We propose an algorithm, HPREF (Hierarchical Partitioning by Repeated Features), that produces a hierarchical partition of a set of clusterings of a fixed dataset, such as sets of clusterings produced by running a clustering algorithm with a range of parameters. This gives geometric structure to such sets of clustering, and can be used to visualize the set of results one obtains by running a clustering algorithm with a range of parameters.
t-SNE and hierarchical clustering are popular methods of exploratory data analysis, particularly in biology. Building on recent advances in speeding up t-SNE and obtaining finer-grained structure, we combine the two to create tree-SNE, a hierarchical clustering and visualization algorithm based on stacked one-dimensional t-SNE embeddings. We also introduce alpha-clustering, which recommends the optimal cluster assignment, without foreknowledge of the number of clusters, based off of the cluster stability across multiple scales. We demonstrate the effectiveness of tree-SNE and alpha-clustering …
It is becoming increasingly important for machine learning methods to make predictions that are interpretable as well as accurate. In many practical applications, it is of interest which features and feature interactions are relevant to the prediction task. We present a novel method, Selective Bayesian Forest Classifier, that strikes a balance between predictive power and interpretability by simultaneously performing classification, feature selection, feature interaction detection and visualization. It builds parsimonious yet flexible models using tree-structured Bayesian networks, and samples…
Cluster and then Embed: A Modular Approach for Visualization
Department of Mathematics, University of California, San Diego（数学系，加州大学圣地亚哥分校）；Halıcıoğlu Data Science Institute, University of California, San Diego（Halıcıoğlu数据科学研究所，加州大学圣地亚哥分校）
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 …
We present a visualization algorithm based on a novel unsupervised Siamese neural network training regime and loss function, called Differentiating Embedding Networks (DEN). The Siamese neural network finds differentiating or similar features between specific pairs of samples in a dataset, and uses these features to embed the dataset in a lower dimensional space where it can be visualized. Unlike existing visualization algorithms such as UMAP or $t$-SNE, DEN is parametric, meaning it can be interpreted by techniques such as SHAP. To interpret DEN, we create an end-to-end parametric clustering …
Rice University（莱斯大学）；Baylor College of Medicine（贝勒医学院）
Convex clustering is a promising new approach to the classical problem of clustering, combining strong performance in empirical studies with rigorous theoretical foundations. Despite these advantages, convex clustering has not been widely adopted, due to its computationally intensive nature and its lack of compelling visualizations. To address these impediments, we introduce Algorithmic Regularization, an innovative technique for obtaining high-quality estimates of regularization paths using an iterative one-step approximation scheme. We justify our approach with a novel theoretical result, gu…
Vironova AB（Vironova公司）；KTH Royal Institute of Technology（瑞典皇家理工学院）
In this paper we propose an adaptive approach for clustering and visualization of data by an orthogonalization process. Starting with the data points being represented by a Markov process using the diffusion map framework, the method adaptively increase the orthogonality of the clusters by applying a feedback mechanism inspired by the Gromov-Wasserstein distance. This mechanism iteratively increases the spectral gap and refines the orthogonality of the data to achieve a clustering with high specificity. By using the diffusion map framework and representing the relation between data points usin…
Westlake University（西湖大学）；Westlake Institute for Advanced Study（西湖高等研究院）
High dimensional data analysis for exploration and discovery includes three fundamental tasks: dimensionality reduction, clustering, and visualization. When the three associated tasks are done separately, as is often the case thus far, inconsistencies can occur among the tasks in terms of data geometry and others. This can lead to confusing or misleading data interpretation. In this paper, we propose a novel neural network-based method, called Consistent Representation Learning (CRL), to accomplish the three associated tasks end-to-end and improve the consistencies. The CRL network consists of…
Institute for Information and Communication Technologies, Electronics and Applied Mathematics (ICTEAM)（信息与通信技术、电子与应用数学研究所（ICTEAM））；Center for Operations Research and Econometrics (CORE)（运筹学与计量经济学中心（CORE））；Université catholique de Louvain（天主教鲁汶大学）
A main challenge in mining network-based data is finding effective ways to represent or encode graph structures so that it can be efficiently exploited by machine learning algorithms. Several methods have focused in network representation at node/edge or substructure level. However, many real life challenges such as time-varying, multilayer, chemical compounds and brain networks involve analysis of a family of graphs instead of single one opening additional challenges in graph comparison and representation. Traditional approaches for learning representations relies on hand-crafting specialized…
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, calle…
University of Hasan 1st（哈桑一世大学）；University of Abdelmalek Essaâdi（阿卜杜勒马利克·埃萨迪大学）
The mixture models have become widely used in clustering, given its probabilistic framework in which its based, however, for modern databases that are characterized by their large size, these models behave disappointingly in setting out the model, making essential the selection of relevant variables for this type of clustering. After recalling the basics of clustering based on a model, this article will examine the variable selection methods for model-based clustering, as well as presenting opportunities for improvement of these methods.
We present a framework for clustering with cluster-specific feature selection. The framework, CRAFT, is derived from asymptotic log posterior formulations of nonparametric MAP-based clustering models. CRAFT handles assorted data, i.e., both numeric and categorical data, and the underlying objective functions are intuitively appealing. The resulting algorithm is simple to implement and scales nicely, requires minimal parameter tuning, obviates the need to specify the number of clusters a priori, and compares favorably with other methods on real datasets.
Johannes Kepler University Linz（约翰内斯·开普勒大学林茨）；Imperial College London（帝国理工学院）；Salesbeat GmbH（Salesbeat有限责任公司）；IBM Research（IBM研究院）；The University of British Columbia（不列颠哥伦比亚大学）
Classifiers are among the most widely used supervised machine learning algorithms. Many classification models exist, and choosing the right one for a given task is difficult. During model selection and debugging, data scientists need to assess classifiers' performances, evaluate their learning behavior over time, and compare different models. Typically, this analysis is based on single-number performance measures such as accuracy. A more detailed evaluation of classifiers is possible by inspecting class errors. The confusion matrix is an established way for visualizing these class errors, but …
Dimension reduction and visualization of high-dimensional data have become very important research topics because of the rapid growth of large databases in data science. In this paper, we propose using a generalized sigmoid function to model the distance similarity in both high- and low-dimensional spaces. In particular, the parameter b is introduced to the generalized sigmoid function in low-dimensional space, so that we can adjust the heaviness of the function tail by changing the value of b. Using both simulated and real-world data sets, we show that our proposed method can generate visuali…
Sparse linear prediction methods suffer from decreased prediction accuracy when the predictor variables have cluster structure (e.g. there are highly correlated groups of variables). To improve prediction accuracy, various methods have been proposed to identify variable clusters from the data and integrate cluster information into a sparse modeling process. But none of these methods achieve satisfactory performance for prediction, variable selection and variable clustering simultaneously. This paper presents Variable Cluster Principal Component Regression (VC-PCR), a prediction method that sup…
One of the longstanding problems in spectral graph clustering (SGC) is the so-called model order selection problem: automated selection of the correct number of clusters. This is equivalent to the problem of finding the number of connected components or communities in an undirected graph. In this paper, we propose AMOS, an automated model order selection algorithm for SGC. Based on a recent analysis of clustering reliability for SGC under the random interconnection model, AMOS works by incrementally increasing the number of clusters, estimating the quality of identified clusters, and providing…
In a wide variety of situations, anomalies in the behaviour of a complex system, whose health is monitored through the observation of a random vector X = (X1,. .. , X d) valued in R d , correspond to the simultaneous occurrence of extreme values for certain subgroups $α$ $\subset$ {1,. .. , d} of variables Xj. Under the heavy-tail assumption, which is precisely appropriate for modeling these phenomena, statistical methods relying on multivariate extreme value theory have been developed in the past few years for identifying such events/subgroups. This paper exploits this approach much further b…
Texas A&M University（德克萨斯农工大学）；Yale School of Medicine（耶鲁医学院）
Visual summarization of clinical data collected on patients contained within the electronic health record (EHR) may enable precise and rapid triage at the time of patient presentation to an emergency department (ED). The triage process is critical in the appropriate allocation of resources and in anticipating eventual patient disposition, typically admission to the hospital or discharge home. EHR data are high-dimensional and complex, but offer the opportunity to discover and characterize underlying data-driven patient phenotypes. These phenotypes will enable improved, personalized therapeutic…
We consider a problem of grouping multiple graphs into several clusters using singular value thesholding and non-negative factorization. We derive a model selection information criterion to estimate the number of clusters. We demonstrate our approach using "Swimmer data set" as well as simulated data set, and compare its performance with two standard clustering algorithms.
One of the longstanding open problems in spectral graph clustering (SGC) is the so-called model order selection problem: automated selection of the correct number of clusters. This is equivalent to the problem of finding the number of connected components or communities in an undirected graph. We propose automated model order selection (AMOS), a solution to the SGC model selection problem under a random interconnection model (RIM) using a novel selection criterion that is based on an asymptotic phase transition analysis. AMOS can more generally be applied to discovering hidden block diagonal s…
Model-based clustering is a popular approach for clustering multivariate data which has seen applications in numerous fields. Nowadays, high-dimensional data are more and more common and the model-based clustering approach has adapted to deal with the increasing dimensionality. In particular, the development of variable selection techniques has received a lot of attention and research effort in recent years. Even for small size problems, variable selection has been advocated to facilitate the interpretation of the clustering results. This review provides a summary of the methods developed for …
We present a nonparametric method for selecting informative features in high-dimensional clustering problems. We start with a screening step that uses a test for multimodality. Then we apply kernel density estimation and mode clustering to the selected features. The output of the method consists of a list of relevant features, and cluster assignments. We provide explicit bounds on the error rate of the resulting clustering. In addition, we provide the first error bounds on mode based clustering.
Stability selection (Meinshausen and Buhlmann, 2010) makes any feature selection method more stable by returning only those features that are consistently selected across many subsamples. We prove (in what is, to our knowledge, the first result of its kind) that for data containing highly correlated proxies for an important latent variable, the lasso typically selects one proxy, yet stability selection with the lasso can fail to select any proxy, leading to worse predictive performance than the lasso alone. We introduce cluster stability selection, which exploits the practitioner's knowledge t…
