scholarly journals Classification of Infrared Objects in Manifold Space Using Kullback-Leibler Divergence of Gaussian Distributions of Image Points

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 434 ◽  
Author(s):  
Huilin Ge ◽  
Zhiyu Zhu ◽  
Kang Lou ◽  
Wei Wei ◽  
Runbang Liu ◽  
...  
Keyword(s):  
Manifold Learning ◽  
Gaussian Distribution ◽  
Classification Accuracy ◽  
Infrared Image ◽  
Data Sets ◽  
Dimensional Manifold ◽  
Infrared Images ◽  
Leibler Divergence ◽  
Data Points ◽  
Low Dimensional

Infrared image recognition technology can work day and night and has a long detection distance. However, the infrared objects have less prior information and external factors in the real-world environment easily interfere with them. Therefore, infrared object classification is a very challenging research area. Manifold learning can be used to improve the classification accuracy of infrared images in the manifold space. In this article, we propose a novel manifold learning algorithm for infrared object detection and classification. First, a manifold space is constructed with each pixel of the infrared object image as a dimension. Infrared images are represented as data points in this constructed manifold space. Next, we simulate the probability distribution information of infrared data points with the Gaussian distribution in the manifold space. Then, based on the Gaussian distribution information in the manifold space, the distribution characteristics of the data points of the infrared image in the low-dimensional space are derived. The proposed algorithm uses the Kullback-Leibler (KL) divergence to minimize the loss function between two symmetrical distributions, and finally completes the classification in the low-dimensional manifold space. The efficiency of the algorithm is validated on two public infrared image data sets. The experiments show that the proposed method has a 97.46% classification accuracy and competitive speed in regards to the analyzed data sets.

scholarly journals Enhancing Both Efficiency and Representational Capability of Isomap by Extensive Landmark Selection

2015 ◽  
Vol 2015 ◽  
pp. 1-18 ◽  
Author(s):  
Dong Liang ◽  
Chen Qiao ◽  
Zongben Xu
Keyword(s):  
Manifold Learning ◽  
Computational Efficiency ◽  
New Method ◽  
Data Sets ◽  
Learning Approaches ◽  
Real World Data ◽  
Efficiency Property ◽  
Data Points ◽  
Low Dimensional ◽  
High Computational Efficiency

The problems of improving computational efficiency and extending representational capability are the two hottest topics in approaches of global manifold learning. In this paper, a new method called extensive landmark Isomap (EL-Isomap) is presented, addressing both topics simultaneously. On one hand, originated from landmark Isomap (L-Isomap), which is known for its high computational efficiency property, EL-Isomap also possesses high computational efficiency through utilizing a small set of landmarks to embed all data points. On the other hand, EL-Isomap significantly extends the representational capability of L-Isomap and other global manifold learning approaches by utilizing only an available subset from the whole landmark set instead of all to embed each point. Particularly, compared with other manifold learning approaches, the data manifolds with intrinsic low-dimensional concave topologies and essential loops can be unwrapped by the new method more successfully, which are shown by simulation results on a series of synthetic and real-world data sets. Moreover, the accuracy, robustness, and computational complexity of EL-Isomap are analyzed in this paper, and the relation between EL-Isomap and L-Isomap is also discussed theoretically.

scholarly journals Multiscale Superpixelwise Locality Preserving Projection for Hyperspectral Image Classification

2019 ◽  
Vol 9 (10) ◽  
pp. 2161
Author(s):  
Lin He ◽  
Xianjun Chen ◽  
Jun Li ◽  
Xiaofeng Xie
Keyword(s):  
Manifold Learning ◽  
Hyperspectral Image ◽  
Decision Fusion ◽  
Hyperspectral Data ◽  
Data Sets ◽  
Dimensional Manifold ◽  
Locality Preserving Projection ◽  
Locality Preserving ◽  
Low Dimensional ◽  
Low Dimensional Manifold

Manifold learning is a powerful dimensionality reduction tool for a hyperspectral image (HSI) classification to relieve the curse of dimensionality and to reveal the intrinsic low-dimensional manifold. However, a specific characteristic of HSIs, i.e., irregular spatial dependency, is not taken into consideration in the method design, which can yield many spatially homogenous subregions in an HSI scence. Conventional manifold learning methods, such as a locality preserving projection (LPP), pursue a unified projection on the entire HSI, while neglecting the local homogeneities on the HSI manifold caused by those spatially homogenous subregions. In this work, we propose a novel multiscale superpixelwise LPP (MSuperLPP) for HSI classification to overcome the challenge. First, we partition an HSI into homogeneous subregions with a multiscale superpixel segmentation. Then, on each scale, subregion specific LPPs and the associated preliminary classifications are performed. Finally, we aggregate the classification results from all scales using a decision fusion strategy to achieve the final result. Experimental results on three real hyperspectral data sets validate the effectiveness of our method.

An Incremental Isomap Method for Hyperspectral Dimensionality Reduction and Classification

2021 ◽  
Vol 87 (6) ◽  
pp. 445-455
Author(s):  
Yi Ma ◽  
Zezhong Zheng ◽  
Yutang Ma ◽  
Mingcang Zhu ◽  
Ran Huang ◽  
...  
Keyword(s):  
Manifold Learning ◽  
Nearest Neighbor ◽  
Hyperspectral Image ◽  
Hyperspectral Data ◽  
Training Data ◽  
Support Vector ◽  
Data Sets ◽  
K Nearest Neighbor ◽  
Data Set ◽  
Data Points

Many manifold learning algorithms conduct an eigen vector analysis on a data-similarity matrix with a size of N×N, where N is the number of data points. Thus, the memory complexity of the analysis is no less than O(N2). We pres- ent in this article an incremental manifold learning approach to handle large hyperspectral data sets for land use identification. In our method, the number of dimensions for the high-dimensional hyperspectral-image data set is obtained with the training data set. A local curvature varia- tion algorithm is utilized to sample a subset of data points as landmarks. Then a manifold skeleton is identified based on the landmarks. Our method is validated on three AVIRIS hyperspectral data sets, outperforming the comparison algorithms with a k–nearest-neighbor classifier and achieving the second best performance with support vector machine.

Learning Manifolds

2012 ◽  
pp. 374-402
Author(s):  
Diana Mateus ◽  
Christian Wachinger ◽  
Selen Atasoy ◽  
Loren Schwarz ◽  
Nassir Navab
Keyword(s):  
Manifold Learning ◽  
Domain Knowledge ◽  
Dimensional Space ◽  
Human Motion ◽  
Motion Modeling ◽  
Learning Methods ◽  
Data Representations ◽  
Non Linear ◽  
Data Points ◽  
Low Dimensional

Computer aided diagnosis is often confronted with processing and analyzing high dimensional data. One alternative to deal with such data is dimensionality reduction. This chapter focuses on manifold learning methods to create low dimensional data representations adapted to a given application. From pairwise non-linear relations between neighboring data-points, manifold learning algorithms first approximate the low dimensional manifold where data lives with a graph; then, they find a non-linear map to embed this graph into a low dimensional space. Since the explicit pairwise relations and the neighborhood system can be designed according to the application, manifold learning methods are very flexible and allow easy incorporation of domain knowledge. The authors describe different assumptions and design elements that are crucial to building successful low dimensional data representations with manifold learning for a variety of applications. In particular, they discuss examples for visualization, clustering, classification, registration, and human-motion modeling.

Study of Fault Diagnosis Based on Manifold Learning

2013 ◽  
Vol 312 ◽  
pp. 650-654 ◽  
Author(s):  
Yi Lin He ◽  
Guang Bin Wang ◽  
Fu Ze Xu
Keyword(s):  
Fault Diagnosis ◽  
Manifold Learning ◽  
Linear Manifold ◽  
Rotating Machinery ◽  
Dimensional Manifold ◽  
Advantages And Disadvantages ◽  
Non Linear ◽  
Future Direction ◽  
Low Dimensional ◽  
Machinery Fault Diagnosis

Characteristic signals in rotating machinery fault diagnosis with the issues of complex and difficult to deal with, while the use of non-linear manifold learning method can effectively extract low-dimensional manifold characteristics embedded in the high-dimensional non-linear data. It greatly maintains the overall geometric structure of the signals and improves the efficiency and reliability of the rotating machinery fault diagnosis. According to the development prospects of manifold learning, this paper describes four classical manifold learning methods and each advantages and disadvantages. It reviews the research status and application of fault diagnosis based on manifold learning, as well as future direction of researches in the field of manifold learning fault diagnosis.

scholarly journals Manifold Learning of Dynamic Functional Connectivity Reliably Identifies Functionally Consistent Coupling Patterns in Human Brains

2019 ◽  
Vol 9 (11) ◽  
pp. 309
Author(s):  
Yuyuan Yang ◽  
Lubin Wang ◽  
Yu Lei ◽  
Yuyang Zhu ◽  
Hui Shen
Keyword(s):  
Functional Connectivity ◽  
Sleep Deprivation ◽  
Manifold Learning ◽  
Temporal Dynamics ◽  
Functional Coupling ◽  
Dimensional Manifold ◽  
Dynamic Functional Connectivity ◽  
Local Linear Embedding ◽  
Human Connectome Project ◽  
Low Dimensional

Most previous work on dynamic functional connectivity (dFC) has focused on analyzing temporal traits of functional connectivity (similar coupling patterns at different timepoints), dividing them into functional connectivity states and detecting their between-group differences. However, the coherent functional connectivity of brain activity among the temporal dynamics of functional connectivity remains unknown. In the study, we applied manifold learning of local linear embedding to explore the consistent coupling patterns (CCPs) that reflect functionally homogeneous regions underlying dFC throughout the entire scanning period. By embedding the whole-brain functional connectivity in a low-dimensional manifold space based on the Human Connectome Project (HCP) resting-state data, we identified ten stable patterns of functional coupling across regions that underpin the temporal evolution of dFC. Moreover, some of these CCPs exhibited significant neurophysiological meaning. Furthermore, we apply this method to HCP rsfMR and tfMRI data as well as sleep-deprivation data and found that the topological organization of these low-dimensional structures has high potential for predicting sleep-deprivation states (classification accuracy of 92.3%) and task types (100% identification for all seven tasks).In summary, this work provides a methodology for distilling coherent low-dimensional functional connectivity structures in complex brain dynamics that play an important role in performing tasks or characterizing specific states of the brain.

scholarly journals Unsupervised Metric Learning Using Low Dimensional Embedding

2018 ◽  
Author(s):  
Parag Jain
Keyword(s):  
Manifold Learning ◽  
Euclidean Distance ◽  
Metric Learning ◽  
Special Property ◽  
Dimensional Manifold ◽  
Laplacian Eigenmaps ◽  
Learning Techniques ◽  
Out Of Sample ◽  
Low Dimensional ◽  
Project Data

Unsupervised metric learning has been generally studied as a byproduct of dimensionality reduction or manifold learning techniques. Manifold learning techniques like Diusion maps, Laplacian eigenmaps has a special property that embedded space is Euclidean. Although laplacian eigenmaps can provide us with some (dis)similarity information it does not provide with a metric which can further be used on out-of-sample data. On other hand supervised metric learning technique like ITML which can learn a metric needs labeled data for learning. In this work propose methods for incremental unsupervised metric learning. In rst approach Laplacian eigenmaps is used along with Information Theoretic Metric Learning(ITML) to form an unsupervised metric learning method. We rst project data into a low dimensional manifold using Laplacian eigenmaps, in embedded space we use euclidean distance to get an idea of similarity between points. If euclidean distance between points in embedded space is below a threshold t1 value we consider them as similar points and if it is greater than a certain threshold t2 we consider them as dissimilar points. Using this we collect a batch of similar and dissimilar points which are then used as a constraints for ITML algorithm and learn a metric. To prove this concept we have tested our approach on various UCI machine learning datasets. In second approach we propose Incremental Diusion Maps by updating SVD in a batch-wise manner.

LTSA Algorithm for Dimension Reduction of Microarray Data

2013 ◽  
Vol 645 ◽  
pp. 192-195 ◽  
Author(s):  
Xiao Zhou Chen
Keyword(s):  
Dimensionality Reduction ◽  
Dimension Reduction ◽  
Manifold Learning ◽  
Microarray Data ◽  
Learning Algorithm ◽  
Medical Applications ◽  
Data Sets ◽  
Learning Method ◽  
Data Dimensionality Reduction ◽  
Low Dimensional

Dimension reduction is an important issue to understand microarray data. In this study, we proposed a efficient approach for dimensionality reduction of microarray data. Our method allows to apply the manifold learning algorithm to analyses dimensionality reduction of microarray data. The intra-/inter-category distances were used as the criteria to quantitatively evaluate the effects of data dimensionality reduction. Colon cancer and leukaemia gene expression datasets are selected for our investigation. When the neighborhood parameter was effectivly set, all the intrinsic dimension numbers of data sets were low. Therefore, manifold learning is used to study microarray data in the low-dimensional projection space. Our results indicate that Manifold learning method possesses better effects than the linear methods in analysis of microarray data, which is suitable for clinical diagnosis and other medical applications.

AN ALGORITHMIC COMPUTATION OF CORRELATION DIMENSION FROM TIME SERIES

2007 ◽  
Vol 21 (02n03) ◽  
pp. 129-138 ◽  
Author(s):  
K. P. HARIKRISHNAN ◽  
G. AMBIKA ◽  
R. MISRA
Keyword(s):  
Time Series ◽  
Hypothesis Testing ◽  
Correlation Dimension ◽  
Visual Inspection ◽  
Chaotic Systems ◽  
Synthetic Data ◽  
Data Sets ◽  
Data Points ◽  
Scaling Region ◽  
Low Dimensional

We present an algorithmic scheme to compute the correlation dimension D2 of a time series, without requiring the visual inspection of the scaling region in the correlation sum. It is based on the standard Grassberger–Proccacia [GP] algorithm for computing D2. The scheme is tested using synthetic data sets from several standard chaotic systems as well as by adding noise to low-dimensional chaotic data. We show that the scheme is efficient with a few thousand data points and is most suitable when a nonsubjective comparison of D2 values of two time series is required, such as, in hypothesis testing.

An improved Isomap method for manifold learning

2017 ◽  
Vol 10 (1) ◽  
pp. 30-40 ◽  
Author(s):  
Taiguo Qu ◽  
Zixing Cai
Keyword(s):  
Manifold Learning ◽  
High Speed ◽  
Shortest Paths ◽  
Computation Time ◽  
Data Sets ◽  
Content Type ◽  
Data Points ◽  
S Curve ◽  
Neighbourhood Graph ◽  
Isometric Feature Mapping

Purpose Isometric feature mapping (Isomap) is a very popular manifold learning method and is widely used in dimensionality reduction and data visualization. The most time-consuming step in Isomap is to compute the shortest paths between all pairs of data points based on a neighbourhood graph. The classical Isomap (C-Isomap) is very slow, due to the use of Floyd’s algorithm to compute the shortest paths. The purpose of this paper is to speed up Isomap. Design/methodology/approach Through theoretical analysis, it is found that the neighbourhood graph in Isomap is sparse. In this case, the Dijkstra’s algorithm with Fibonacci heap (Fib-Dij) is faster than Floyd’s algorithm. In this paper, an improved Isomap method based on Fib-Dij is proposed. By using Fib-Dij to replace Floyd’s algorithm, an improved Isomap method is presented in this paper. Findings Using the S-curve, the Swiss-roll, the Frey face database, the mixed national institute of standards and technology database of handwritten digits and a face image database, the performance of the proposed method is compared with C-Isomap, showing the consistency with C-Isomap and marked improvements in terms of the high speed. Simulations also demonstrate that Fib-Dij reduces the computation time of the shortest paths from O(N3) to O(N2lgN). Research limitations/implications Due to the limitations of the computer, the sizes of the data sets in this paper are all smaller than 3,000. Therefore, researchers are encouraged to test the proposed algorithm on larger data sets. Originality/value The new method based on Fib-Dij can greatly improve the speed of Isomap.

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