We address the problem of simultaneously learning a k-means clustering and deep feature representation from unlabelled data, which is of interest due to the potential of deep k-means to outperform traditional two-step feature extraction and shallow-clustering strategies. We achieve this by developing a gradient-estimator for the non-differentiable k-means objective via the Gumbel-Softmax reparameterisation trick. In contrast to previous attempts at deep clustering, our concrete k-means model can be optimised with respect to the canonical k-means objective and is easily trained end-to-end without resorting to alternating optimisation. We demonstrate the efficacy of our method on standard clustering benchmarks.
Discrete random variables are natural components of probabilistic clustering models. A number of VAE variants with discrete latent variables have been developed. Training such methods requires marginalizing over the discrete latent variables, causing training time complexity to be linear in the number clusters. By applying a continuous relaxation to the discrete variables in these methods we can achieve a reduction in the training time complexity to be constant in the number of clusters used. We demonstrate that in practice for one such method, the Gaussian Mixture VAE, the use of a continuous…
Deep clustering has increasingly been demonstrating superiority over conventional shallow clustering algorithms. Deep clustering algorithms usually combine representation learning with deep neural networks to achieve this performance, typically optimizing a clustering and non-clustering loss. In such cases, an autoencoder is typically connected with a clustering network, and the final clustering is jointly learned by both the autoencoder and clustering network. Instead, we propose to learn an autoencoded embedding and then search this further for the underlying manifold. For simplicity, we the…
Recently, a number of works have studied clustering strategies that combine classical clustering algorithms and deep learning methods. These approaches follow either a sequential way, where a deep representation is learned using a deep autoencoder before obtaining clusters with k-means, or a simultaneous way, where deep representation and clusters are learned jointly by optimizing a single objective function. Both strategies improve clustering performance, however the robustness of these approaches is impeded by several deep autoencoder setting issues, among which the weights initialization, t…
Tokyo Institute of Technology（东京工业大学）；Fujitsu Limited（富士通有限公司）；RIKEN AIP（理化学研究所人工智能研究中心）
We consider the scenario of deep clustering, in which the available prior knowledge is limited. In this scenario, few existing state-of-the-art deep clustering methods can perform well for both non-complex topology and complex topology datasets. To address the problem, we propose a constraint utilizing symmetric InfoNCE, which helps an objective of deep clustering method in the scenario train the model so as to be efficient for not only non-complex topology but also complex topology datasets. Additionally, we provide several theoretical explanations of the reason why the constraint can enhance…
Subspace clustering aims to cluster unlabeled data that lies in a union of low-dimensional linear subspaces. Deep subspace clustering approaches based on auto-encoders have become very popular to solve subspace clustering problems. However, the training of current deep methods converges slowly, which is much less efficient than traditional approaches. We propose a Residual Encoder-Decoder network for deep Subspace Clustering (RED-SC), which symmetrically links convolutional and deconvolutional layers with skip-layer connections, with which the training converges much faster. We use a self-expr…
University of California, Davis（加州大学戴维斯分校）；Google Research（谷歌研究院）
The area of constrained clustering has been extensively explored by researchers and used by practitioners. Constrained clustering formulations exist for popular algorithms such as k-means, mixture models, and spectral clustering but have several limitations. A fundamental strength of deep learning is its flexibility, and here we explore a deep learning framework for constrained clustering and in particular explore how it can extend the field of constrained clustering. We show that our framework can not only handle standard together/apart constraints (without the well documented negative effect…
Generating interpretable visualizations from complex data is a common problem in many applications. Two key ingredients for tackling this issue are clustering and representation learning. However, current methods do not yet successfully combine the strengths of these two approaches. Existing representation learning models which rely on latent topological structure such as self-organising maps, exhibit markedly lower clustering performance compared to recent deep clustering methods. To close this performance gap, we (a) present a novel way to fit self-organizing maps with probabilistic cluster …
The task of clustering unlabeled time series and sequences entails a particular set of challenges, namely to adequately model temporal relations and variable sequence lengths. If these challenges are not properly handled, the resulting clusters might be of suboptimal quality. As a key solution, we present a joint clustering and feature learning framework for time series based on deep learning. For a given set of time series, we train a recurrent network to represent, or embed, each time series in a vector space such that a divergence-based clustering loss function can discover the underlying c…
Beijing University of Posts and Telecommunications（北京邮电大学）；Tencent（腾讯）；Tsinghua University（清华大学）
Clustering is a fundamental task in data analysis. Recently, deep clustering, which derives inspiration primarily from deep learning approaches, achieves state-of-the-art performance and has attracted considerable attention. Current deep clustering methods usually boost the clustering results by means of the powerful representation ability of deep learning, e.g., autoencoder, suggesting that learning an effective representation for clustering is a crucial requirement. The strength of deep clustering methods is to extract the useful representations from the data itself, rather than the structur…
University of Quebec at Montreal（蒙特利尔魁北克大学）；University of Windsor（温莎大学）
Clustering using deep autoencoders has been thoroughly investigated in recent years. Current approaches rely on simultaneously learning embedded features and clustering the data points in the latent space. Although numerous deep clustering approaches outperform the shallow models in achieving favorable results on several high-semantic datasets, a critical weakness of such models has been overlooked. In the absence of concrete supervisory signals, the embedded clustering objective function may distort the latent space by learning from unreliable pseudo-labels. Thus, the network can learn non-re…
Southwest University（西南大学）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；George Mason University（乔治梅森大学）
Multi-view clustering aims at integrating complementary information from multiple heterogeneous views to improve clustering results. Existing multi-view clustering solutions can only output a single clustering of the data. Due to their multiplicity, multi-view data, can have different groupings that are reasonable and interesting from different perspectives. However, how to find multiple, meaningful, and diverse clustering results from multi-view data is still a rarely studied and challenging topic in multi-view clustering and multiple clusterings. In this paper, we introduce a deep matrix fac…
We propose a deep learning approach for discovering kernels tailored to identifying clusters over sample data. Our neural network produces sample embeddings that are motivated by--and are at least as expressive as--spectral clustering. Our training objective, based on the Hilbert Schmidt Information Criterion, can be optimized via gradient adaptations on the Stiefel manifold, leading to significant acceleration over spectral methods relying on eigendecompositions. Finally, our trained embedding can be directly applied to out-of-sample data. We show experimentally that our approach outperforms …
We study in this paper the problem of jointly clustering and learning representations. As several previous studies have shown, learning representations that are both faithful to the data to be clustered and adapted to the clustering algorithm can lead to better clustering performance, all the more so that the two tasks are performed jointly. We propose here such an approach for $k$-Means clustering based on a continuous reparametrization of the objective function that leads to a truly joint solution. The behavior of our approach is illustrated on various datasets showing its efficacy in learni…
University of Electronic Science and Technology of China（电子科技大学）；Harbin Institute of Technology（哈尔滨工业大学）；Peng Cheng Lab（鹏城实验室）
Multi-view clustering has attracted increasing attentions recently by utilizing information from multiple views. However, existing multi-view clustering methods are either with high computation and space complexities, or lack of representation capability. To address these issues, we propose deep embedded multi-view clustering with collaborative training (DEMVC) in this paper. Firstly, the embedded representations of multiple views are learned individually by deep autoencoders. Then, both consensus and complementary of multiple views are taken into account and a novel collaborative training sch…
UiT the Arctic University of Norway（挪威北极大学）；University of Exeter（埃克塞特大学）；University of Manitoba（曼尼托巴大学）；Norwegian Computing Center（挪威计算中心）
A promising direction in deep learning research consists in learning representations and simultaneously discovering cluster structure in unlabeled data by optimizing a discriminative loss function. As opposed to supervised deep learning, this line of research is in its infancy, and how to design and optimize suitable loss functions to train deep neural networks for clustering is still an open question. Our contribution to this emerging field is a new deep clustering network that leverages the discriminative power of information-theoretic divergence measures, which have been shown to be effecti…
UiT The Arctic University of Norway（挪威北极圈大学）；Institute of Information Systems（信息系统研究所）
Deep embedded clustering has become a dominating approach to unsupervised categorization of objects with deep neural networks. The optimization of the most popular methods alternates between the training of a deep autoencoder and a k-means clustering of the autoencoder's embedding. The diachronic setting, however, prevents the former to benefit from valuable information acquired by the latter. In this paper, we present an alternative where the autoencoder and the clustering are learned simultaneously. This is achieved by providing novel theoretical insight, where we show that the objective fun…
Deep Learning (DL) has shown great promise in the unsupervised task of clustering. That said, while in classical (i.e., non-deep) clustering the benefits of the nonparametric approach are well known, most deep-clustering methods are parametric: namely, they require a predefined and fixed number of clusters, denoted by K. When K is unknown, however, using model-selection criteria to choose its optimal value might become computationally expensive, especially in DL as the training process would have to be repeated numerous times. In this work, we bridge this gap by introducing an effective deep-c…
Joint SDU-NTU Centre for Artificial Intelligence Research, Shandong University（山东大学-南洋理工大学人工智能联合研究中心,山东大学）；College of Computer and Information Sciences, Southwest University（西南大学计算机与信息科学学院）；School of Software, Shandong University（山东大学软件学院）；CEMSE, King Abdullah University of Science and Technology（计算机、工程与数学科学学院,沙特阿拉伯国王阿卜杜拉科技大学）；Department of Computer Science, George Mason University（乔治梅森大学计算机科学系）
Multi-view clustering aims at exploiting information from multiple heterogeneous views to promote clustering. Most previous works search for only one optimal clustering based on the predefined clustering criterion, but devising such a criterion that captures what users need is difficult. Due to the multiplicity of multi-view data, we can have meaningful alternative clusterings. In addition, the incomplete multi-view data problem is ubiquitous in real world but has not been studied for multiple clusterings. To address these issues, we introduce a deep incomplete multi-view multiple clusterings …
AITRICS；Kakao Corporation；University of Oxford & Deepmind（牛津大学 & Deepmind）
We propose a deep amortized clustering (DAC), a neural architecture which learns to cluster datasets efficiently using a few forward passes. DAC implicitly learns what makes a cluster, how to group data points into clusters, and how to count the number of clusters in datasets. DAC is meta-learned using labelled datasets for training, a process distinct from traditional clustering algorithms which usually require hand-specified prior knowledge about cluster shapes/structures. We empirically show, on both synthetic and image data, that DAC can efficiently and accurately cluster new datasets comi…
We present the first deep learning based architecture for collective matrix tri-factorization (DCMTF) of arbitrary collections of matrices, also known as augmented multi-view data. DCMTF can be used for multi-way spectral clustering of heterogeneous collections of relational data matrices to discover latent clusters in each input matrix, across both dimensions, as well as the strengths of association across clusters. The source code for DCMTF is available on our public repository: https://bitbucket.org/cdal/dcmtf_generic
University of Technology Sydney（悉尼科技大学）；Monash University（莫纳什大学）
Graph clustering is a fundamental task which discovers communities or groups in networks. Recent studies have mostly focused on developing deep learning approaches to learn a compact graph embedding, upon which classic clustering methods like k-means or spectral clustering algorithms are applied. These two-step frameworks are difficult to manipulate and usually lead to suboptimal performance, mainly because the graph embedding is not goal-directed, i.e., designed for the specific clustering task. In this paper, we propose a goal-directed deep learning approach, Deep Attentional Embedded Graph …
Amity Institute of Information Technology（阿米提信息技术学院）；Amity University（阿米提大学）；Coventry University（考文垂大学）
In this paper, we have proposed a deep quantum SVM formulation, and further demonstrated a quantum-clustering framework based on the quantum deep SVM formulation, deep convolutional neural networks, and quantum K-Means clustering. We have investigated the run time computational complexity of the proposed quantum deep clustering framework and compared with the possible classical implementation. Our investigation shows that the proposed quantum version of deep clustering formulation demonstrates a significant performance gain (exponential speed up gains in many sections) against the possible cla…
National Engineering School of Tunis（突尼斯国立工程师学院）；University of Tunis El Manar（突尼斯埃尔马纳尔大学）；Ryerson University（瑞尔森大学）；Higher School of Communication of Tunis（突尼斯高等通信学院）；University of Carthage（迦太基大学）
In unsupervised learning, there is no apparent straightforward cost function that can capture the significant factors of variations and similarities. Since natural systems have smooth dynamics, an opportunity is lost if an unsupervised objective function remains static during the training process. The absence of concrete supervision suggests that smooth dynamics should be integrated. Compared to classical static cost functions, dynamic objective functions allow to better make use of the gradual and uncertain knowledge acquired through pseudo-supervision. In this paper, we propose Dynamic Autoe…
Department of Computer Science, UC Davis（加州大学戴维斯分校计算机科学系）
Fair clustering under the disparate impact doctrine requires that population of each protected group should be approximately equal in every cluster. Previous work investigated a difficult-to-scale pre-processing step for $k$-center and $k$-median style algorithms for the special case of this problem when the number of protected groups is two. In this work, we consider a more general and practical setting where there can be many protected groups. To this end, we propose Deep Fair Clustering, which learns a discriminative but fair cluster assignment function. The experimental results on three pu…
The University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）
Clustering and prediction are two primary tasks in the fields of unsupervised and supervised learning, respectively. Although much of the recent advances in machine learning have been centered around those two tasks, the interdependent, mutually beneficial relationship between them is rarely explored. One could reasonably expect appropriately clustering the data would aid the downstream prediction task and, conversely, a better prediction performance for the downstream task could potentially inform a more appropriate clustering strategy. In this work, we focus on the latter part of this mutual…
Unsupervised learning of time series data, also known as temporal clustering, is a challenging problem in machine learning. Here we propose a novel algorithm, Deep Temporal Clustering (DTC), to naturally integrate dimensionality reduction and temporal clustering into a single end-to-end learning framework, fully unsupervised. The algorithm utilizes an autoencoder for temporal dimensionality reduction and a novel temporal clustering layer for cluster assignment. Then it jointly optimizes the clustering objective and the dimensionality reduction objec tive. Based on requirement and application, …
VU University Amsterdam（阿姆斯特丹自由大学）；BrainCreators B.V.（BrainCreators公司）
Finding well-defined clusters in data represents a fundamental challenge for many data-driven applications, and largely depends on good data representation. Drawing on literature regarding representation learning, studies suggest that one key characteristic of good latent representations is the ability to produce semantically mixed outputs when decoding linear interpolations of two latent representations. We propose the Mixing Consistent Deep Clustering method which encourages interpolations to appear realistic while adding the constraint that interpolations of two data points must look like o…
We propose a training scheme to train neural network-based source separation algorithms from scratch when parallel clean data is unavailable. In particular, we demonstrate that an unsupervised spatial clustering algorithm is sufficient to guide the training of a deep clustering system. We argue that previous work on deep clustering requires strong supervision and elaborate on why this is a limitation. We demonstrate that (a) the single-channel deep clustering system trained according to the proposed scheme alone is able to achieve a similar performance as the multi-channel teacher in terms of …
University of Electronic Science and Technology of China（电子科技大学）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）；Lehigh University（理海大学）
Cluster analysis plays an indispensable role in machine learning and data mining. Learning a good data representation is crucial for clustering algorithms. Recently, deep clustering, which can learn clustering-friendly representations using deep neural networks, has been broadly applied in a wide range of clustering tasks. Existing surveys for deep clustering mainly focus on the single-view fields and the network architectures, ignoring the complex application scenarios of clustering. To address this issue, in this paper we provide a comprehensive survey for deep clustering in views of data so…
University of Electronic Science and Technology of China（电子科技大学）
Recently, deep clustering, which is able to perform feature learning that favors clustering tasks via deep neural networks, has achieved remarkable performance in image clustering applications. However, the existing deep clustering algorithms generally need the number of clusters in advance, which is usually unknown in real-world tasks. In addition, the initial cluster centers in the learned feature space are generated by $k$-means. This only works well on spherical clusters and probably leads to unstable clustering results. In this paper, we propose a two-stage deep density-based image cluste…
Image clustering is an important but challenging task in machine learning. As in most image processing areas, the latest improvements came from models based on the deep learning approach. However, classical deep learning methods have problems to deal with spatial image transformations like scale and rotation. In this paper, we propose the use of visual attention techniques to reduce this problem in image clustering methods. We evaluate the combination of a deep image clustering model called Deep Adaptive Clustering (DAC) with the Spatial Transformer Networks (STN). The proposed model is evalua…
In this paper we propose a Deep Autoencoder MIxture Clustering (DAMIC) algorithm based on a mixture of deep autoencoders where each cluster is represented by an autoencoder. A clustering network transforms the data into another space and then selects one of the clusters. Next, the autoencoder associated with this cluster is used to reconstruct the data-point. The clustering algorithm jointly learns the nonlinear data representation and the set of autoencoders. The optimal clustering is found by minimizing the reconstruction loss of the mixture of autoencoder network. Unlike other deep clusteri…
Liaoning Technical University（辽宁工程技术大学）；Haixi Institute, Chinese Academy of Sciences（中国科学院海西研究院）；Technical University of Munich（慕尼黑工业大学）；Hong Kong Polytechnic University（香港理工大学）
The high dimensionality of hyperspectral images often results in the degradation of clustering performance. Due to the powerful ability of deep feature extraction and non-linear feature representation, the clustering algorithm based on deep learning has become a hot research topic in the field of hyperspectral remote sensing. However, most deep clustering algorithms for hyperspectral images utilize deep neural networks as feature extractor without considering prior knowledge constraints that are suitable for clustering. To solve this problem, we propose an intra-class distance constrained deep…
Deep clustering has the potential to learn a strong representation and hence better clustering performance compared to traditional clustering methods such as $k$-means and spectral clustering. However, this strong representation learning ability may make the clustering unfair by discovering surrogates for protected information which we empirically show in our experiments. In this work, we study a general notion of group-level fairness for both binary and multi-state protected status variables (PSVs). We begin by formulating the group-level fairness problem as an integer linear programming form…
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Intel Labs China（英特尔中国研究院）
Traditional clustering methods often perform clustering with low-level indiscriminative representations and ignore relationships between patterns, resulting in slight achievements in the era of deep learning. To handle this problem, we develop Deep Discriminative Clustering (DDC) that models the clustering task by investigating relationships between patterns with a deep neural network. Technically, a global constraint is introduced to adaptively estimate the relationships, and a local constraint is developed to endow the network with the capability of learning high-level discriminative represe…
Xidian University（西安电子科技大学）；Southern University of Science and Technology（南方科技大学）；Shanghai Jiao Tong University（上海交通大学）；Tencent AI Lab（腾讯人工智能实验室）
The clustering methods have recently absorbed even-increasing attention in learning and vision. Deep clustering combines embedding and clustering together to obtain optimal embedding subspace for clustering, which can be more effective compared with conventional clustering methods. In this paper, we propose a joint learning framework for discriminative embedding and spectral clustering. We first devise a dual autoencoder network, which enforces the reconstruction constraint for the latent representations and their noisy versions, to embed the inputs into a latent space for clustering. As such …
We propose Deep Closed-Form Subspace Clustering (DCFSC), a new embarrassingly simple model for subspace clustering with learning non-linear mapping. Compared with the previous deep subspace clustering (DSC) techniques, our DCFSC does not have any parameters at all for the self-expressive layer. Instead, DCFSC utilizes the implicit data-driven self-expressive layer derived from closed-form shallow auto-encoder. Moreover, DCFSC also has no complicated optimization scheme, unlike the other subspace clustering methods. With its extreme simplicity, DCFSC has significant memory-related benefits over…
Columbia University（哥伦比亚大学）；Mitsubishi Electric Research Laboratories (MERL)（三菱电机研究实验室（MERL））
Deep clustering is the first method to handle general audio separation scenarios with multiple sources of the same type and an arbitrary number of sources, performing impressively in speaker-independent speech separation tasks. However, little is known about its effectiveness in other challenging situations such as music source separation. Contrary to conventional networks that directly estimate the source signals, deep clustering generates an embedding for each time-frequency bin, and separates sources by clustering the bins in the embedding space. We show that deep clustering outperforms con…
Clustering is an essential problem in machine learning and data mining. One vital factor that impacts clustering performance is how to learn or design the data representation (or features). Fortunately, recent advances in deep learning can learn unsupervised features effectively, and have yielded state of the art performance in many classification problems, such as character recognition, object recognition and document categorization. However, little attention has been paid to the potential of deep learning for unsupervised clustering problems. In this paper, we propose a deep belief network w…
The dissimilarity mixture autoencoder (DMAE) is a neural network model for feature-based clustering that incorporates a flexible dissimilarity function and can be integrated into any kind of deep learning architecture. It internally represents a dissimilarity mixture model (DMM) that extends classical methods like K-Means, Gaussian mixture models, or Bregman clustering to any convex and differentiable dissimilarity function through the reinterpretation of probabilities as neural network representations. DMAE can be integrated with deep learning architectures into end-to-end models, allowing th…
University of Vienna（维也纳大学）；Ludwig Maximilian University of Munich（慕尼黑大学）
The field of deep clustering combines deep learning and clustering to learn representations that improve both the learned representation and the performance of the considered clustering method. Most existing deep clustering methods are designed for a single clustering method, e.g., k-means, spectral clustering, or Gaussian mixture models, but it is well known that no clustering algorithm works best in all circumstances. Consensus clustering tries to alleviate the individual weaknesses of clustering algorithms by building a consensus between members of a clustering ensemble. Currently, there is…
Clustering is essential to many tasks in pattern recognition and computer vision. With the advent of deep learning, there is an increasing interest in learning deep unsupervised representations for clustering analysis. Many works on this domain rely on variants of auto-encoders and use the encoder outputs as representations/features for clustering. In this paper, we show that an l2 normalization constraint on these representations during auto-encoder training, makes the representations more separable and compact in the Euclidean space after training. This greatly improves the clustering accura…
LIGM, Ecole des Ponts, Univ Gustave Eiffel, CNRS（法国国立桥路学校（Ecole des Ponts）、古斯塔夫·埃菲尔大学（Univ Gustave Eiffel）、法国国家科学研究中心（CNRS））
Recent advances in image clustering typically focus on learning better deep representations. In contrast, we present an orthogonal approach that does not rely on abstract features but instead learns to predict image transformations and performs clustering directly in image space. This learning process naturally fits in the gradient-based training of K-means and Gaussian mixture model, without requiring any additional loss or hyper-parameters. It leads us to two new deep transformation-invariant clustering frameworks, which jointly learn prototypes and transformations. More specifically, we use…
Beckman Institute, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校贝克曼研究所）；Michigan State University（密歇根州立大学）；Hefei University of Technology（合肥工业大学）
While sparse coding-based clustering methods have shown to be successful, their bottlenecks in both efficiency and scalability limit the practical usage. In recent years, deep learning has been proved to be a highly effective, efficient and scalable feature learning tool. In this paper, we propose to emulate the sparse coding-based clustering pipeline in the context of deep learning, leading to a carefully crafted deep model benefiting from both. A feed-forward network structure, named TAGnet, is constructed based on a graph-regularized sparse coding algorithm. It is then trained with task-spe…
In this paper, we propose a methodology to improvise the technique of deep transfer clustering (DTC) when applied to the less variant data distribution. Clustering can be considered as the most important unsupervised learning problem. A simple definition of clustering can be stated as "the process of organizing objects into groups, whose members are similar in some way". Image clustering is a crucial but challenging task in the domain machine learning and computer vision. We have discussed the clustering of the data collection where the data is less variant. We have discussed the improvement b…
