Efficient Image Inpainting Using Dimensional Space Reduction via Adaptive Patch-based Concept and Rank Lowering Technique

In this paper, we present a new algorithm for image inpainting using low dimensional feature space. In our method, projecting a low dimensional space from the original space is accomplished firstly using SVD, which is named low rank component, and then the missing pixels are filled in the new space. Finally, the original image is inpainted so that adaptive patch size is considered by quad-tree based on the previous step. In our algorithm, the missing pixels in the target region are estimated twice, one in low dimension feature space and another in the original space. It is noticeable that both processes estimate the unknown pixels using patch-based idea and rank lowering concept. Experimental results of this algorithm show better consistency in comparison with state-of-the-art methods.

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Hybrid approaches to feature subset selection for data classification in high-dimensional feature space

Artificial Intelligence Research ◽

10.5430/air.v9n1p45 ◽

2020 ◽

Vol 9 (1) ◽

pp. 45

Author(s):

Maysa Ibrahem Almulla Khalaf ◽

John Q Gan

Keyword(s):

Dimensional Space ◽

Subset Selection ◽

Feature Space ◽

Feature Subset Selection ◽

High Dimensional ◽

Support Vector ◽

Feature Subset ◽

Linear Discriminant ◽

Hybrid Approaches ◽

Low Dimensional

This paper proposes two hybrid feature subset selection approaches based on the combination (union or intersection) of both supervised and unsupervised filter approaches before using a wrapper, aiming to obtain low-dimensional features with high accuracy and interpretability and low time consumption. Experiments with the proposed hybrid approaches have been conducted on seven high-dimensional feature datasets. The classifiers adopted are support vector machine (SVM), linear discriminant analysis (LDA), and K-nearest neighbour (KNN). Experimental results have demonstrated the advantages and usefulness of the proposed methods in feature subset selection in high-dimensional space in terms of the number of selected features and time spent to achieve the best classification accuracy.

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The Value of Manifold Learning Algorithms in Simplifying Complex Datasets for More Efficacious Analysis

Sciential - McMaster Undergraduate Science Journal ◽

10.15173/sciential.v1i5.2537 ◽

2020 ◽

pp. 13-20

Author(s):

Muhammad Amjad

Keyword(s):

Data Analysis ◽

Manifold Learning ◽

Dimensional Space ◽

Feature Space ◽

Topological Data Analysis ◽

High Dimensional ◽

Dimensional Manifold ◽

Low Dimensional ◽

Low Dimensional Manifold ◽

Complex Datasets

Advances in manifold learning have proven to be of great benefit in reducing the dimensionality of large complex datasets. Elements in an intricate dataset will typically belong in high-dimensional space as the number of individual features or independent variables will be extensive. However, these elements can be integrated into a low-dimensional manifold with well-defined parameters. By constructing a low-dimensional manifold and embedding it into high-dimensional feature space, the dataset can be simplified for easier interpretation. In spite of this elemental dimensionality reduction, the dataset’s constituents do not lose any information, but rather filter it with the hopes of elucidating the appropriate knowledge. This paper will explore the importance of this method of data analysis, its applications, and its extensions into topological data analysis.

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Predicting miRNA-Disease Associations by Incorporating Projections in Low-Dimensional Space and Local Topological Information

Genes ◽

10.3390/genes10090685 ◽

2019 ◽

Vol 10 (9) ◽

pp. 685 ◽

Cited By ~ 1

Author(s):

Xuan ◽

Zhang ◽

Li ◽

Zhao

Keyword(s):

Dimensional Space ◽

Characteristic Curve ◽

Feature Space ◽

Superior Performance ◽

Topological Information ◽

Heterogeneous Information ◽

Feature Representations ◽

Disease Associations ◽

Precision Recall Curve ◽

Low Dimensional

Predicting the potential microRNA (miRNA) candidates associated with a disease helps in exploring the mechanisms of disease development. Most recent approaches have utilized heterogeneous information about miRNAs and diseases, including miRNA similarities, disease similarities, and miRNA-disease associations. However, these methods do not utilize the projections of miRNAs and diseases in a low-dimensional space. Thus, it is necessary to develop a method that can utilize the effective information in the low-dimensional space to predict potential disease-related miRNA candidates. We proposed a method based on non-negative matrix factorization, named DMAPred, to predict potential miRNA-disease associations. DMAPred exploits the similarities and associations of diseases and miRNAs, and it integrates local topological information of the miRNA network. The likelihood that a miRNA is associated with a disease also depends on their projections in low-dimensional space. Therefore, we project miRNAs and diseases into low-dimensional feature space to yield their low-dimensional and dense feature representations. Moreover, the sparse characteristic of miRNA-disease associations was introduced to make our predictive model more credible. DMAPred achieved superior performance for 15 well-characterized diseases with AUCs (area under the receiver operating characteristic curve) ranging from 0.860 to 0.973 and AUPRs (area under the precision-recall curve) ranging from 0.118 to 0.761. In addition, case studies on breast, prostatic, and lung neoplasms demonstrated the ability of DMAPred to discover potential disease-related miRNAs.

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High-dimensional Similarity Learning via Dual-sparse Random Projection

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2018/417 ◽

2018 ◽

Author(s):

Dezhong Yao ◽

Peilin Zhao ◽

Tuan-Anh Nguyen Pham ◽

Gao Cong

Keyword(s):

Dimensional Space ◽

Computational Cost ◽

Optimal Solution ◽

Random Projection ◽

Projection Methods ◽

Low Rank ◽

High Dimensional ◽

Similarity Learning ◽

Reduced Space ◽

Low Dimensional

We investigate how to adopt dual random projection for high-dimensional similarity learning. For a high-dimensional similarity learning problem, projection is usually adopted to map high-dimensional features into low-dimensional space, in order to reduce the computational cost. However, dimensionality reduction method sometimes results in unstable performance due to the suboptimal solution in original space. In this paper, we propose a dual random projection framework for similarity learning to recover the original optimal solution from subspace optimal solution. Previous dual random projection methods usually make strong assumptions about the data, which need to be low rank or have a large margin. Those assumptions limit dual random projection applications in similarity learning. Thus, we adopt a dual-sparse regularized random projection method that introduces a sparse regularizer into the reduced dual problem. As the original dual solution is a sparse one, applying a sparse regularizer in the reduced space relaxes the low-rank assumption. Experimental results show that our method enjoys higher effectiveness and efficiency than state-of-the-art solutions.

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Zero Shot Learning via Low-rank Embedded Semantic AutoEncoder

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2018/345 ◽

2018 ◽

Cited By ~ 15

Author(s):

Yang Liu ◽

Quanxue Gao ◽

Jin Li ◽

Jungong Han ◽

Ling Shao

Keyword(s):

State Of The Art ◽

Feature Space ◽

Original Data ◽

Semantic Space ◽

Dimensional Subspace ◽

Low Rank ◽

Visual Features ◽

Visual Feature ◽

Benchmark Datasets ◽

Low Dimensional

Zero-shot learning (ZSL) has been widely researched and get successful in machine learning. Most existing ZSL methods aim to accurately recognize objects of unseen classes by learning a shared mapping from the feature space to a semantic space. However, such methods did not investigate in-depth whether the mapping can precisely reconstruct the original visual feature. Motivated by the fact that the data have low intrinsic dimensionality e.g. low-dimensional subspace. In this paper, we formulate a novel framework named Low-rank Embedded Semantic AutoEncoder (LESAE) to jointly seek a low-rank mapping to link visual features with their semantic representations. Taking the encoder-decoder paradigm, the encoder part aims to learn a low-rank mapping from the visual feature to the semantic space, while decoder part manages to reconstruct the original data with the learned mapping. In addition, a non-greedy iterative algorithm is adopted to solve our model. Extensive experiments on six benchmark datasets demonstrate its superiority over several state-of-the-art algorithms.

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Analyzing Intra-Speaker and Inter-Speaker Vocal Tract Impedance Characteristics in a Low-Dimensional Feature Space Using t-SNE

10.21437/interspeech.2019-1492 ◽

2019 ◽

Author(s):

Balamurali B.T. ◽

Jer-Ming Chen

Keyword(s):

Vocal Tract ◽

Feature Space ◽

Impedance Characteristics ◽

Low Dimensional

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A Generative-Discriminative Framework that Integrates Imaging, Genetic, and Diagnosis into Coupled Low Dimensional Space

NeuroImage ◽

10.1016/j.neuroimage.2021.118200 ◽

2021 ◽

pp. 118200

Author(s):

Sayan Ghosal ◽

Qiang Chen ◽

Giulio Pergola ◽

Aaron L. Goldman ◽

William Ulrich ◽

...

Keyword(s):

Dimensional Space ◽

Low Dimensional

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Supervised dimensionality reduction for big data

Nature Communications ◽

10.1038/s41467-021-23102-2 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Joshua T. Vogelstein ◽

Eric W. Bridgeford ◽

Minh Tang ◽

Da Zheng ◽

Christopher Douville ◽

...

Keyword(s):

Dimensionality Reduction ◽

Data Science ◽

Real Data ◽

Low Rank ◽

Conditional Moment ◽

Desktop Computer ◽

Reduction Techniques ◽

Reduction Methods ◽

The Individual ◽

Low Dimensional

AbstractTo solve key biomedical problems, experimentalists now routinely measure millions or billions of features (dimensions) per sample, with the hope that data science techniques will be able to build accurate data-driven inferences. Because sample sizes are typically orders of magnitude smaller than the dimensionality of these data, valid inferences require finding a low-dimensional representation that preserves the discriminating information (e.g., whether the individual suffers from a particular disease). There is a lack of interpretable supervised dimensionality reduction methods that scale to millions of dimensions with strong statistical theoretical guarantees. We introduce an approach to extending principal components analysis by incorporating class-conditional moment estimates into the low-dimensional projection. The simplest version, Linear Optimal Low-rank projection, incorporates the class-conditional means. We prove, and substantiate with both synthetic and real data benchmarks, that Linear Optimal Low-Rank Projection and its generalizations lead to improved data representations for subsequent classification, while maintaining computational efficiency and scalability. Using multiple brain imaging datasets consisting of more than 150 million features, and several genomics datasets with more than 500,000 features, Linear Optimal Low-Rank Projection outperforms other scalable linear dimensionality reduction techniques in terms of accuracy, while only requiring a few minutes on a standard desktop computer.

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Artifacts in Simultaneous hdEEG/fMRI Imaging: A Nonlinear Dimensionality Reduction Approach

Sensors ◽

10.3390/s19204454 ◽

2019 ◽

Vol 19 (20) ◽

pp. 4454 ◽

Cited By ~ 2

Author(s):

Marek Piorecky ◽

Vlastimil Koudelka ◽

Jan Strobl ◽

Martin Brunovsky ◽

Vladimir Krajca

Keyword(s):

Data Structure ◽

Spatial Clustering ◽

Dimensional Space ◽

Head Movements ◽

Nonlinear Dimensionality Reduction ◽

Space Resolution ◽

Additional Information ◽

Nonlinear Dimension ◽

The Time Domain ◽

Low Dimensional

Simultaneous recordings of electroencephalogram (EEG) and functional magnetic resonance imaging (fMRI) are at the forefront of technologies of interest to physicians and scientists because they combine the benefits of both modalities—better time resolution (hdEEG) and space resolution (fMRI). However, EEG measurements in the scanner contain an electromagnetic field that is induced in leads as a result of gradient switching slight head movements and vibrations, and it is corrupted by changes in the measured potential because of the Hall phenomenon. The aim of this study is to design and test a methodology for inspecting hidden EEG structures with respect to artifacts. We propose a top-down strategy to obtain additional information that is not visible in a single recording. The time-domain independent component analysis algorithm was employed to obtain independent components and spatial weights. A nonlinear dimension reduction technique t-distributed stochastic neighbor embedding was used to create low-dimensional space, which was then partitioned using the density-based spatial clustering of applications with noise (DBSCAN). The relationships between the found data structure and the used criteria were investigated. As a result, we were able to extract information from the data structure regarding electrooculographic, electrocardiographic, electromyographic and gradient artifacts. This new methodology could facilitate the identification of artifacts and their residues from simultaneous EEG in fMRI.

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