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.

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.

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.

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 IWKNN: An Effective Bluetooth Positioning Method Based on Isomap and WKNN

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Qi Wang ◽  
Yingying Feng ◽  
Xiangde Zhang ◽  
Yanrui Sun ◽  
Xiaojun Lu
Keyword(s):  
Euclidean Distance ◽  
Nearest Neighbor ◽  
Research Topic ◽  
Dimensional Manifold ◽  
Received Signal Strength Indicator ◽  
Localization Accuracy ◽  
Positioning Method ◽  
Low Dimensional ◽  
Low Dimensional Manifold ◽  
Huge Challenge

Recently, Bluetooth-based indoor positioning has become a hot research topic. However, the instability of Bluetooth RSSI (Received Signal Strength Indicator) promotes a huge challenge in localization accuracy. To improve the localization accuracy, this paper measures the distance of RSSI vectors on their low-dimensional manifold and proposes a novel positioning method IWKNN (Isomap-based Weighted K-Nearest Neighbor). The proposed method firstly uses Isomap to generate low-dimensional embedding for RSSI vectors. Then, the distance of two given RSSI vectors is measured by Euclidean distance of their low-dimensional embeddings. Finally, the position is calculated by WKNN. Experiment indicates that the proposed approach is more robust and accurate.

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

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.

MANIFOLD LEARNING FOR ROBOT NAVIGATION

2006 ◽  
Vol 16 (05) ◽  
pp. 383-392 ◽  
Author(s):  
NARONGDECH KEERATIPRANON ◽  
FREDERIC MAIRE ◽  
HENRY HUANG
Keyword(s):  
Dimensionality Reduction ◽  
Manifold Learning ◽  
Robot Navigation ◽  
Internal Representation ◽  
Polygonal Line ◽  
Range Data ◽  
Navigation Systems ◽  
Learning Techniques ◽  
Linear Dimensionality Reduction ◽  
Low Dimensional

In this paper we introduce methods to build a SOM that can be used as an isometric map for mobile robots. That is, given a dataset of sensor readings collected at points uniformly distributed with respect to the ground, we wish to build a SOM whose neurons (prototype vectors in sensor space) correspond to points uniformly distributed on the ground. Manifold learning techniques have already been used for dimensionality reduction of sensor space in navigation systems. Our focus is on the isometric property of the SOM. For reliable path-planning and information sharing between several robots, it is desirable that the robots build an internal representation of the sensor manifold, a map, that is isometric with the environment. We show experimentally that standard Non-Linear Dimensionality Reduction (NLDR) algorithms do not provide isometric maps for range data and bearing data. However, the auxiliary low dimensional manifolds created can be used to improve the distribution of the neurons of a SOM (that is, make the neurons more evenly distributed with respect to the ground). We also describe a method to create an isometric map from a sensor readings collected along a polygonal line random walk.

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.

Novel Convolutional Restricted Boltzmann Machine manifold learning inspired dynamic user clustering hybrid precoding for millimeter-wave massive multiple-input multiple-output systems

2021 ◽  
Vol 17 (11) ◽  
pp. 155014772110553
Author(s):  
Xiaoping Zhou ◽  
Haichao Liu ◽  
Bin Wang ◽  
Qian Zhang ◽  
Yang Wang
Keyword(s):  
Millimeter Wave ◽  
Manifold Learning ◽  
Multiple Input Multiple Output ◽  
Restricted Boltzmann Machine ◽  
Boltzmann Machine ◽  
Hybrid Precoding ◽  
User Clustering ◽  
Multiple Input ◽  
Input Multiple Output ◽  
Low Dimensional

Millimeter-wave massive multiple-input multiple-output is a key technology in 5G communication system. In particular, the hybrid precoding method has the advantages of being power efficient and less expensive than the full-digital precoding method, so it has attracted more and more attention. The effectiveness of this method in simple systems has been well verified, but its performance is still unknown due to many problems in real communication such as interference from other users and base stations, and users are constantly on the move. In this article, we propose a dynamic user clustering hybrid precoding method in the high-dimensional millimeter-wave multiple-input multiple-output system, which uses low-dimensional manifolds to avoid complicated calculations when there are many antennas. We model each user set as a novel Convolutional Restricted Boltzmann Machine manifold, and the problem is transformed into cluster-oriented multi-manifold learning. The novel Convolutional Restricted Boltzmann Machine manifold learning seeks to learn embedded low-dimensional manifolds through manifold learning in the face of user mobility in clusters. Through proper user clustering, the hybrid precoding is investigated for the sum-rate maximization problem by manifold quasi-conjugate gradient methods. This algorithm avoids the traditional method of processing high-dimensional channel parameters, achieves a high signal-to-noise ratio, and reduces computational complexity. The simulation result table shows that this method can get almost the best summation rate and higher spectral efficiency compared with the traditional method.

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