Multilook SAR Image Segmentation with an Unknown Number of Clusters Using a Gamma Mixture Model and Hierarchical Clustering.

Categorical data clustering has been attracted a lot of attention recently due to its necessary in the real-world applications. Many clustering methods have been proposed for categorical data. However, most of the existing algorithms require the predefined number of clusters which is usually unavailable in real-world problems. Only a few works focused on automatic clustering, but mainly handled for numerical data. This study develops a novel automatic fuzzy clustering using non-dominated sorting particle swarm optimization (AFC-NSPSO) algorithm for categorical data. The proposed AFC-NSPSO algorithm can automatically identify the optimal number of clusters and exploit the clustering result with the corresponding selected number of clusters. In addition, a new technique is investigated to identify the maximum number of clusters in a dataset based on the local density. To select a final solution in the first Pareto front, some internal validation indices are used. The performance of the proposed AFC-NSPSO on the real-world datasets collected from the UCI machine learning repository exhibits effectiveness compared with some other existing automatic categorical clustering algorithms. Besides, this study also applies the proposed algorithm to analyze a real-world case study with an unknown number of clusters.

BackgroundA potential benefit of profiling of tissue samples using microarrays is the generation of molecular fingerprints that will define subtypes of disease. Hierarchical clustering has been the primary analytical tool used to define disease subtypes from microarray experiments in cancer settings. Assessing cluster reliability poses a major complication in analyzing output from clustering procedures. While most work has focused on estimating the number of clusters in a dataset, the question of stability of individual-level clusters has not been addressed.ResultsWe address this problem by developing cluster stability scores using subsampling techniques. These scores exploit the redundancy in biologically discriminatory information on the chip. Our approach is generic and can be used with any clustering method. We propose procedures for calculating cluster stability scores for situations involving both known and unknown numbers of clusters. We also develop cluster-size adjusted stability scores. The method is illustrated by application to data three cancer studies; one involving childhood cancers, the second involving B-cell lymphoma, and the final is from a malignant melanoma study.AvailabilityCode implementing the proposed analytic method can be obtained at the second author's website.

A hierarchical Gamma Mixture Model-based method for estimating the number of clusters in complex data

The paper investigates how to optimize the performances of unsupervised log-ratio based change detection algorithms for two-date 1-look amplitude SAR images. The usual approach of pre-processing the SAR images at different dates with state-of-the-art despeckling filters is critically discussed. Those adaptive filters are very efficient, also for the challenging case of 1-look images, for speckle reduction of single-date image data and then for providing reliable classification, detection, or parameter estimation results. However, they are not able to ease the discrimination of statistical from structural changes in 1-look SAR images for which reliable point-target detection is nearly impractical. A simple, yet very effective, multiscale method for change detection and automatic change mapping is proposed and tested on simulated 1-look SAR images. The adopted pre-processing is based on guided image filtering with different window sizes. It improves the detection of changed regions without introducing any geometrical constraint and significantly reduces the false alarm rate. Experimental tests on simulated SAR images and Spotlight COSMO-SkyMed images demonstrate the advantages of the proposed algorithm.

This paper presents a new clustering technique named STep- wise Automatic Rival- penalized (STAR) k-means algorithm (denoted as k*-means), which is actually a generalized version of the conventional k-means (MacQueen 1967). Not only is this new algorithm applicable to ellipse-shaped data clusters rather than just to ball-shaped ones like the k-means algorithm, but also it can perform appropriate clustering without knowing cluster number by gradually penalizing the winning chance of those extra seed points during learning competition. Although the existing RPCL (Xu et al. 1993) can automatically select the cluster number as well by driving extra seed points far away from the input data set, its performance is much sensitive to the selection of the de-learning rate. To our best knowledge, there is still no theoretical result to guide its selection as yet. In contrast, the proposed k*-means algorithm need not determine this rate. We have qualitatively analyzed its rival-penalized mechanism with the results well-justified by the experiments.

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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K$</tex> 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-clustering method that does not require knowing the value of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K$</tex> as it infers it during the learning. Using a split/merge framework, a dynamic architecture that adapts to the changing <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K$</tex> , and a novel loss, our proposed method outperforms existing nonparametric methods (both classical and deep ones). While the very few existing deep nonparametric methods lack scalability, we demonstrate ours by being the first to report the performance of such a method on ImageNet. We also demonstrate the importance of inferring <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K$</tex> by showing how methods that fix it deteriorate in performance when their assumed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K$</tex> value gets further from the ground-truth one, especially on imbalanced datasets. Our code is available at https://github.com/BGU-CS-VIL/DeepDPM.

To identify novel dynamic patterns of gene expression, we develop a statistical method to cluster noisy measurements of gene expression collected from multiple replicates at multiple time points, with an unknown number of clusters. We propose a random-effects mixture model coupled with a Dirichlet-process prior for clustering. The mixture model formulation allows for probabilistic cluster assignments. The random-effects formulation allows for attributing the total variability in the data to the sources that are consistent with the experimental design, particularly when the noise level is high and the temporal dependence is not strong. The Dirichlet-process prior induces a prior distribution on partitions and helps to estimate the number of clusters (or mixture components) from the data. We further tackle two challenges associated with Dirichlet-process prior-based methods. One is efficient sampling. We develop a novel Metropolis–Hastings Markov Chain Monte Carlo (MCMC) procedure to sample the partitions. The other is efficient use of the MCMC samples in forming clusters. We propose a two-step procedure for posterior inference, which involves resampling and relabeling, to estimate the posterior allocation probability matrix. This matrix can be directly used in cluster assignments, while describing the uncertainty in clustering. We demonstrate the effectiveness of our model and sampling procedure through simulated data. Applying our method to a real data set collected from Drosophila adult muscle cells after five-minute Notch activation, we identify 14 clusters of different transcriptional responses among 163 differentially expressed genes, which provides novel insights into underlying transcriptional mechanisms in the Notch signaling pathway. The algorithm developed here is implemented in the R package DIRECT, available on CRAN.

Hidden Markov random field (HMRF) models are widely used for image segmentation, as they appear naturally in problems where a spatially constrained clustering scheme is asked for. A major limitation of HMRF models concerns the automatic selection of the proper number of their states, i.e., the number of region clusters derived by the image segmentation procedure. Existing methods, including likelihood- or entropy-based criteria, and reversible Markov chain Monte Carlo methods, usually tend to yield noisy model size estimates while imposing heavy computational requirements. Recently, Dirichlet process (DP, infinite) mixture models have emerged in the cornerstone of nonparametric Bayesian statistics as promising candidates for clustering applications where the number of clusters is unknown a priori; infinite mixture models based on the original DP or spatially constrained variants of it have been applied in unsupervised image segmentation applications showing promising results. Under this motivation, to resolve the aforementioned issues of HMRF models, in this paper, we introduce a nonparametric Bayesian formulation for the HMRF model, the infinite HMRF model, formulated on the basis of a joint Dirichlet process mixture (DPM) and Markov random field (MRF) construction. We derive an efficient variational Bayesian inference algorithm for the proposed model, and we experimentally demonstrate its advantages over competing methodologies.

One of the central issues in statistics and machine learning is how to select an adequate model that can automatically adapt its complexity to the observed data. In the present paper, we focus on the issue of determining the structure of clustered data, both in terms of finding the appropriate number of clusters and of modelling the right dependence structure between the observations. Bayesian nonparametric (BNP) models, which do not impose an upper limit on the number of clusters, are appropriate to avoid the required guess on the number of clusters but have been mainly developed for independent data. In contrast, Markov random fields (MRF) have been extensively used to model dependencies in a tractable manner but usually reduce to finite cluster numbers when clustering tasks are addressed. Our main contribution is to propose a general scheme to design tractable BNP-MRF priors that combine both features: no commitment to an arbitrary number of clusters and a dependence modelling. A key ingredient in this construction is the availability of a stick-breaking representation which has the threefold advantage to allowing us to extend standard discrete MRFs to infinite state space, to design a tractable estimation algorithm using variational approximation and to derive theoretical properties on the predictive distribution and the number of clusters of the proposed model. This approach is illustrated on a challenging natural image segmentation task for which it shows good performance with respect to the literature.

To the Editor: We read with great interest the article by Hadanny et al,1 published in Neurosurgery. In this study, the authors used an approach which augmented unsupervised and supervised machine learning methods to predict response to spinal cord stimulators. This paper is an excellent example of how both approaches can be used together to prognosticate on patient outcomes, and the methodological implications span beyond the impact on patients with spinal cord stimulators. Unsupervised machine learning (UML) operates on the premise that the ground truth is not known—for this reason, there are no training data involved in the model. The outcomes of UML algorithms are usually unique clusters identified in the data set. This varies from supervised machine learning (SML) algorithms, which construct a model based on known input and output data. In the literature, UML methods are commonly used to identify novel and emergent phenotypes, whereas SML has commonly been used to perform outcome prediction.2,3 When using UML methods, there are several important parameters to consider which may influence the outcomes seen. First parameter is the cluster number identification. In this paper, the authors used the K-nearest neighbor algorithm (KNN), preceded by an elbow-based cluster optimization step. The KNN algorithm itself is not a completely unsupervised algorithm and requires the inclusion of the number of preset clusters. It requires a cluster optimization step to identify this parameter. In their supplementary methods, they argue that, using the elbow method, a pseudoelbow was created at K = 3. As a result, the decision is made that two clusters exist in the data. We encourage the authors to consider the use of other approaches to validate this finding, including the silhouette method, which has been shown to be more robust and quantifiable in some cases and may be less prone to subjective examination of the analyst.4 The number of clusters is also not readily apparent in the reprojections to the principal component analysis domain space. We suggest the use of other dimensionality reduction approaches to visualize the clusters, namely t-distributed stochastic network embedding or uniform manifold approximation and projection. While the clustering should remain in the multidimensional space, dimensionality reduction approaches have been useful in visualizing multidimensional data otherwise difficult to appreciate. Second parameter is the algorithm itself. KNN is a very well-documented partitioning algorithm. However, it has several limitations. First, the algorithm requires the use of numerical data, which may distort the categorical data, such as patient biological sex, diagnosis, smoking status, and present inherent to the data set. In addition, the sample size required for use of the KNN method is also relatively large, with some studies suggesting the need for a sample size of 2^n, where n is the number of features (24 features in this study).5,6 Other clustering algorithms, such as hierarchical clustering, have been shown to be far more effective for smaller data sets, and we encourage the authors to explore the use of more robust algorithms that would better fit the constraints of the data. As more neurosurgical studies use machine learning, specifically UML, approaches for the analysis of data, it becomes very important for researchers to consider the aforementioned parameters to strengthen their observations and findings. We applaud Hadanny et al1 for an excellent presentation of how both UML and SML approaches can be augmented, and we look forward to additional novel contributions using both approaches in the future to better help understand complex disease processes and ultimately help patients.

SAR despeckling via classification-based nonlocal and local sparse representation

Image segmentation actually could be regarded as a computer vision pre-processing step of cloud computing and big data analysis. Active contour model is a new research direction for images segmentation in synthetic aperture radar(SAR) images. However, due to the SAR images have speckle noise and low signal-to-clutter ratio, active contour models cannot produce satisfied segmentation results. To solve these issues, active contours driven by visual saliency fitting energy is proposed in this paper. First, a saliency map is calculated by improved local contrast measure. Then, a visual saliency fitting energy is proposed based on saliency map and local binary fitting energy. The saliency map has a higher signal-to-clutter ratio and the local binary fitting energy is an active contour model that can effectively segment images with intensity inhomogeneity. In this way, the proposed method has a better segmentation result. The experiments on ship chips in SAR images demonstrate that the proposed method is robust to speckle noise and the segmentation result has good connectivity and integrity for entire ship targets.

Clustering is a group of unsupervised statistical techniques commonly used in many disciplines. Considering their applications to fish abundance data, many technical details need to be considered to ensure reasonable interpretation. However, the reliability and stability of the clustering methods have rarely been studied in the contexts of fisheries. This study presents an intensive evaluation of three common clustering methods, including hierarchical clustering (HC), K-means (KM), and expectation-maximization (EM) methods, based on fish community surveys in the coastal waters of Shandong, China. We evaluated the performances of these three methods considering different numbers of clusters, data size, and data transformation approaches, focusing on the consistency validation using the index of average proportion of non-overlap (APN). The results indicate that the three methods tend to be inconsistent in the optimal number of clusters. EM showed relatively better performances to avoid unbalanced classification, whereas HC and KM provided more stable clustering results. Data transformation including scaling, square-root, and log-transformation had substantial influences on the clustering results, especially for KM. Moreover, transformation also influenced clustering stability, wherein scaling tended to provide a stable solution at the same number of clusters. The APN values indicated improved stability with increasing data size, and the effect leveled off over 70 samples in general and most quickly in EM. We conclude that the best clustering method can be chosen depending on the aim of the study and the number of clusters. In general, KM is relatively robust in our tests. We also provide recommendations for future application of clustering analyses. This study is helpful to ensure the credibility of the application and interpretation of clustering methods.

Recommendations for validating hierarchical clustering in consumer sensory projects

Hierarchical clustering is one of the most suitable tools to discover the underlying true structure of a dataset in the case of unsupervised learning where the ground truth is unknown and classical machine learning classifiers are not suitable. In many real applications, it provides a perspective on inner data structure and is preferred to partitional methods. However, determining the resulting number of clusters in hierarchical clustering requires human expertise to deduce this from the dendrogram and this represents a major challenge in making a fully automatic system such as the ones required for decision support in Industry 4.0. This research proposes a general criterion to perform the cut of a dendrogram automatically, by comparing six original criteria based on the Calinski-Harabasz index. The performance of each criterion on 95 real-life dendrograms of different topologies is evaluated against the number of classes proposed by the experts and a winner criterion is determined. This research is framed in a bigger project to build an Intelligent Decision Support system to assess the performance of 3D printers based on sensor data in real-time, although the proposed criteria can be used in other real applications of hierarchical clustering.The methodology is applied to a real-life dataset from the 3D printers and the huge reduction in CPU time is also shown by comparing the CPU time before and after this modification of the entire clustering method. It also reduces the dependability on human-expert to provide the number of clusters by inspecting the dendrogram. Further, such a process allows applying hierarchical clustering in an automatic mode in real-life industrial applications and allows the continuous monitoring of real 3D printers in production, and helps in building an Intelligent Decision Support System to detect operational modes, anomalies, and other behavioral patterns.