Self-supervision is key to extending use of deep learning for label scarce domains. For most of self-supervised approaches data transformations play an important role. However, up until now the impact of transformations have not been studied. Furthermore, different transformations may have different impact on the system. We provide novel insights into the use of data transformation in self-supervised tasks, specially pertaining to clustering. We show theoretically and empirically that certain set of transformations are helpful in convergence of self-supervised clustering. We also show the cases when the transformations are not helpful or in some cases even harmful. We show faster convergence rate with valid transformations for convex as well as certain family of non-convex objectives along with the proof of convergence to the original set of optima. We have synthetic as well as real world data experiments. Empirically our results conform with the theoretical insights provided.
Bootstrap Deep Spectral Clustering with Optimal Transport
College of Electronic and Information Engineering, Tongji University（同济大学电子与信息工程学院）；College of Electronic and Information Engineering, Shanghai Institute of Intelligent Science and Technology, Tongji University（上海智能科学与技术研究院，同济大学电子与信息工程学院）；Shanghai Research Institute for Intelligent Autonomous Systems, Tongji University（上海智能自主系统研究院，同济大学）；Faculty of Data Science, City University of Macau（澳门城市大学数据科学学院）；Faculty of Computer Science, University of Vienna（维也纳大学计算机科学学院）；Singapore Institute of Technology（新加坡理工学院）
We propose the first qualitative hypothesis characterizing the behavior of visual transformation based self-supervision, called the VTSS hypothesis. Given a dataset upon which a self-supervised task is performed while predicting instantiations of a transformation, the hypothesis states that if the predicted instantiations of the transformations are already present in the dataset, then the representation learned will be less useful. The hypothesis was derived by observing a key constraint in the application of self-supervision using a particular transformation. This constraint, which we term th…
Semi-supervised clustering methods incorporate a limited amount of supervision into the clustering process. Typically, this supervision is provided by the user in the form of pairwise constraints. Existing methods use such constraints in one of the following ways: they adapt their clustering procedure, their similarity metric, or both. All of these approaches operate within the scope of individual clustering algorithms. In contrast, we propose to use constraints to choose between clusterings generated by very different unsupervised clustering algorithms, run with different parameter settings. …
In this paper, we propose a novel unsupervised clustering approach exploiting the hidden information that is indirectly introduced through a pseudo classification objective. Specifically, we randomly assign a pseudo parent-class label to each observation which is then modified by applying the domain specific transformation associated with the assigned label. Generated pseudo observation-label pairs are subsequently used to train a neural network with Auto-clustering Output Layer (ACOL) that introduces multiple softmax nodes for each pseudo parent-class. Due to the unsupervised objective based …
UiT The Arctic University of Norway（挪威北极大学）；Norwegian Computing Center（挪威计算中心）；University of Copenhagen（哥本哈根大学）
Self-supervised learning is a central component in recent approaches to deep multi-view clustering (MVC). However, we find large variations in the development of self-supervision-based methods for deep MVC, potentially slowing the progress of the field. To address this, we present DeepMVC, a unified framework for deep MVC that includes many recent methods as instances. We leverage our framework to make key observations about the effect of self-supervision, and in particular, drawbacks of aligning representations with contrastive learning. Further, we prove that contrastive alignment can negati…
BCAM-Basque Center of Applied Mathematics（巴斯克应用数学中心）
Different types of training data have led to numerous schemes for supervised classification. Current learning techniques are tailored to one specific scheme and cannot handle general ensembles of training data. This paper presents a unifying framework for supervised classification with general ensembles of training data, and proposes the learning methodology of generalized robust risk minimization (GRRM). The paper shows how current and novel supervision schemes can be addressed under the proposed framework by representing the relationship between examples at test and training via probabilisti…
Pairwise "same-cluster" queries are one of the most widely used forms of supervision in semi-supervised clustering. However, it is impractical to ask human oracles to answer every query correctly. In this paper, we study the influence of allowing "not-sure" answers from a weak oracle and propose an effective algorithm to handle such uncertainties in query responses. Two realistic weak oracle models are considered where ambiguity in answering depends on the distance between two points. We show that a small query complexity is adequate for effective clustering with high probability by providing …
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…
Clustering ensemble is one of the most recent advances in unsupervised learning. It aims to combine the clustering results obtained using different algorithms or from different runs of the same clustering algorithm for the same data set, this is accomplished using on a consensus function, the efficiency and accuracy of this method has been proven in many works in literature. In the first part of this paper we make a comparison among current approaches to clustering ensemble in literature. All of these approaches consist of two main steps: the ensemble generation and consensus function. In the …
A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The corresponding subspace clustering problem has been extensively studied in the literature to partition such high-dimensional data into clusters corresponding to their underlying low-dimensional subspaces. However, low-dimensional intrinsic structures are often violated for real-world observations, as they can be corrupted by errors or deviate from ideal models…
Peking University（北京大学）；Institute of Big Data Technologies（大数据技术研究院）
Subspace clustering (SC) refers to the problem of clustering high-dimensional data into a union of low-dimensional subspaces. Based on spectral clustering, state-of-the-art approaches solve SC problem within a two-stage framework. In the first stage, data representation techniques are applied to draw an affinity matrix from the original data. In the second stage, spectral clustering is directly applied to the affinity matrix so that data can be grouped into different subspaces. However, the affinity matrix obtained in the first stage usually fails to reveal the authentic relationship between d…
Unsupervised clustering of temporal data is both challenging and crucial in machine learning. In this paper, we show that neither traditional clustering methods, time series specific or even deep learning-based alternatives generalise well when both varying sampling rates and high dimensionality are present in the input data. We propose a novel approach to temporal clustering, in which we (1) transform the input time series into a distance-based projected representation by using similarity measures suitable for dealing with temporal data,(2) feed these projections into a multi-layer CNN-GRU au…
Concept drift in learning and classification occurs when the statistical properties of either the data features or target change over time; evidence of drift has appeared in search data, medical research, malware, web data, and video. Drift adaptation has not yet been addressed in high dimensional, noisy, low-context data such as streaming text, video, or images due to the unique challenges these domains present. We present a two-fold approach to deal with concept drift in these domains: a density-based clustering approach to deal with virtual concept drift (change in statistical properties of…
Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a unified framework that includes low, moderate and high dimensions, we study multidimensional scaling in the setting of clustering noisy data. Our results suggest that, the classical multidimensional scaling can be modified to further improve the quality of embedded samples, especially when the noise level increases. To this end, we propose {\it modified multidim…
University of Waterloo（滑铁卢大学）；University of Illinois at Urbana（伊利诺伊大学厄巴纳分校）
Mixtures of Gaussians, factor analyzers (probabilistic PCA) and hidden Markov models are staples of static and dynamic data modeling and image and video modeling in particular. We show how topographic transformations in the input, such as translation and shearing in images, can be accounted for in these models by including a discrete transformation variable. The resulting models perform clustering, dimensionality reduction and time-series analysis in a way that is invariant to transformations in the input. Using the EM algorithm, these transformation-invariant models can be fit to static data …
Humans do not acquire perceptual abilities in the way we train machines. While machine learning algorithms typically operate on large collections of randomly-chosen, explicitly-labeled examples, human acquisition relies more heavily on multimodal unsupervised learning (as infants) and active learning (as children). With this motivation, we present a learning framework for sound representation and recognition that combines (i) a self-supervised objective based on a general notion of unimodal and cross-modal coincidence, (ii) a clustering objective that reflects our need to impose categorical st…
Jagiellonian University（雅盖隆大学）；Instituto de Telecomunicações（电信研究所）；Instituto Superior Técnico（高等技术学院）；Universidade de Lisboa（里斯本大学）
In this paper, we introduce a neural network framework for semi-supervised clustering (SSC) with pairwise (must-link or cannot-link) constraints. In contrast to existing approaches, we decompose SSC into two simpler classification tasks/stages: the first stage uses a pair of Siamese neural networks to label the unlabeled pairs of points as must-link or cannot-link; the second stage uses the fully pairwise-labeled dataset produced by the first stage in a supervised neural-network-based clustering method. The proposed approach, S3C2 (Semi-Supervised Siamese Classifiers for Clustering), is motiva…
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…
Clustering is ubiquitous in data analysis, including analysis of time series. It is inherently subjective: different users may prefer different clusterings for a particular dataset. Semi-supervised clustering addresses this by allowing the user to provide examples of instances that should (not) be in the same cluster. This paper studies semi-supervised clustering in the context of time series. We show that COBRAS, a state-of-the-art semi-supervised clustering method, can be adapted to this setting. We refer to this approach as COBRAS-TS. An extensive experimental evaluation supports the follow…
The $K$-means algorithm is extended to allow for partitioning of skewed groups. Our algorithm is called TiK-Means and contributes a $K$-means type algorithm that assigns observations to groups while estimating their skewness-transformation parameters. The resulting groups and transformation reveal general-structured clusters that can be explained by inverting the estimated transformation. Further, a modification of the jump statistic chooses the number of groups. Our algorithm is evaluated on simulated and real-life datasets and then applied to a long-standing astronomical dispute regarding th…
Joint alignment of a collection of functions is the process of independently transforming the functions so that they appear more similar to each other. Typically, such unsupervised alignment algorithms fail when presented with complex data sets arising from multiple modalities or make restrictive assumptions about the form of the functions or transformations, limiting their generality. We present a transformed Bayesian infinite mixture model that can simultaneously align and cluster a data set. Our model and associated learning scheme offer two key advantages: the optimal number of clusters is…
ICSI and Department of Statistics University of California, Berkeley（加州大学伯克利分校统计系与ICSI）；G-STATS Data Science Chair, GIPSA-lab University Grenobles-Alpes（格勒诺布尔-阿尔卑斯大学GIPSA-lab实验室G-STATS数据科学讲席）
Given a large data matrix, sparsifying, quantizing, and/or performing other entry-wise nonlinear operations can have numerous benefits, ranging from speeding up iterative algorithms for core numerical linear algebra problems to providing nonlinear filters to design state-of-the-art neural network models. Here, we exploit tools from random matrix theory to make precise statements about how the eigenspectrum of a matrix changes under such nonlinear transformations. In particular, we show that very little change occurs in the informative eigenstructure even under drastic sparsification/quantizati…
IIT Jodhpur（印度理工学院焦特布尔分校）；Flipkart Internet Pvt Ltd（Flipkart互联网私人有限公司）；IIT Delhi（印度理工学院德里分校）
Generative adversarial networks (GANs) have shown remarkable success in generation of data from natural data manifolds such as images. In several scenarios, it is desirable that generated data is well-clustered, especially when there is severe class imbalance. In this paper, we focus on the problem of clustering in generated space of GANs and uncover its relationship with the characteristics of the latent space. We derive from first principles, the necessary and sufficient conditions needed to achieve faithful clustering in the GAN framework: (i) presence of a multimodal latent space with adju…
Time series clustering is a challenging task due to the specific nature of the data. Classical approaches do not perform well and need to be adapted either through a new distance measure or a data transformation. In this paper we investigate the combination of a convolutional autoencoder and a k-medoids algorithm to perfom time series clustering. The convolutional autoencoder allows to extract meaningful features and reduce the dimension of the data, leading to an improvement of the subsequent clustering. Using simulation and energy related data to validate the approach, experimental results s…
University of Electronic Science and Technology of China（电子科技大学）
Nowadays, data are generated massively and rapidly from scientific fields as bioinformatics, neuroscience and astronomy to business and engineering fields. Cluster analysis, as one of the major data analysis tools, is therefore more significant than ever. We propose in this work an effective Semi-supervised Divisive Clustering algorithm (SDC). Data points are first organized by a minimal spanning tree. Next, this tree structure is transitioned to the in-tree structure, and then divided into sub-trees under the supervision of the labeled data, and in the end, all points in the sub-trees are dir…
Self-supervised learning, which learns by constructing artificial labels given only the input signals, has recently gained considerable attention for learning representations with unlabeled datasets, i.e., learning without any human-annotated supervision. In this paper, we show that such a technique can be used to significantly improve the model accuracy even under fully-labeled datasets. Our scheme trains the model to learn both original and self-supervised tasks, but is different from conventional multi-task learning frameworks that optimize the summation of their corresponding losses. Our m…
Wuhan University of Technology（武汉理工大学）；University of Surrey（萨里大学）；Wuhan University（武汉大学）
Motivation: Identifying interaction clusters of large gene regulatory networks (GRNs) is critical for its further investigation, while this task is very challenging, attributed to data noise in experiment data, large scale of GRNs, and inconsistency between gene expression profiles and function modules, etc. It is promising to semi-supervise this process by prior information, but shortage of prior information sometimes make it very challenging. Meanwhile, it is also annoying, and sometimes impossible to discovery gold standard for evaluation of clustering results.\\ Results: With assistance of…
