scholarly journals PCA reduced Gaussian mixture models with applications in superresolution

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Johannes Hertrich ◽  
Dang-Phuong-Lan Nguyen ◽  
Jean-Francois Aujol ◽  
Dominique Bernard ◽  
Yannick Berthoumieu ◽  
...  
Keyword(s):  
Mixture Model ◽  
Optimization Problems ◽  
Rapid Development ◽  
Gaussian Mixture Models ◽  
Principal Component ◽  
Gaussian Mixture ◽  
Data Sets ◽  
Constrained Problems ◽  
Dimensional Parameters ◽  
Low Dimensional

<p style='text-indent:20px;'>Despite the rapid development of computational hardware, the treatment of large and high dimensional data sets is still a challenging problem. The contribution of this paper to the topic is twofold. First, we propose a Gaussian mixture model in conjunction with a reduction of the dimensionality of the data in each component of the model by principal component analysis, which we call PCA-GMM. To learn the (low dimensional) parameters of the mixture model we propose an EM algorithm whose M-step requires the solution of constrained optimization problems. Fortunately, these constrained problems do not depend on the usually large number of samples and can be solved efficiently by an (inertial) proximal alternating linearized minimization algorithm. Second, we apply our PCA-GMM for the superresolution of 2D and 3D material images based on the approach of Sandeep and Jacob. Numerical results confirm the moderate influence of the dimensionality reduction on the overall superresolution result.</p>

Local preserving projections-based feature selection and Gaussian mixture model for machine health assessment

2011 ◽  
Vol 225 (7) ◽  
pp. 1703-1717 ◽  
Author(s):  
J Yu ◽  
M Liu ◽  
H Wu
Keyword(s):  
Feature Selection ◽  
Gaussian Mixture Model ◽  
Mixture Model ◽  
Health Assessment ◽  
Principal Component ◽  
Gaussian Mixture ◽  
Health State ◽  
Structure Information ◽  
Machine Health ◽  
Low Dimensional

The sensitivity of various features that are characteristics of machine health may vary significantly under different working conditions. Thus, it is critical to devise a systematic feature selection (FS) approach that provides a useful and automatic guidance on choosing the most effective features for machine health assessment. This article proposes a locality preserving projections (LPP)-based FS approach. Different from principal component analysis (PCA) that aims to discover the global structure of the Euclidean space, LPP can find a good linear embedding that preserves local structure information. This may enable LPP to find more meaningful low-dimensional information hidden in the high-dimensional observations compared with PCA. The LPP-based FS approach is based on unsupervised learning technique, which does not need too much prior knowledge to improve its utility in real-world applications. The effectiveness of the proposed approach was evaluated experimentally on bearing test-beds. A novel machine health assessment indication, Gaussian mixture model-based Mahalanobis distance is proposed to provide a comprehensible indication for quantifying machine health state. The proposed approach has shown to provide the better performance with reduced feature inputs than using all original candidate features. The experimental results indicate its potential applications as an effective tool for machine health assessment.

scholarly journals Gaussian Mixture Models Based on Principal Components and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Nada A. Alqahtani ◽  
Zakiah I. Kalantan
Keyword(s):  
Mixture Model ◽  
Principal Components ◽  
Gaussian Mixture Models ◽  
Expectation Maximization Algorithm ◽  
Large Data ◽  
Real Data ◽  
R Package ◽  
Gaussian Mixture ◽  
Machine Learning Algorithms ◽  
Data Sets

Data scientists use various machine learning algorithms to discover patterns in large data that can lead to actionable insights. In general, high-dimensional data are reduced by obtaining a set of principal components so as to highlight similarities and differences. In this work, we deal with the reduced data using a bivariate mixture model and learning with a bivariate Gaussian mixture model. We discuss a heuristic for detecting important components by choosing the initial values of location parameters using two different techniques: cluster means, k-means and hierarchical clustering, and default values in the “mixtools” R package. The parameters of the model are obtained via an expectation maximization algorithm. The criteria from Bayesian point are evaluated for both techniques, demonstrating that both techniques are efficient with respect to computation capacity. The effectiveness of the discussed techniques is demonstrated through a simulation study and using real data sets from different fields.

scholarly journals Individual Tree Extraction from Terrestrial LiDAR Point Clouds Based on Transfer Learning and Gaussian Mixture Model Separation

2021 ◽  
Vol 13 (2) ◽  
pp. 223
Author(s):  
Zhenyang Hui ◽  
Shuanggen Jin ◽  
Dajun Li ◽  
Yao Yevenyo Ziggah ◽  
Bo Liu
Keyword(s):  
Transfer Learning ◽  
Gaussian Mixture Model ◽  
Mixture Model ◽  
Principal Component ◽  
Point Clouds ◽  
Gaussian Mixture ◽  
Individual Tree ◽  
Terrestrial Lidar ◽  
Initial Segmentation ◽  
Tree Extraction

Individual tree extraction is an important process for forest resource surveying and monitoring. To obtain more accurate individual tree extraction results, this paper proposed an individual tree extraction method based on transfer learning and Gaussian mixture model separation. In this study, transfer learning is first adopted in classifying trunk points, which can be used as clustering centers for tree initial segmentation. Subsequently, principal component analysis (PCA) transformation and kernel density estimation are proposed to determine the number of mixed components in the initial segmentation. Based on the number of mixed components, the Gaussian mixture model separation is proposed to separate canopies for each individual tree. Finally, the trunk stems corresponding to each canopy are extracted based on the vertical continuity principle. Six tree plots with different forest environments were used to test the performance of the proposed method. Experimental results show that the proposed method can achieve 87.68% average correctness, which is much higher than that of other two classical methods. In terms of completeness and mean accuracy, the proposed method also outperforms the other two methods.

scholarly journals Comparison of dimensionality reduction and clustering methods for SARS-CoV-2 genome

2021 ◽  
Vol 10 (4) ◽  
pp. 2170-2180
Author(s):  
Untari N. Wisesty ◽  
Tati Rajab Mengko
Keyword(s):  
Dimensionality Reduction ◽  
Dimensional Reduction ◽  
Clustering Algorithm ◽  
Sequence Data ◽  
Clustering Algorithms ◽  
Gaussian Mixture Models ◽  
Reduction Process ◽  
Principal Component ◽  
Gaussian Mixture ◽  
Clustering Methods

This paper aims to conduct an analysis of the SARS-CoV-2 genome variation was carried out by comparing the results of genome clustering using several clustering algorithms and distribution of sequence in each cluster. The clustering algorithms used are K-means, Gaussian mixture models, agglomerative hierarchical clustering, mean-shift clustering, and DBSCAN. However, the clustering algorithm has a weakness in grouping data that has very high dimensions such as genome data, so that a dimensional reduction process is needed. In this research, dimensionality reduction was carried out using principal component analysis (PCA) and autoencoder method with three models that produce 2, 10, and 50 features. The main contributions achieved were the dimensional reduction and clustering scheme of SARS-CoV-2 sequence data and the performance analysis of each experiment on each scheme and hyper parameters for each method. Based on the results of experiments conducted, PCA and DBSCAN algorithm achieve the highest silhouette score of 0.8770 with three clusters when using two features. However, dimensionality reduction using autoencoder need more iterations to converge. On the testing process with Indonesian sequence data, more than half of them enter one cluster and the rest are distributed in the other two clusters.

scholarly journals Hyperspectral Unmixing with Gaussian Mixture Model and Low-Rank Representation

2019 ◽  
Vol 11 (8) ◽  
pp. 911 ◽  
Author(s):  
Yong Ma ◽  
Qiwen Jin ◽  
Xiaoguang Mei ◽  
Xiaobing Dai ◽  
Fan Fan ◽  
...  
Keyword(s):  
Gaussian Mixture Model ◽  
Mixture Model ◽  
Spatial Data ◽  
Principal Component ◽  
Gaussian Mixture ◽  
Low Rank ◽  
Hyperspectral Unmixing ◽  
Low Rank Representation ◽  
Synthetic Datasets ◽  
Endmember Variability

Gaussian mixture model (GMM) has been one of the most representative models for hyperspectral unmixing while considering endmember variability. However, the GMM unmixing models only have proper smoothness and sparsity prior constraints on the abundances and thus do not take into account the possible local spatial correlation. When the pixels that lie on the boundaries of different materials or the inhomogeneous region, the abundances of the neighboring pixels do not have those prior constraints. Thus, we propose a novel GMM unmixing method based on superpixel segmentation (SS) and low-rank representation (LRR), which is called GMM-SS-LRR. we adopt the SS in the first principal component of HSI to get the homogeneous regions. Moreover, the HSI to be unmixed is partitioned into regions where the statistical property of the abundance coefficients have the underlying low-rank property. Then, to further exploit the spatial data structure, under the Bayesian framework, we use GMM to formulate the unmixing problem, and put the low-rank property into the objective function as a prior knowledge, using generalized expectation maximization to solve the objection function. Experiments on synthetic datasets and real HSIs demonstrated that the proposed GMM-SS-LRR is efficient compared with other current popular methods.

A framework for petrophysically and geologically guided geophysical inversion using a dynamic Gaussian mixture model prior

2019 ◽  
Vol 219 (3) ◽  
pp. 1989-2012 ◽  
Author(s):  
Thibaut Astic ◽  
Douglas W Oldenburg
Keyword(s):  
Objective Function ◽  
Gaussian Mixture Model ◽  
Mixture Model ◽  
Optimization Problems ◽  
Reference Model ◽  
Gaussian Mixture ◽  
Geological Data ◽  
Geophysical Inversion ◽  
Geophysical Model ◽  
Geological Information

SUMMARY We propose a new framework for incorporating petrophysical and geological information into voxel-based geophysical inversion. By developing the geophysical inverse problem from a probabilistic perspective, we redesign the objective function and the iteration steps as a suite of cyclic optimization problems in which three separate MAP optimization problems are solved using geophysical, petrophysical and geological data, respectively. By quantitatively linking these data into a single framework, we recover a final inverted model that reproduces the observed, or desired, petrophysical and geological features while fitting the geophysical data. To achieve our goal we replace the Gaussian prior, used in the Tikhonov inversion approach, by a Gaussian mixture model. After each geophysical model update, the mixture parameters (means, variances and proportions) are determined by the geophysical model and the expected characteristics of the lithologies through another optimization process using the expectation–maximization algorithm. We then classify the model cells into rock units according to the petrophysical and geological information. These two additional steps over the petrophysical and geological data result in a dynamic update of the reference model and associated weights and guide the inversion towards reproducing the expected petrophysical and geological characteristics. The resulting geophysical objective function does not require extra terms to include the additional petrophysical and geological information; this is an important distinction between our work and previous frameworks that carry out joint geophysical and petrophysical data inversion. We highlight different capabilities of our methodology by inverting magnetotelluric and direct-current resistivity data in 1-D and 2-D, respectively. Finally, we apply our framework to inverting airborne frequency domain data, acquired in Australia, for the detection and characterization of saline contamination of freshwater.

scholarly journals Image Denoising Based on Improved Gaussian Mixture Model

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Hui Wei ◽  
Wei Zheng
Keyword(s):  
Mixture Models ◽  
Image Denoising ◽  
Gaussian Mixture Model ◽  
Mixture Model ◽  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
Denoising Method ◽  
L2 Norm ◽  
Image Area ◽  
The Difference

An image denoising method is proposed based on the improved Gaussian mixture model to reduce the noises and enhance the image quality. Unlike the traditional image denoising methods, the proposed method models the pixel information in the neighborhood around each pixel in the image. The Gaussian mixture model is employed to measure the similarity between pixels by calculating the L2 norm between the Gaussian mixture models corresponding to the two pixels. The Gaussian mixture model can model the statistical information such as the mean and variance of the pixel information in the image area. The L2 norm between the two Gaussian mixture models represents the difference in the local grayscale intensity and the richness of the details of the pixel information around the two pixels. In this sense, the L2 norm between Gaussian mixture models can more accurately measure the similarity between pixels. The experimental results show that the proposed method can improve the denoising performance of the images while retaining the detailed information of the image.

scholarly journals Petrophysically and geologically guided multi-physics inversion using a dynamic Gaussian mixture model

2020 ◽  
Vol 224 (1) ◽  
pp. 40-68 ◽  
Author(s):  
Thibaut Astic ◽  
Lindsey J Heagy ◽  
Douglas W Oldenburg
Keyword(s):  
Gaussian Mixture Model ◽  
Mixture Model ◽  
Gaussian Mixture ◽  
Quantitative Information ◽  
Geophysical Data ◽  
Magnetic Data ◽  
Data Sets ◽  
Data Set ◽  
Geophysical Surveys ◽  
Geological Information

SUMMARY In a previous paper, we introduced a framework for carrying out petrophysically and geologically guided geophysical inversions. In that framework, petrophysical and geological information is modelled with a Gaussian mixture model (GMM). In the inversion, the GMM serves as a prior for the geophysical model. The formulation and applications were confined to problems in which a single physical property model was sought, and a single geophysical data set was available. In this paper, we extend that framework to jointly invert multiple geophysical data sets that depend on multiple physical properties. The petrophysical and geological information is used to couple geophysical surveys that, otherwise, rely on independent physics. This requires advancements in two areas. First, an extension from a univariate to a multivariate analysis of the petrophysical data, and their inclusion within the inverse problem, is necessary. Secondly, we address the practical issues of simultaneously inverting data from multiple surveys and finding a solution that acceptably reproduces each one, along with the petrophysical and geological information. To illustrate the efficacy of our approach and the advantages of carrying out multi-physics inversions coupled with petrophysical and geological information, we invert synthetic gravity and magnetic data associated with a kimberlite deposit. The kimberlite pipe contains two distinct facies embedded in a host rock. Inverting the data sets individually, even with petrophysical information, leads to a binary geological model: background or undetermined kimberlite. A multi-physics inversion, with petrophysical information, differentiates between the two main kimberlite facies of the pipe. Through this example, we also highlight the capabilities of our framework to work with interpretive geological assumptions when minimal quantitative information is available. In those cases, the dynamic updates of the GMM allow us to perform multi-physics inversions by learning a petrophysical model.

scholarly journals A coarse-to-fine scheme for groupwise registration of multisensor images

2016 ◽  
Vol 13 (6) ◽  
pp. 172988141667330 ◽  
Author(s):  
Yinghao Li ◽  
Zhongshi He ◽  
Hao Zhu ◽  
Dongsheng Zou ◽  
Weiwei Zhang
Keyword(s):  
Mixture Model ◽  
Image Data ◽  
Gaussian Mixture ◽  
Reference Image ◽  
Data Sets ◽  
Coarse Registration ◽  
Image Set ◽  
Groupwise Registration ◽  
Improved Performance ◽  
Coarse To Fine

Ensemble registration is concerned with a group of images that need to be registered simultaneously. It is challenging but important for many image analysis tasks such as vehicle detection and medical image fusion. To solve this problem effectively, a novel coarse-to-fine scheme for groupwise image registration is proposed. First, in the coarse registration step, unregistered images are divided into reference image set and float image set. The images of the two sets are registered based on segmented region matching. The coarse registration results are used as an initial solution for the next step. Then, in the fine registration step, a Gaussian mixture model with a local template is used to model the joint intensity of coarse-registered images. Meanwhile, a minimum message length criterion-based method is employed to determine the unknown number of mixing components. Based on this mixture model, a maximum likelihood framework is used to register a group of images. To evaluate the performance of the proposed approach, some representative groupwise registration approaches are compared on different image data sets. The experimental results show that the proposed approach has improved performance compared to conventional approaches.

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