With the dawn of the Big Data era, data sets are growing rapidly. Data is streaming from everywhere - from cameras, mobile phones, cars, and other electronic devices. Clustering streaming data is a very challenging problem. Unlike the traditional clustering algorithms where the dataset can be stored and scanned multiple times, clustering streaming data has to satisfy constraints such as limit memory size, real-time response, unknown data statistics and an unknown number of clusters. In this paper, we present a novel online clustering algorithm which can be used to cluster streaming data without knowing the number of clusters a priori. Results on both synthetic and real datasets show that the proposed algorithm produces partitions which are close to what you could get if you clustered the whole data at one time.
Northwestern Polytechnical University（西北工业大学）；Université de Technologie de Compiègne（贡比涅技术大学）；Institut Universitaire de France（法国大学研究院）
The Gaussian mixture model (GMM) provides a simple yet principled framework for clustering, with properties suitable for statistical inference. In this paper, we propose a new model-based clustering algorithm, called EGMM (evidential GMM), in the theoretical framework of belief functions to better characterize cluster-membership uncertainty. With a mass function representing the cluster membership of each object, the evidential Gaussian mixture distribution composed of the components over the powerset of the desired clusters is proposed to model the entire dataset. The parameters in EGMM are e…
Penalized K-Nearest-Neighbor-Graph Based Metrics for Clustering
CIFASIS（法阿国际信息与系统科学中心）；French Argentine International Center for Information and Systems Sciences（法阿国际信息与系统科学中心）；UPCAM；UNR–CONICET（罗萨里奥国立大学-阿根廷国家科学与技术研究理事会）
Indian Statistical Institute（印度统计研究所）；Jadavpur University（贾达普大学）
Many real-world clustering problems are plagued by incomplete data characterized by missing or absent features for some or all of the data instances. Traditional clustering methods cannot be directly applied to such data without preprocessing by imputation or marginalization techniques. In this article, we overcome this drawback by utilizing a penalized dissimilarity measure which we refer to as the Feature Weighted Penalty based Dissimilarity (FWPD). Using the FWPD measure, we modify the traditional k-means clustering algorithm and the standard hierarchical agglomerative clustering algorithms…
Shenzhen Research Institute of Big Data（深圳大数据研究院）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；University of Minnesota（明尼苏达大学）；University of Southern California（南加州大学）
The non-negative matrix factorization (NMF) model with an additional orthogonality constraint on one of the factor matrices, called the orthogonal NMF (ONMF), has been found a promising clustering model and can outperform the classical K-means. However, solving the ONMF model is a challenging optimization problem because the coupling of the orthogonality and non-negativity constraints introduces a mixed combinatorial aspect into the problem due to the determination of the correct status of the variables (positive or zero). Most of the existing methods directly deal with the orthogonality const…
Gaussian Mixture Models are one of the most studied and mature models in unsupervised learning. However, outliers are often present in the data and could influence the cluster estimation. In this paper, we study a new model that assumes that data comes from a mixture of a number of Gaussians as well as a uniform ``background'' component assumed to contain outliers and other non-interesting observations. We develop a novel method based on robust loss minimization that performs well in clustering such GMM with a uniform background. We give theoretical guarantees for our clustering algorithm to o…
We introduce an unsupervised clustering algorithm to improve training efficiency and accuracy in predicting energies using molecular-orbital-based machine learning (MOB-ML). This work determines clusters via the Gaussian mixture model (GMM) in an entirely automatic manner and simplifies an earlier supervised clustering approach [J. Chem. Theory Comput., 15, 6668 (2019)] by eliminating both the necessity for user-specified parameters and the training of an additional classifier. Unsupervised clustering results from GMM have the advantage of accurately reproducing chemically intuitive groupings …
While GAN is a powerful model for generating images, its inability to infer a latent space directly limits its use in applications requiring an encoder. Our paper presents a simple architectural setup that combines the generative capabilities of GAN with an encoder. We accomplish this by combining the encoder with the discriminator using shared weights, then training them simultaneously using a new loss term. We model the output of the encoder latent space via a GMM, which leads to both good clustering using this latent space and improved image generation by the GAN. Our framework is generic a…
Scripps Institution of Oceanography, UCSD（斯克里普斯海洋研究所，加州大学圣迭戈分校）；Naval Undersea Warfare Center Newport（纽波特海军水下作战中心）
Deep clustering was applied to unlabeled, automatically detected signals in a coral reef soundscape to distinguish fish pulse calls from segments of whale song. Deep embedded clustering (DEC) learned latent features and formed classification clusters using fixed-length power spectrograms of the signals. Handpicked spectral and temporal features were also extracted and clustered with Gaussian mixture models (GMM) and conventional clustering. DEC, GMM, and conventional clustering were tested on simulated datasets of fish pulse calls (fish) and whale song units (whale) with randomized bandwidth, …
Clustering consists of a popular set of techniques used to separate data into interesting groups for further analysis. Many data sources on which clustering is performed are well-known to contain random and systematic measurement errors. Such errors may adversely affect clustering. While several techniques have been developed to deal with this problem, little is known about the effectiveness of these solutions. Moreover, no work to-date has examined the effect of systematic errors on clustering solutions. In this paper, we perform a Monte Carlo study to investigate the sensitivity of two commo…
The paper has been withdrawn since more effective experiments should be completed. Auto-encoders (AE) has been widely applied in different fields of machine learning. However, as a deep model, there are a large amount of learnable parameters in the AE, which would cause over-fitting and slow learning speed in practice. Many researchers have been study the intrinsic structure of AE and showed different useful methods to regularize those parameters. In this paper, we present a novel regularization method based on a clustering algorithm which is able to classify the parameters into different grou…
Functional magnetic resonance imaging (fMRI) data have become increasingly available and are useful for describing functional connectivity (FC), the relatedness of neuronal activity in regions of the brain. This FC of the brain provides insight into certain neurodegenerative diseases and psychiatric disorders, and thus is of clinical importance. To help inform physicians regarding patient diagnoses, unsupervised clustering of subjects based on FC is desired, allowing the data to inform us of groupings of patients based on shared features of connectivity. Since heterogeneity in FC is present ev…
The University of Tokyo（东京大学）；University of Innsbruck（因斯布鲁克大学）
Clustering algorithms are a cornerstone of machine learning applications. Recently, a quantum algorithm for clustering based on the k-means algorithm has been proposed by Kerenidis, Landman, Luongo and Prakash. Based on their work, we propose a quantum expectation-maximization (EM) algorithm for Gaussian mixture models (GMMs). The robustness and quantum speedup of the algorithm is demonstrated. We also show numerically the advantage of GMM over k-means for non-trivial cluster data.
Università degli Studi di Perugia（佩鲁贾大学）；University College Dublin（都柏林大学学院）
Gaussian Mixture models (GMMs) are a powerful tool for clustering, classification and density estimation when clustering structures are embedded in the data. The presence of missing values can largely impact the GMMs estimation process, thus handling missing data turns out to be a crucial point in clustering, classification and density estimation. Several techniques have been developed to impute the missing values before model estimation. Among these, multiple imputation is a simple and useful general approach to handle missing data. In this paper we propose two different methods to fit Gaussi…
Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing (local) maximum likelihood estimate (MLE). It can be used in an extensive range of problems, including the clustering of data based on the Gaussian mixture model (GMM). Numerical instability and convergence problems may arise in situations where the sample size is not much larger than the data dimensionality. In such low sample support (LSS) settings, the covariance matrix update in the EM-GMM algorithm may become singular or poorly conditioned, causing the algorithm to crash. On the other hand, in many …
City University of Hong Kong（香港城市大学）；Delft University of Technology（代尔夫特理工大学）；Nanyang Technological University（南洋理工大学）；Nanjing University of Aeronautics and Astronautics（南京航空航天大学）
Safety is a top priority for civil aviation. New anomaly detection methods, primarily clustering methods, have been developed to monitor pilot operations and detect any risks from such flight data. However, all existing anomaly detection methods are offlline learning - the models are trained once using historical data and used for all future predictions. In practice, new flight data are accumulated continuously and analyzed every month at airlines. Clustering such dynamically growing data is challenging for an offlline method because it is memory and time intensive to re-train the model every …
Institut FEMTO-ST（FEMTO-ST研究所）；Université Bourgogne Franche-Comté（勃艮第-弗朗什-孔泰大学）；Université de technologie de Compiègne（贡比涅技术大学）；CNRS（法国国家科学研究中心）；Heudiasyc（Heudiasyc实验室）；Institut universitaire de France（法兰西大学研究院）
The interpretation of unlabeled acoustic emission (AE) data classically relies on general-purpose clustering methods. While several external criteria have been used in the past to select the hyperparameters of those algorithms, few studies have paid attention to the development of dedicated objective functions in clustering methods able to cope with the specificities of AE data. We investigate how to explicitly represent clusters onsets in mixture models in general, and in Gaussian Mixture Models (GMM) in particular. By modifying the internal criterion of such models, we propose the first clus…
ETH Zürich（苏黎世联邦理工学院）；University Children’s Hospital Regensburg (KUNO)（雷根斯堡大学儿童医院（KUNO））；University of Regensburg（雷根斯堡大学）
Constrained clustering has gained significant attention in the field of machine learning as it can leverage prior information on a growing amount of only partially labeled data. Following recent advances in deep generative models, we propose a novel framework for constrained clustering that is intuitive, interpretable, and can be trained efficiently in the framework of stochastic gradient variational inference. By explicitly integrating domain knowledge in the form of probabilistic relations, our proposed model (DC-GMM) uncovers the underlying distribution of data conditioned on prior clusteri…
Dankook University（檀国大学）；Yonsei University（延世大学）；University of Suwon（水原大学）；Hanyang University（汉阳大学）
Giving or recommending appropriate content based on the quality of experience is the most important and challenging issue in recommender systems. As collaborative filtering (CF) is one of the most prominent and popular techniques used for recommender systems, we propose a new clustering-based CF (CBCF) method using an incentivized/penalized user (IPU) model only with ratings given by users, which is thus easy to implement. We aim to design such a simple clustering-based approach with no further prior information while improving the recommendation accuracy. To be precise, the purpose of CBCF wi…
Soft Clustering Anchors for Self-Supervised Speech Representation Learning in Joint Embedding Prediction Architectures
Carnegie Mellon University（卡内基梅隆大学）；New York University（纽约大学）；James Silberrad Brown Center for AI（詹姆斯·西伯拉德·布朗人工智能中心）；Columbia University（哥伦比亚大学）；Northeastern University（东北大学）；Stanford University（斯坦福大学）；Amazon GenAI（亚马逊生成人工智能）
This paper represents a preliminary (pre-reviewing) version of a sublinear variational algorithm for isotropic Gaussian mixture models (GMMs). Further developments of the algorithm for GMMs with diagonal covariance matrices (instead of isotropic clusters) and their corresponding benchmarking results have been published by TPAMI (doi:10.1109/TPAMI.2021.3133763) in the paper "A Variational EM Acceleration for Efficient Clustering at Very Large Scales". We kindly refer the reader to the TPAMI paper instead of this much earlier arXiv version (the TPAMI paper is also open access). Publicly availabl…
Regularization and Optimization in Model-Based Clustering
PSR；Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio)（里约热内卢天主教大学（PUC-Rio））；LAMPS；CIRRELT；SCALE-AI Chair in Data-Driven Supply Chains（SCALE-AI数据驱动供应链讲席）；Polytechnique Montréal（蒙特利尔理工学院）
University of Granada（格拉纳达大学）；Simula Metropolitan Center for Digital Engineering（Simula大都会数字工程中心）；University of Copenhagen（哥本哈根大学）
Matrix factorization methods are extensively employed to understand complex data. In this paper, we introduce the cross-product penalized component analysis (XCAN), a sparse matrix factorization based on the optimization of a loss function that allows a trade-off between variance maximization and structural preservation. The approach is based on previous developments, notably (i) the Sparse Principal Component Analysis (SPCA) framework based on the LASSO, (ii) extensions of SPCA to constrain both modes of the factorization, like co-clustering or the Penalized Matrix Decomposition (PMD), and (i…
Huazhong University of Science and Technology（华中科技大学）
With the inflation of the data, clustering analysis, as a branch of unsupervised learning, lacks unified understanding and application of its mathematical law. Based on the view of fixed point, this paper restates the model-based clustering and proposes a unified clustering framework. In order to find fixed points as cluster centers, the framework iteratively constructs the contraction map, which strongly reveals the convergence mechanism and interconnections among algorithms. By specifying a contraction map, Gaussian mixture model (GMM) can be mapped to the framework as an application. We hop…
We study two practically important cases of model based clustering using Gaussian Mixture Models: (1) when there is misspecification and (2) on high dimensional data, in the light of recent advances in Gradient Descent (GD) based optimization using Automatic Differentiation (AD). Our simulation studies show that EM has better clustering performance, measured by Adjusted Rand Index, compared to GD in cases of misspecification, whereas on high dimensional data GD outperforms EM. We observe that both with EM and GD there are many solutions with high likelihood but poor cluster interpretation. To …
The information bottleneck (IB) approach to clustering takes a joint distribution $P\!\left(X,Y\right)$ and maps the data $X$ to cluster labels $T$ which retain maximal information about $Y$ (Tishby et al., 1999). This objective results in an algorithm that clusters data points based upon the similarity of their conditional distributions $P\!\left(Y\mid X\right)$. This is in contrast to classic "geometric clustering'' algorithms such as $k$-means and gaussian mixture models (GMMs) which take a set of observed data points $\left\{ \mathbf{x}_{i}\right\} _{i=1:N}$ and cluster them based upon the…
Using Machine Learning for Lunar Mineralogy-I: Hyperspectral Imaging of Volcanic Samples
Leiden Institute of Advanced Computer Science（莱顿高级计算机科学研究所）；Leiden Observatory, Leiden University（莱顿大学莱顿天文台）；School of Astronomy, Institute for Research in Fundamental Sciences (IPM)（基础科学研究所（IPM）天文学院）；ESTEC European Space Agency（欧洲空间局ESTEC）；Huygens-Kamerlingh Onnes Laboratory, Leiden University（莱顿大学惠更斯-卡末林·昂内斯实验室）
We aim to develop clustering models to obtain behavioral representations from continuous multimodal mobile sensing data towards relapse prediction tasks. The identified clusters could represent different routine behavioral trends related to daily living of patients as well as atypical behavioral trends associated with impending relapse. We used the mobile sensing data obtained in the CrossCheck project for our analysis. Continuous data from six different mobile sensing-based modalities (e.g. ambient light, sound/conversation, acceleration etc.) obtained from a total of 63 schizophrenia patient…
Eindhoven University of Technology（埃因霍温理工大学）；Philips Research（飞利浦研究院）；Tilburg University（蒂尔堡大学）
During the past two decades, methods for identifying groups with different trends in longitudinal data have become of increasing interest across many areas of research. To support researchers, we summarize the guidance from the literature regarding longitudinal clustering. Moreover, we present a selection of methods for longitudinal clustering, including group-based trajectory modeling (GBTM), growth mixture modeling (GMM), and longitudinal k-means (KML). The methods are introduced at a basic level, and strengths, limitations, and model extensions are listed. Following the recent developments …
Jagiellonian University（雅盖隆大学）；Technical University of Munich（慕尼黑工业大学）
In this paper, we propose a semi-supervised clustering method, CEC-IB, that models data with a set of Gaussian distributions and that retrieves clusters based on a partial labeling provided by the user (partition-level side information). By combining the ideas from cross-entropy clustering (CEC) with those from the information bottleneck method (IB), our method trades between three conflicting goals: the accuracy with which the data set is modeled, the simplicity of the model, and the consistency of the clustering with side information. Experiments demonstrate that CEC-IB has a performance com…
We address the new problem of estimating a piece-wise constant signal with the purpose of detecting its change points and the levels of clusters. Our approach is to model it as a nonparametric penalized least square model selection on a family of models indexed over the collection of partitions of the design points and propose a computationally efficient algorithm to approximately solve it. Statistically, minimizing such a penalized criterion yields an approximation to the maximum a posteriori probability (MAP) estimator. The criterion is then analyzed and an oracle inequality is derived using…
We propose and study a novel graph clustering method for data with an intrinsic network structure. Similar to spectral clustering, we exploit an intrinsic network structure of data to construct Euclidean feature vectors. These feature vectors can then be fed into basic clustering methods such as k-means or Gaussian mixture model (GMM) based soft clustering. What sets our approach apart from spectral clustering is that we do not use the eigenvectors of a graph Laplacian to construct the feature vectors. Instead, we use the solutions of total variation minimization problems to construct feature …
Energy companies often implement various demand response (DR) programs to better match electricity demand and supply by offering the consumers incentives to reduce their demand during critical periods. Classifying clients according to their consumption patterns enables targeting specific groups of consumers for DR. Traditional clustering algorithms use standard distance measurement to find the distance between two points. The results produced by clustering algorithms such as K-means, K-medoids, and Gaussian Mixture Models depend on the clustering parameters or initial clusters. In contrast, ou…
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Univ. Grenoble Alpes（格勒诺布尔-阿尔卑斯大学）；CNRS（法国国家科学研究中心）；Grenoble INP（格勒诺布尔理工学院）；University of Washington（华盛顿大学）
We propose Rademacher complexity bounds for multiclass classifiers trained with a two-step semi-supervised model. In the first step, the algorithm partitions the partially labeled data and then identifies dense clusters containing $κ$ predominant classes using the labeled training examples such that the proportion of their non-predominant classes is below a fixed threshold. In the second step, a classifier is trained by minimizing a margin empirical loss over the labeled training set and a penalization term measuring the disability of the learner to predict the $κ$ predominant classes of the i…
King Digital Entertainment, Activision Blizzard Group（动视暴雪集团King数字娱乐公司）；Uppsala University（乌普萨拉大学）
Deep clustering (DC) has become the state-of-the-art for unsupervised clustering. In principle, DC represents a variety of unsupervised methods that jointly learn the underlying clusters and the latent representation directly from unstructured datasets. However, DC methods are generally poorly applied due to high operational costs, low scalability, and unstable results. In this paper, we first evaluate several popular DC variants in the context of industrial applicability using eight empirical criteria. We then choose to focus on variational deep clustering (VDC) methods, since they mostly mee…
In machine learning and data mining, Cluster analysis is one of the most widely used unsupervised learning technique. Philosophy of this algorithm is to find similar data items and group them together based on any distance function in multidimensional space. These methods are suitable for finding groups of data that behave in a coherent fashion. The perspective may vary for clustering i.e. the way we want to find similarity, some methods are based on distance such as K-Means technique and some are probability based, like GMM. Understanding prominent segment of data is always challenging as mul…
Laboratoire des Signaux et Systèmes (L2S)（信号与系统实验室）；CentraleSupélec-CNRS-Université Paris-Sud（巴黎中央理工-高等电力学院-法国国家科学研究中心-巴黎第十一大学）；Université Paris-Saclay（巴黎萨克雷大学）；Instituto de Cálculo（计算研究所）；Universidad de Buenos Aires（布宜诺斯艾利斯大学）；IMAS-CONICET（阿根廷国家科学技术研究委员会数学应用研究所）
Though very popular, it is well known that the EM for GMM algorithm suffers from non-Gaussian distribution shapes, outliers and high-dimensionality. In this paper, we design a new robust clustering algorithm that can efficiently deal with noise and outliers in diverse data sets. As an EM-like algorithm, it is based on both estimations of clusters centers and covariances. In addition, using a semi-parametric paradigm, the method estimates an unknown scale parameter per data-point. This allows the algorithm to accommodate for heavier tails distributions and outliers without significantly loosing…
Gaussian mixture models (GMM) are the most widely used statistical model for the $k$-means clustering problem and form a popular framework for clustering in machine learning and data analysis. In this paper, we propose a natural semi-random model for $k$-means clustering that generalizes the Gaussian mixture model, and that we believe will be useful in identifying robust algorithms. In our model, a semi-random adversary is allowed to make arbitrary "monotone" or helpful changes to the data generated from the Gaussian mixture model. Our first contribution is a polynomial time algorithm that pro…
