scholarly journals An Efficient Kriging Modeling Method Based on Multidimensional Scaling for High-Dimensional Problems

Algorithms ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 3
Author(s):  
Yu Ge ◽  
Junjun Shi ◽  
Yaohui Li ◽  
Jingfang Shen
Keyword(s):  
Multidimensional Scaling ◽  
Dimensionality Reduction ◽  
Flight Control ◽  
Distance Matrix ◽  
Modeling Method ◽  
Inner Product ◽  
High Dimensional ◽  
Design Data ◽  
Field Problem ◽  
Product Matrix

Kriging-based modeling has been widely used in computationally intensive simulations. However, the Kriging modeling of high-dimensional problems not only takes more time, but also leads to the failure of model construction. To this end, a Kriging modeling method based on multidimensional scaling (KMDS) is presented to avoid the “dimensional disaster”. Under the condition of keeping the distance between the sample points before and after the dimensionality reduction unchanged, the KMDS method, which mainly calculates each element in the inner product matrix due to the mapping relationship between the distance matrix and the inner product matrix, completes the conversion of design data from high dimensional to low dimensional. For three benchmark functions with different dimensions and the aviation field problem of aircraft longitudinal flight control, the proposed method is compared with other dimensionality reduction methods. The KMDS method has better modeling efficiency while meeting certain accuracy requirements.

scholarly journals A generalization of t-SNE and UMAP to single-cell multimodal omics

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Van Hoan Do ◽  
Stefan Canzar
Keyword(s):  
Dimensionality Reduction ◽  
Single Cell ◽  
Cell Types ◽  
High Dimensional ◽  
Omics Data ◽  
Relative Contribution ◽  
Reduction Techniques ◽  
Dimensionality Reduction Techniques ◽  
Concise Representation ◽  
Cellular Identity

AbstractEmerging single-cell technologies profile multiple types of molecules within individual cells. A fundamental step in the analysis of the produced high-dimensional data is their visualization using dimensionality reduction techniques such as t-SNE and UMAP. We introduce j-SNE and j-UMAP as their natural generalizations to the joint visualization of multimodal omics data. Our approach automatically learns the relative contribution of each modality to a concise representation of cellular identity that promotes discriminative features but suppresses noise. On eight datasets, j-SNE and j-UMAP produce unified embeddings that better agree with known cell types and that harmonize RNA and protein velocity landscapes.

scholarly journals Parallel Framework for Dimensionality Reduction of Large-Scale Datasets

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Sai Kiranmayee Samudrala ◽  
Jaroslaw Zola ◽  
Srinivas Aluru ◽  
Baskar Ganapathysubramanian
Keyword(s):  
Dimensionality Reduction ◽  
Organic Solar Cells ◽  
Large Scale ◽  
Parallel Implementation ◽  
High Dimensional Data ◽  
Real Life ◽  
Processing Parameters ◽  
High Dimensional ◽  
Morphology Evolution ◽  
Reduction Techniques

Dimensionality reduction refers to a set of mathematical techniques used to reduce complexity of the original high-dimensional data, while preserving its selected properties. Improvements in simulation strategies and experimental data collection methods are resulting in a deluge of heterogeneous and high-dimensional data, which often makes dimensionality reduction the only viable way to gain qualitative and quantitative understanding of the data. However, existing dimensionality reduction software often does not scale to datasets arising in real-life applications, which may consist of thousands of points with millions of dimensions. In this paper, we propose a parallel framework for dimensionality reduction of large-scale data. We identify key components underlying the spectral dimensionality reduction techniques, and propose their efficient parallel implementation. We show that the resulting framework can be used to process datasets consisting of millions of points when executed on a 16,000-core cluster, which is beyond the reach of currently available methods. To further demonstrate applicability of our framework we perform dimensionality reduction of 75,000 images representing morphology evolution during manufacturing of organic solar cells in order to identify how processing parameters affect morphology evolution.

Development for modification of Torgerson projection method using cumulative curve analysis in outlier detection problem for high-dimensional data

2020 ◽  
pp. 119-129
Author(s):  
Никита Сергеевич Олейник ◽  
Владислав Юрьевич Щеколдин
Keyword(s):  
Multidimensional Scaling ◽  
Outlier Detection ◽  
High Dimensional Data ◽  
Quality Data ◽  
Multidimensional Data ◽  
High Dimensional ◽  
Detection Problem ◽  
Gravity Center ◽  
Largest Eigenvalues ◽  
Cumulative Curves

Рассмотрена задача выявления аномальных наблюдений в данных больших размерностей на основе метода многомерного шкалирования с учетом возможности построения качественной визуализации данных. Предложен алгоритм модифицированного метода главных проекций Торгерсона, основанный на построении подпространства проектирования исходных данных путем изменения способа факторизации матрицы скалярных произведений при помощи метода анализа кумулятивных кривых. Построено и проанализировано эмпирическое распределение F -меры для разных вариантов проектирования исходных данных Purpose. Purpose of the article. The paper aims at the development of methods for multidimensional data presentation for solving classification problems based on the cumulative curves analysis. The paper considers the outlier detection problem for high-dimensional data based on the multidimensional scaling, in order to construct high-quality data visualization. An abnormal observation (or outlier), according to D. Hawkins, is an observation that is so different from others that it may be assumed as appeared in the sample in a fundamentally different way. Methods. One of the conceptual approaches that allow providing the classification of sample observations is multidimensional scaling, representing by the classical Orlochi method, the Torgerson main projections and others. The Torgerson method assumes that when converting data to construct the most convenient classification, the origin must be placed at the gravity center of the analyzed data, after which the matrix of scalar products of vectors with the origin at the gravity center is calculated, the two largest eigenvalues and corresponding eigenvectors are chosen and projection matrix is evaluated. Moreover, the method assumes the linear partitioning of regular and anomalous observations, which arises rarely. Therefore, it is logical to choose among the possible axes for designing those that allow obtaining more effective results for solving the problem of detecting outlier observations. A procedure of modified CC-ABOD (Cumulative Curves for Angle Based Outlier Detection) to estimate the visualization quality has been applied. It is based on the estimation of the variances of angles assumed by particular observation and remaining observations in multidimensional space. Further the cumulative curves analysis is implemented, which allows partitioning out groups of closely localized observations (in accordance with the chosen metric) and form classes of regular, intermediate, and anomalous observations. Results. A proposed modification of the Torgerson method is developed. The F1-measure distribution is constructed and analyzed for different design options in the source data. An analysis of the empirical distribution showed that in a number of cases the best axes are corresponding to the second, third, or even fourth largest eigenvalues. Findings. The multidimensional scaling methods for constructing visualizations of multi-dimensional data and solving problems of outlier detection have been considered. It was found out that the determination of design is an ambiguous problem.

Multi-Instance Dimensionality Reduction via Sparsity and Orthogonality

2018 ◽  
Vol 30 (12) ◽  
pp. 3281-3308
Author(s):  
Hong Zhu ◽  
Li-Zhi Liao ◽  
Michael K. Ng
Keyword(s):  
Dimensionality Reduction ◽  
Optimization Problem ◽  
Augmented Lagrangian ◽  
Main Idea ◽  
Real Data ◽  
Learning Performance ◽  
High Dimensional ◽  
Data Sets ◽  
Outer Loop ◽  
Orthogonality Constraints

We study a multi-instance (MI) learning dimensionality-reduction algorithm through sparsity and orthogonality, which is especially useful for high-dimensional MI data sets. We develop a novel algorithm to handle both sparsity and orthogonality constraints that existing methods do not handle well simultaneously. Our main idea is to formulate an optimization problem where the sparse term appears in the objective function and the orthogonality term is formed as a constraint. The resulting optimization problem can be solved by using approximate augmented Lagrangian iterations as the outer loop and inertial proximal alternating linearized minimization (iPALM) iterations as the inner loop. The main advantage of this method is that both sparsity and orthogonality can be satisfied in the proposed algorithm. We show the global convergence of the proposed iterative algorithm. We also demonstrate that the proposed algorithm can achieve high sparsity and orthogonality requirements, which are very important for dimensionality reduction. Experimental results on both synthetic and real data sets show that the proposed algorithm can obtain learning performance comparable to that of other tested MI learning algorithms.

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