deal with complex situations.

Exact Dimensionality Selection for Bayesian PCA

We present a Bayesian model selection approach to estimate the intrinsic dimensionality of a high-dimensional dataset. To this end, we introduce a novel formulation of the probabilisitic principal component analysis model based on a normal-gamma prior distribution. In this context, we exhibit a closed-form expression of the marginal likelihood which allows to infer an optimal number of components. We also propose a heuristic based on the expected shape of the marginal likelihood curve in order to choose the hyperparameters. In non-asymptotic frameworks, we show on simulated data that this exact dimensionality selection approach is competitive with both Bayesian and frequentist state-of-the-art methods.

Bayesian Variable Selection for Globally Sparse Probabilistic PCA

Sparse versions of principal component analysis (PCA) have imposed themselves as simple, yet powerful ways of selecting relevant features of high-dimensional data in an unsupervised manner. However, when several sparse principal components are computed, the interpretation of the selected variables is difficult since each axis has its own sparsity pattern and has to be interpreted separately. To overcome this drawback, we propose a Bayesian procedure called globally sparse probabilistic PCA (GSPPCA) that allows to obtain several sparse components with the same sparsity pattern. This allows the practitioner to identify the original variables which are relevant to describe the data. To this end, using Roweis' probabilistic interpretation of PCA and a Gaussian prior on the loading matrix, we provide the first exact computation of the marginal likelihood of a Bayesian PCA model. To avoid the drawbacks of discrete model selection, a simple relaxation of this framework is presented. It allows to find a path of models using a variational expectation-maximization algorithm. The exact marginal likelihood is then maximized over this path. This approach is illustrated on real and synthetic data sets. In particular, using unlabeled microarray data, GSPPCA infers much more relevant gene subsets than traditional sparse PCA algorithms.

Simultaneous model-based clustering and visualization in the Fisher discriminative subspace

Clustering in high-dimensional spaces is nowadays a recurrent problem in many scientific domains but remains a difficult task from both the clustering accuracy and the result understanding points of view. This paper presents a discriminative latent mixture (DLM) model which fits the data in a latent orthonormal discriminative subspace with an intrinsic dimension lower than the dimension of the original space. By constraining model parameters within and between groups, a family of 12 parsimonious DLM models is exhibited which allows to fit onto various situations. An estimation algorithm, called the Fisher-EM algorithm, is also proposed for estimating both the mixture parameters and the discriminative subspace. Experiments on simulated and real datasets show that the proposed approach performs better than existing clustering methods while providing a useful representation of the clustered data. The method is as well applied to the clustering of mass spectrometry data.