Manifold Learning Algorithm Research Articles

A new method of selecting safe neighbors for the Riemannian Manifold Learning algorithm

Manifold learning (ML) comprehends a set of nonlinear techniques for mining and representing high-dimensional data. In this work, we approach the well-known and successful ML technique called Riemannian Manifold Learning (RML). Firstly, we present a geometric interpretation of the main steps of selecting visible and safe neighborhoods to reconstruct geometry and topology in the original RML algorithm. Then, we describe and implement a new method of selecting safe neighbors for this algorithm. Our experimental results on synthetic and real data sets, using open source tools and a public face image database, have showed that the new method proposed shows similar results to the original one and reconstructions that favour local rather than holistic similarities described by the data. Additionally, since the new method proposed requires the specification of only one input parameter, its implementation is simpler and more intuitive than the original one.

Watercore Identification of Xinjiang Fuji Apple Based on Manifold Learning Algorithm and Near Infrared Transmission Spectroscopy

Watercore Identification of Xinjiang Fuji Apple Based on Manifold Learning Algorithm and Near Infrared Transmission Spectroscopy

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

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.

Construction of embedded fMRI resting-state functional connectivity networks using manifold learning

We construct embedded functional connectivity networks (FCN) from benchmark resting-state functional magnetic resonance imaging (rsfMRI) data acquired from patients with schizophrenia and healthy controls based on linear and nonlinear manifold learning algorithms, namely, Multidimensional Scaling, Isometric Feature Mapping, Diffusion Maps, Locally Linear Embedding and kernel PCA. Furthermore, based on key global graph-theoretic properties of the embedded FCN, we compare their classification potential using machine learning. We also assess the performance of two metrics that are widely used for the construction of FCN from fMRI, namely the Euclidean distance and the cross correlation metric. We show that diffusion maps with the cross correlation metric outperform the other combinations.

Manifold Learning Based on Straight-Like Geodesics and Local Coordinates.

In this article, a manifold learning algorithm based on straight-like geodesics and local coordinates is proposed, called SGLC-ML for short. The contribution and innovation of SGLC-ML lie in that; first, SGLC-ML divides the manifold data into a number of straight-like geodesics, instead of a number of local areas like many manifold learning algorithms do. Figuratively speaking, SGLC-ML covers manifold data set with a sparse net woven with threads (straight-like geodesics), while other manifold learning algorithms with a tight roof made of titles (local areas). Second, SGLC-ML maps all straight-like geodesics into straight lines of a low-dimensional Euclidean space. All these straight lines start from the same point and extend along the same coordinate axis. These straight lines are exactly the local coordinates of straight-like geodesics as described in the mathematical definition of the manifold. With the help of local coordinates, dimensionality reduction can be divided into two relatively simple processes: calculation and alignment of local coordinates. However, many manifold learning algorithms seem to ignore the advantages of local coordinates. The experimental results between SGLC-ML and other state-of-the-art algorithms are presented to verify the good performance of SGLC-ML.

Machining process monitoring with vibration signal based manifold learning

Machining process monitoring based on vibration sensing is a growing demand in smart manufacturing. However, in real factories, massive process conditions which include thousands of shapes of workpieces and thousands of combinations of cutting parameters, such as spindle speed, feed rate and cutting depth, are designed and used in manufacturing. Manifold learning is able to extract essential and distinct features from the vibration signal and helps to monitor and recognize different process conditions. In this paper, the dataset, including slight and huge variation of cutting parameters and workpiece shapes, are collected for analysis. Different manifold learning algorithms are utilized and compared to mine the essential features and reduce the interference of non-sensitive features. The generalization ability of different manifold learning algorithms are discussed to fit the various process conditions. Convolutional neural networks are employed to evaluate the monitoring accuracy. The experimental results show that the features obtained by the manifold learning distinguish vibration signals of different cutting parameters in low dimensional space and give a protentional way to construct effective monitoring systems. The generalization ability to different workpieces and cutting parameters and its limitation are discussed.

TSBP: Tangent Space Belief Propagation for Manifold Learning

We present Tangent Space Belief Propagation (TSBP) as a method for graph denoising to improve the robustness of manifold learning algorithms. Dimension reduction by manifold learning relies heavily on the accurate selection of nearest neighbors, which has proven an open problem for sparse and noisy datasets. TSBP uses global nonparametric belief propagation to accurately estimate the tangent spaces of the underlying manifold at each data point. Edges of the neighborhood graph that deviate from the tangent spaces are then removed. The resulting denoised graph can then be embedded into a lower-dimensional space using methods from existing manifold learning algorithms. Artificially generated manifold data, simulated sensor data from a mobile robot, and high dimensional tactile sensory data are used to demonstrate the efficacy of our TSBP method.

Manifold Learning With Localized Procrustes Analysis Based WSN Localization

In this letter, we propose a novel system for localization of a wireless sensor network using the localized Procrustes analysis with manifold learning. Due to different environmental factors, such as noise and fading, the internode distances calculated by the received signal strength indicator are erroneous and may not satisfy the L2 norm. The nodes seemingly lie on an unknown high-dimensional manifold that satisfies the Riemannian manifold assumption. Thus, the problem of localization is transformed into the problem of nonlinear dimensionality reduction. The location of the nodes can be learned through a manifold learning algorithm like Isomap. However, the coordinates so obtained needed to be transformed to obtain the correct locations of the nodes. We use the localized Procrustes analysis in order to align the relative locations to the absolute or global locations. The localized Procrustes analysis considers each sensor node's neighborhood and computes distinct parameters for each sensor based on the transformation parameters of the anchors present in its neighborhood. Experiment results show that our proposed system outperformed existing localization schemes and can localize the nodes with a better accuracy up to 31.27% in contrast to the least square optimization method.

Manifold graph embedding with structure information propagation for community discovery

Community discovery is an important topic of network representation learning. Manifold learning has been widely applied to network representation learning. However, most manifold learning algorithms do not consider the asymmetry of edges which is not accord with the structure of social networks because the influence of nodes is not symmetrical. In this paper, a community discovery algorithm based on manifold graph embedding with structure information propagation mechanism is proposed. The proposed algorithm uses high order approximation matrix to obtain the local and global structure information of a graph, then low rank decomposition is introduced to obtain the node vectors and the context vectors. Finally, the node vectors can be adjusted by structure information. The proposed algorithm and comparison algorithms are conducted on the experimental data sets. The experimental results show that the proposed algorithm outperforms the comparison algorithms on the most experimental data sets. The experimental results prove that the proposed algorithm is an effective algorithm for community discovery.

Global Manifold Learning for Interactive Image Segmentation

This paper presents an interactive image segmen-tation algorithm, in which the segmentation problem is formulated as a global manifold learning process. Based on the principle that the label of each element depends on the influence of all the elements in the image, we extend the conventional local neighborhood or the long range regional relationships to the global relationships over the whole image. A probabilistic framework is established to measure the global effect of each element on all other elements. Based on two different manifold learning styles, the semi-global manifold learning (SGML) and the fully-global manifold learning (FGML) algorithms are proposed to capture the global geometry structure of the data manifold. SGML learns the intrinsic effects of each element separately, equivalent to a matrix diffusion process on an affinity graph. FGML learns the intrinsic effects of all elements together, equivalent to a label pair diffusion process on a higher-order tensor product graph. The global manifold learning helps to overcome the low contrast, weak boundary and texture problems. Extensive experiments on three public interactive segmentation datasets demonstrate the superior performance of the proposed algorithms both in accuracy and efficiency.

Application of locally linear embedding algorithm on hotel data text classification

As a non-linear dimension reduction method, manifold learning algorithm projects high-dimensional input to a low-dimensional space by maintaining the local structure of the data, and discovers the inherent geometric structure hidden in the data. In this paper, we attempt to apply the manifold learning algorithm to the field of Chinese text classification, and use the locally linear embedding algorithm to reduce the dimension of the ctrip hotel review data set. Then, we utilize extreme gradient boosting (XGBoost) and logistic regression to classify the text. Experimental results show that it is effective and feasible to use manifold learning algorithm for text classification. Moreover, the classification effect of logistic regression is better than XGBoost in the text classification of hotel reviews.

A Novel THz Differential Spectral Clustering Recognition Method Based on t-SNE

We apply time-domain spectroscopy (THz) imaging technology to perform nondestructive detection on three industrial ceramic matrix composite (CMC) samples and one silicon slice with defects. In terms of spectrum recognition, a low-resolution THz spectrum image results in an ineffective recognition on sample defect features. Therefore, in this article, we propose a spectrum clustering recognition model based on t-distribution stochastic neighborhood embedding (t-SNE) to address this ineffective sample defect recognition. Firstly, we propose a model to recognize a reduced dimensional clustering of different spectrums drawn from the imaging spectrum data sets, in order to judge whether a sample includes a feature indicating a defect or not in a low-dimensional space. Second, we improve computation efficiency by mapping spectrum data samples from high-dimensional space to low-dimensional space by the use of a manifold learning algorithm (t-SNE). Finally, to achieve a visible observation of sample features in low-dimensional space, we use a conditional probability distribution to measure the distance invariant similarity. Comparative experiments indicate that our model can judge the existence of sample defect features or not through spectrum clustering, as a predetection process for image analysis.

Nonlinear Feature Extraction Through Manifold Learning in an Electronic Tongue Classification Task.

A nonlinear feature extraction-based approach using manifold learning algorithms is developed in order to improve the classification accuracy in an electronic tongue sensor array. The developed signal processing methodology is composed of four stages: data unfolding, scaling, feature extraction, and classification. This study aims to compare seven manifold learning algorithms: Isomap, Laplacian Eigenmaps, Locally Linear Embedding (LLE), modified LLE, Hessian LLE, Local Tangent Space Alignment (LTSA), and t-Distributed Stochastic Neighbor Embedding (t-SNE) to find the best classification accuracy in a multifrequency large-amplitude pulse voltammetry electronic tongue. A sensitivity study of the parameters of each manifold learning algorithm is also included. A data set of seven different aqueous matrices is used to validate the proposed data processing methodology. A leave-one-out cross validation was employed in 63 samples. The best accuracy () was obtained when the methodology uses Mean-Centered Group Scaling (MCGS) for data normalization, the t-SNE algorithm for feature extraction, and k-nearest neighbors (kNN) as classifier.

Semi-supervised optimization algorithm basedon Laplacian Eigenmaps

As a member of many dimensionalityreduction algorithms, manifold learning is the hotspot ofrecent dimensionality reduction algorithm. Despite it isgood at retaining the original space structure, there is nodenying that its effect of classifying still has room forimprovement. Based on Laplacian Eigenmap, which is oneof the manifold learning algorithm, this paper committed tooptimize the algorithm combined with a semi-supervisedlearning ideas, which can improve the recognition rate.Finally, the better method of two forms is tested in thesurface electromyography system and plant leafidentification system. The experimental results show thatthis semi-supervised method does well in classifying.

Development and validation of a 1-year survival prognosis estimation model for Amyotrophic Lateral Sclerosis using manifold learning algorithm UMAP

Amyotrophic Lateral Sclerosis (ALS) is an inexorably progressive neurodegenerative condition with no effective disease modifying therapies. The development and validation of reliable prognostic models is a recognised research priority. We present a prognostic model for survival in ALS where result uncertainty is taken into account. Patient data were reduced and projected onto a 2D space using Uniform Manifold Approximation and Projection (UMAP), a novel non-linear dimension reduction technique. Information from 5,220 patients was included as development data originating from past clinical trials, and real-world population data as validation data. Predictors included age, gender, region of onset, symptom duration, weight at baseline, functional impairment, and estimated rate of functional loss. UMAP projection of patients shows an informative 2D data distribution. As limited data availability precluded complex model designs, the projection was divided into three zones with relevant survival rates. These rates were defined using confidence bounds: high, intermediate, and low 1-year survival rates at respectively 90% (pm 4%), 80% (pm 4%) and 58% (pm 4%). Predicted 1-year survival was estimated using zone membership. This approach requires a limited set of features, is easily updated, improves with additional patient data, and accounts for results uncertainty.

Mass Laplacian Discriminant Analysis and Its Application in Gear Fault Diagnosis

Fault diagnosis is essentially the identification of multiple fault modes. How to extract sensitive features and improve diagnostic accuracy is the key to fault diagnosis. In this paper, a new manifold learning method (Mass Laplacian Discriminant Analysis, MLDA) is proposed. Firstly, it is assumed that each data point in the space is a point with mass, and the mass is defined as the number of data points in a certain area. Then, the idea of universal gravitation is introduced to calculate the virtual universal gravitation between data points. Based on the Laplace eigenmaps algorithm, the gravitational Laplacian matrix between the same kind of data and the heterogeneous data is obtained, and the discriminant function is constructed by the ratio of the virtual gravitation between the heterogeneous data and the virtual gravitation between the similar data; the projection function with the largest discriminant function value is the optimal feature mapping function. Finally, based on the mapping function, the eigenvalues of the training data and the test data are calculated, and the softmax algorithm is used to classify the test data. Experiments on gear fault diagnosis show that this method has higher diagnostic accuracy than other manifold learning algorithms.

A Geometric Clustering Tool (AGCT) to robustly unravel the inner cluster structures of time-series gene expressions.

Systems biology aims at holistically understanding the complexity of biological systems. In particular, nowadays with the broad availability of gene expression measurements, systems biology challenges the deciphering of the genetic cell machinery from them. In order to help researchers, reverse engineer the genetic cell machinery from these noisy datasets, interactive exploratory clustering methods, pipelines and gene clustering tools have to be specifically developed. Prior methods/tools for time series data, however, do not have the following four major ingredients in analytic and methodological view point: (i) principled time-series feature extraction methods, (ii) variety of manifold learning methods for capturing high-level view of the dataset, (iii) high-end automatic structure extraction, and (iv) friendliness to the biological user community. With a view to meet the requirements, we present AGCT (A Geometric Clustering Tool), a software package used to unravel the complex architecture of large-scale, non-necessarily synchronized time-series gene expression data. AGCT capture signals on exhaustive wavelet expansions of the data, which are then embedded on a low-dimensional non-linear map using manifold learning algorithms, where geometric proximity captures potential interactions. Post-processing techniques, including hard and soft information geometric clustering algorithms, facilitate the summarizing of the complete map as a smaller number of principal factors which can then be formally identified using embedded statistical inference techniques. Three-dimension interactive visualization and scenario recording over the processing helps to reproduce data analysis results without additional time. Analysis of the whole-cell Yeast Metabolic Cycle (YMC) moreover, Yeast Cell Cycle (YCC) datasets demonstrate AGCT's ability to accurately dissect all stages of metabolism and the cell cycle progression, independently of the time course and the number of patterns related to the signal. Analysis of Pentachlorophenol iduced dataset demonstrat how AGCT dissects data to identify two networks: Interferon signaling and NRF2-signaling networks.

Boring chatter identification by multi-sensor feature fusion and manifold learning

In the boring process, chatter is easy to occur because of the large overhang of the boring bar and the poor structural stiffness of the system. The key technique to reduce the chatter effect in boring process is to identify the chatter state accurately. In this paper, a method of chatter identification based on multi-sensor feature fusion and manifold learning is proposed. Displacement sensor, acceleration sensor, and acoustic pressure sensor are used to acquire processing signals synchronously, and then triple signals are decomposed by empirical mode decomposition (EMD). The multi-indicators are used to construct high-dimensional space, and then different manifold learning algorithms are used to reduce feature dimensionality. Support vector machine chatter identification models are obtained to verify the effect of boring chatter identification. Multi-sensor feature fusion realizes the complementary of different features and achieves better recognition results. The results show that the proposed method can identify boring chatter effectively. And the best result is obtained by the combination of the displacement sensor and acceleration sensor.

Classification of EEG Signals for Epileptic Seizures Using Feature Dimension Reduction Algorithm based on LPP

Computer-aided diagnosis of epilepsy based on Electroencephalography (EEG) analysis is a beneficial practice which adopts machine learning to increase the recognition rate and saves physicians from long hours of EEG inspection. However multi-channel epilepsy EEG signals reflect significant nonlinearity with different degrees of cross-talk among channels, which further leads to high dimensional features extracted from EEG. These shortcomings make the performance of epilepsy detection with machine learning difficult to improve. In order to get fast and accurate detection performance, a feature dimension reduction algorithm based on epilepsy locality preserving projections (E-LPP) is proposed. E-LPP, by preserving the low-dimensional manifold as much as possible, enables to analyze signals of non-linear, non-stationary and high-dimensional nature. To get the best performance, we determine the hyperparameters of E-LPP by grid search. Subsequently a fusion epilepsy detection framework combined feature extraction with E-LPP is proposed to classify whether subjects’ seizure onset or not. We test our method on two well-known and widely studied datasets which includes ictal and interictal EEG recordings. The experimental result on recall, precision and F1 is superior to the common traditional dimensionality reduction algorithm, manifold learning algorithm and autoencoder based deep learning, which indicates this proposed method not only makes it possible to solve nonlinearity and cross-talk among channels in EEG, but also tackles the inherent difficulties regarding unbalanced epilepsy data with high metrics.

Sequencing seismograms: A panoptic view of scattering in the core-mantle boundary region.

Scattering of seismic waves can reveal subsurface structures but usually in a piecemeal way focused on specific target areas. We used a manifold learning algorithm called "the Sequencer" to simultaneously analyze thousands of seismograms of waves diffracting along the core-mantle boundary and obtain a panoptic view of scattering across the Pacific region. In nearly half of the diffracting waveforms, we detected seismic waves scattered by three-dimensional structures near the core-mantle boundary. The prevalence of these scattered arrivals shows that the region hosts pervasive lateral heterogeneity. Our analysis revealed loud signals due to a plume root beneath Hawaii and a previously unrecognized ultralow-velocity zone beneath the Marquesas Islands. These observations illustrate how approaches flexible enough to detect robust patterns with little to no user supervision can reveal distinctive insights into the deep Earth.