Nonlinear Dimensionality Reduction Algorithm Research Articles

Research on Rotating Machinery Fault Diagnosis Based on Multi-Strategy Feature Extraction

This study proposes a novel feature extraction method that leverages multi-strategy optimization algorithms to enhance the accuracy and efficiency of rotating machinery fault diagnosis. By introducing an improved slime mold algorithm (LTSSMA), it optimizes the penalty factor and decomposition layers in variational mode decomposition (VMD), achieving more precise signal decomposition. The sample entropy generated by VMD forms the basis of the feature vector, and the nonlinear dimensionality reduction algorithm (t-SNE) is applied to reduce dimensions. Finally, the optimized features are classified using a random forest (RF) model, resulting in an 11.3% improvement in fault diagnosis accuracy compared to traditional methods. This method not only accelerates the diagnostic process but also significantly improves fault identification reliability.

Data-driven surrogate model for aerodynamic design using separable shape tensor method

In the context of increasing dimensionality of design variables and the complexity of constraints, the efficacy of Surrogate-Based Optimization (SBO) is limited. The traditional linear and nonlinear dimensionality reduction algorithms are mainly to decompose the mathematical matrix composed of design variables or objective functions in various forms, the smoothness of the design space cannot be guaranteed in the process, and additional constraint functions need to be added in the optimization, which increases the calculation cost. This study presents a new parameterization method to improve both problems of SBO. The new parameterization is addressed by decoupling affine transformations (dilation, rotation, shearing, and translation) within the Grassmannian submanifold, which enables a separate representation of the physical information of the airfoil in a high-dimensional space. Building upon this, Principal Geodesic Analysis (PGA) is employed to achieve geometric control, compress the design space, reduce the number of design variables, reduce the dimensions of design variables and enhance predictive performance during the surrogate optimization process. For comparison, a dimensionality reduction space is defined using 95% of the energy, and RAE 2822 for transonic conditions are used as demonstrations. This method significantly enhances the optimization efficiency of the surrogate model while effectively enabling geometric constraints. In three-dimensional problems, it enables simultaneous design of planar shapes for various components of the aircraft and high-order perturbation deformations. Optimization was applied to the ONERA M6 wing, achieving a lift-drag ratio of 18.09, representing a 27.25% improvement compared to the baseline configuration. In comparison to conventional surrogate model optimization methods, which only achieved a 17.97% improvement, this approach demonstrates its superiority.

Contrastive Learning Dimensionality Reduction Method Based on Manifold Learning

With the development of the times, more and more high-dimensional datasets come into people's view. In order to reduce the time complexity and space complexity of downstream tasks, data dimensionality reduction becomes the primary choice. Classical dimensionality reduction algorithms are mainly divided into linear dimensionality reduction algorithms and nonlinear dimensionality reduction algorithms. Some of the traditional dimensionality reduction methods have the problems of not considering the nonlinear structure of the original dataset and the existence of weak generalisation, which makes the dimensionality reduction effect not good or model need to be recalculated because of the addition of new samples. In order to solve these problems, the research in this paper is a comparative learning dimensionality reduction method based on manifold learning. The idea of manifold learning using geodesic distance can fully consider the nonlinear structure of the original dataset. In this paper, comparative learning is the main framework. When the neural network completes the training, it only need to take the new data as input to calculate, the result can be obtained, no need to reconstruct the model which means the generality is high. Starting from the related work, this paper briefly introduces manifold learning, comparative learning and neural network algorithms. Subsequently, an innovative model is proposed, including three modules, Isomap to extract nonlinear structure, expanding neighbourhood to make pseudo-labels, and comparative learning training. Detailed analyses are carried out through experiments, comparing with PCA and LLE algorithms with the geodetic distance retention rate as an indicator, which proves that the data dimensionality reduction method of this model is more effective and ubiquitous.

An adaptive sampling algorithm for reduced‐order models using Isomap

AbstractThe use of reduced‐order models (ROMs) in physics‐based modeling and simulation is a popular tool for drastically lowering the computational cost associated with high‐fidelity simulations. ROMs use training data from a set of computed high‐fidelity simulations with different design parameters that control physical and geometric properties of the full‐order model. The quality of the training data dictates the performance of the ROM, making the choice of training design parameters important. A widely used method for generating training parameters for ROMs is Latin hypercube sampling (LHS), a statistical method that aims to maximize the distance and minimize the correlation amongst produced samples. However, LHS fails to account for the physics of the full‐order model and can lead to an over‐representation of some physical regimes in the training data while neglecting others. In this work, we present a computationally efficient adaptive sampling method for ROMs using Isomap, a versatile algorithm for nonlinear dimensionality reduction. Using an initial number of samples, the adaptive sampling algorithm iteratively generates samples based on a low‐dimensional manifold of the training data. When applied to two external aerodynamics problems, the proposed adaptive sampling algorithm offers significantly improved performance in predicting physical fields and coefficients of lift and drag for a given computational budget for both non‐intrusive and projection‐based ROMs.

A fast, scalable and versatile tool for analysis of single-cell omics data.

Single-cell omics technologies have revolutionized the study of gene regulation in complex tissues. A major computational challenge in analyzing these datasets is to project the large-scale and high-dimensional data into low-dimensional space while retaining the relative relationships between cells. This low dimension embedding is necessary to decompose cellular heterogeneity and reconstruct cell-type-specific gene regulatory programs. Traditional dimensionality reduction techniques, however, face challenges in computational efficiency and in comprehensively addressing cellular diversity across varied molecular modalities. Here we introduce a nonlinear dimensionality reduction algorithm, embodied in the Python package SnapATAC2, which not only achieves a more precise capture of single-cell omics data heterogeneities but also ensures efficient runtime and memory usage, scaling linearly with the number of cells. Our algorithm demonstrates exceptional performance, scalability and versatility across diverse single-cell omics datasets, including single-cell assay for transposase-accessible chromatin using sequencing, single-cell RNA sequencing, single-cell Hi-C and single-cell multi-omics datasets, underscoring its utility in advancing single-cell analysis.

Combustion instability analysis in an ethylene-fueled scramjet combustor under various fuel penetration height conditions using an image-based nonlinear dimensionality reduction method

The present study investigates the effects of fuel penetration height on combustion instabilities in an ethylene-fueled scramjet model combustor with a cavity flameholder. Experiments were performed at the stagnation temperature of 1900 K, the stagnation pressure of 0.37 MPa, and the Mach number of 2. Three fuel injection orifice diameters:2.3, 2.4, and 2.5 mm, were tested to elucidate the effects of ethylene penetration height on combustion instabilities. Furthermore, high-speed measurements of CH* chemiluminescence and shadowgraphs were performed with high-speed video cameras. To examine the dynamics of the combustion instabilities, time-resolved CH* chemiluminescence images and shock parameters, extracted from snapshots of shadowgraphs, were analyzed using a non-linear dimensionality reduction algorithm: Gaussian Process Dynamical Model (GPDM). Thereafter, further analyses on the acquired latent variables were conducted with Recurrence Plot (RP). The experimental results showed that the fuel equivalence ratio (ϕ) range for cavity shear-layer combustion mode expanded as d decreased. Furthermore, for ϕ = 0.18, the instability behavior remarkably changed at around d = 2.4 mm. Therefore, the instability dynamics for ϕ = 0.18 were investigated using GPDM and RP including results from our previous study (d = 2, 3, and 4 mm), revealing differences in the instability behaviors. For d = 3 and 4 mm, jet-wake combustion and ram combustion modes were established alternately with a frequency of about 1600 Hz. In contrast, at d = 2.4 and 2.5 mm, although a similar instability in the d = 4 mm case was present at almost the same oscillation frequency, a different instability behavior was also confirmed. This additional instability exhibited an intermediate state between jet-wake combustion and ram combustion modes. These two instabilities emerged aperiodically. For an unstable combustion in shear layer observed for d = 2 and 2.3 mm, corresponding RPs exhibited black patches, indicating that the oscillation amplitude diminished substantially.

Multiple-frequency attribute blending via adaptive uniform manifold approximation and projection and its application on hydrocarbon reservoir delineation

Multifrequency attribute blending is a highly effective tool for characterizing hydrocarbon reservoirs. It begins by extracting multifrequency attributes of seismic data based on time-frequency transformation. Subsequently, a blending algorithm is used to fuse the extracted multifrequency components, thereby obtaining the interpretation results of the interested reservoirs. The red-green-blue (RGB) algorithm is commonly used to fuse the multifrequency components. However, it should be noted that the RGB blending algorithm can only fuse three frequency components, i.e., the low-, middle-, and high-frequency components. Moreover, it can occasionally introduce ambiguities, making it difficult to interpret areas that appear white or yellow. To address these issues, we develop a workflow for multiple-frequency component analysis to delineate hydrocarbon reservoirs. First, we apply the generalized S-transform to obtain the multiple-frequency components of seismic data. Then, the correlation analysis is developed and implemented to select the sensitive frequency components. Finally, we use the uniform manifold approximation and projection, a nonlinear dimension reduction algorithm, to blend the extracted multiple-frequency components and obtain reservoir interpretation results. We apply the suggested workflow to synthetic data and a 3D field data volume to evaluate its effectiveness. Our mathematical analysis demonstrates that the suggested workflow can effectively fuse multiple-frequency components to accurately characterize hydrocarbon reservoirs.

Predicting cognitive decline in a low‐dimensional representation of brain morphology

AbstractBackgroundIdentifying early signs of neurodegeneration due to Alzheimer’s disease (AD) is a necessary first step towards preventing cognitive decline. Individual cortical thickness measures, available after processing anatomical magnetic resonance imaging (MRI), are sensitive markers of neurodegeneration. However, cortical decline in aging and high inter‐individual variability complicates the determination of AD‐related neurodegeneration on trajectories. Further, the high‐dimensional nature of these trajectories necessitate the use of a transformation into lower‐dimensional spaces in order to perform comparative statistical analyses, model decline, and identify criteria differentiating pathological from normal trajectories.MethodIn this project, we computed trajectories in a 2D representation of a 62‐dimensional manifold of individual cortical thickness measures. To compute this representation, we used a nonlinear dimension reduction algorithm called Uniform Manifold Approximation and Projection (UMAP). We first created a UMAP embedding on measurements from 6,237 cognitively healthy participants (3,556 women) aged 18 to 100 years old from the NOMIS database. We then projected longitudinal data from 537 mild cognitively impaired (MCI) subjects and 340 AD subjects from ADNI into this embedding. Each participant had multiple visits (n = 2), one year apart. Finally, differences in trajectories were analysed by clustering the reduced data and comparing the positional variations through time between MCI and AD subjects. The validity of the approach was verified through cross‐validation.ResultFirst, the embedding was shown to be positively associated (r = 0.65) with participants' age (see figure 1) in the NOMIS data. When projected in this space, differences between ADNI’s MCI and AD distributions were found (see figure 2). Average trajectories between clusters were shown to be significantly different between MCI and AD subjects (see figure 3). Moreover, we showed that some clusters and trajectories between clusters were more prone to host AD subjects. Finally, cross‐validation showed an accuracy of up to 72% at predicting cognitive decline in MCI participants over 2,000 bootstrap iterations.ConclusionA 2D low‐dimensional cortical thickness representation embeds sufficient discriminatory information as to predict decline to AD in MCI participants with strong accuracy.

Predicting cognitive decline in a low‐dimensional representation of brain morphology

AbstractBackgroundIdentifying early signs of neurodegeneration due to Alzheimer’s disease (AD) is a necessary first step towards preventing cognitive decline. Individual cortical thickness measures, available after processing anatomical magnetic resonance imaging (MRI), are sensitive markers of neurodegeneration. However, cortical decline in aging and high inter‐individual variability complicates the determination of AD‐related neurodegeneration on trajectories. Further, the high‐dimensional nature of these trajectories necessitate the use of a transformation into lower‐dimensional spaces in order to perform comparative statistical analyses, model decline, and identify criteria differentiating pathological from normal trajectories.MethodIn this project, we computed trajectories in a 2D representation of a 62‐dimensional manifold of individual cortical thickness measures. To compute this representation, we used a nonlinear dimension reduction algorithm called Uniform Manifold Approximation and Projection (UMAP). We first created a UMAP embedding on measurements from 6,237 cognitively healthy participants (3,556 women) aged 18 to 100 years old from the NOMIS database. We then projected longitudinal data from 537 mild cognitively impaired (MCI) subjects and 340 AD subjects from ADNI into this embedding. Each participant had multiple visits (n ≥ 2), one year apart. Finally, differences in trajectories were analysed by clustering the reduced data and comparing the positional variations through time between MCI and AD subjects. The validity of the approach was verified through cross‐validation.ResultFirst, the embedding was shown to be positively associated (r = 0.65) with participants' age (see figure 1) in the NOMIS data. When projected in this space, differences between ADNI’s MCI and AD distributions were found (see figure 2). Average trajectories between clusters were shown to be significantly different between MCI and AD subjects (see figure 3). Moreover, we showed that some clusters and trajectories between clusters were more prone to host AD subjects. Finally, cross‐validation showed an accuracy of up to 72% at predicting cognitive decline in MCI participants over 2,000 bootstrap iterations.ConclusionA 2D low‐dimensional cortical thickness representation embeds sufficient discriminatory information as to predict decline to AD in MCI participants with strong accuracy.

Predicting cognitive decline in a low-dimensional representation of brain morphology

Identifying early signs of neurodegeneration due to Alzheimer’s disease (AD) is a necessary first step towards preventing cognitive decline. Individual cortical thickness measures, available after processing anatomical magnetic resonance imaging (MRI), are sensitive markers of neurodegeneration. However, normal aging cortical decline and high inter-individual variability complicate the comparison and statistical determination of the impact of AD-related neurodegeneration on trajectories. In this paper, we computed trajectories in a 2D representation of a 62-dimensional manifold of individual cortical thickness measures. To compute this representation, we used a novel, nonlinear dimension reduction algorithm called Uniform Manifold Approximation and Projection (UMAP). We trained two embeddings, one on cortical thickness measurements of 6237 cognitively healthy participants aged 18–100 years old and the other on 233 mild cognitively impaired (MCI) and AD participants from the longitudinal database, the Alzheimer’s Disease Neuroimaging Initiative database (ADNI). Each participant had multiple visits (n ge 2), one year apart. The first embedding’s principal axis was shown to be positively associated (r = 0.65) with participants’ age. Data from ADNI is projected into these 2D spaces. After clustering the data, average trajectories between clusters were shown to be significantly different between MCI and AD subjects. Moreover, some clusters and trajectories between clusters were more prone to host AD subjects. This study was able to differentiate AD and MCI subjects based on their trajectory in a 2D space with an AUC of 0.80 with 10-fold cross-validation.

Reduced Deep Convolutional Activation Features (R-DeCAF) in Histopathology Images to Improve the Classification Performance for Breast Cancer Diagnosis.

Breast cancer is the second most common cancer among women worldwide, and the diagnosis by pathologists is a time-consuming procedure and subjective. Computer-aided diagnosis frameworks are utilized to relieve pathologist workload by classifying the data automatically, in which deep convolutional neural networks (CNNs) are effective solutions. The features extracted from the activation layer of pre-trained CNNs are called deep convolutional activation features (DeCAF). In this paper, we have analyzed that all DeCAF features are not necessarily led to higher accuracy in the classification task and dimension reduction plays an important role. We have proposed reduced DeCAF (R-DeCAF) for this purpose, and different dimension reduction methods are applied to achieve an effective combination of features by capturing the essence of DeCAF features. This framework uses pre-trained CNNs such as AlexNet, VGG-16, and VGG-19 as feature extractors in transfer learning mode. The DeCAF features are extracted from the first fully connected layer of the mentioned CNNs, and a support vector machine is used for classification. Among linear and nonlinear dimensionality reduction algorithms, linear approaches such as principal component analysis (PCA) represent a better combination among deep features and lead to higher accuracy in the classification task using a small number of features considering a specific amount of cumulative explained variance (CEV) of features. The proposed method is validated using experimental BreakHis and ICIAR datasets. Comprehensive results show improvement in the classification accuracy up to 4.3% with a feature vector size (FVS) of 23 and CEV equal to 0.15.

3D biplanar reconstruction of lower limbs using nonlinear statistical models.

Three-dimensional (3D) reconstruction of lower limbs is of great interest in surgical planning, computer assisted surgery, and for biomechanical applications. The use of 3D imaging modalities such as computed tomography (CT) scan and magnetic resonance imaging (MRI) has limitations such as high radiation and expense. Therefore, three-dimensional reconstruction methods from biplanar X-ray images represent an attractive alternative. In this paper, we present a new unsupervised 3D reconstruction method for the patella, talus, and pelvis using calibrated biplanar (45- and 135-degree oblique) radiographic images and a prior information on the geometric/anatomical structure of these complex bones. A multidimensional scaling (MDS)-based nonlinear dimensionality reduction algorithm is applied to exploit this prior geometric/anatomical information. It represents relevant deformations existing in the training set. Our method is based on a hybrid-likelihood using regions and contours. The edge-based notion represents the relation between the external contours of the bone projections and an edge potential field estimated on the radiographic images. Region-based notion is the non-overlapping ratio between segmented and projected bone regions of interest (RoIs). Our automatic 3D reconstruction model entails stochastically minimizing an energy function allowing an estimation of deformation parameters of the bone shape. This 3D reconstruction method has been successfully tested on 13 biplanar radiographic image pairs, yielding very promising results.

A Weak-Coupling Flow-Power Forecasting Method for Small Hydropower Station Group

Due to the need for rural revitalization and renewable energy utilization, a large quantity of small hydropower stations is emerging, with weak-coupling flow-power features. However, a weak spatial coupling exists between the distribution of small hydropower station groups (SHSGs) and gaging stations since the small hydropower stations are usually located in remote areas lacking hydrographic facilities. That may cause weak or no coupling between the hydroregime and the power output of small hydropower plants in the target basin, thus hindering accurate power forecasting. To meet the need for short-term power generation prediction for SHSGs in intensive management areas, we propose a data-driven power-forecasting model which can mine the correlation information of weakly coupled basins while transferring hydrological knowledge to uncoupled basins. First, to make the task data domains before and after migration more similar, a similar watershed matching algorithm based on the nonlinear dimensionality reduction algorithm (Isomap) and the k -means++ algorithm is proposed; then a short-term interpretable runoff prediction model is pretrained, and features are extracted in the source basin using the temporal fusion transformer (TFT) network. After that, a heuristic ensemble fine-tuning model based on the k -fold cross-validation fine-tuning method and heuristic ensemble algorithm is proposed to transfer the public knowledge of the source basin to the uncoupled basin. Then, a TFT network is used to mine the weak-coupling relationship between the hydrological regime and the output power of an SHSG. Finally, the validity of the model is verified with an example from a European region. After considering the weakly coupled flow-power characteristics, the mean absolute percentage error (MAPE) of three SHSGs’ power prediction by the proposed method is on average 34.8% lower than that of the method without considering the hydrological information.

Wassmap: Wasserstein Isometric Mapping for Image Manifold Learning

In this paper, we propose Wasserstein Isometric Mapping (Wassmap), a nonlinear dimensionality reduction technique that provides solutions to some drawbacks in existing global nonlinear dimensionality reduction algorithms in imaging applications. Wassmap represents images via probability measures in Wasserstein space, then uses pairwise Wasserstein distances between the associated measures to produce a low-dimensional, approximately isometric embedding. We show that the algorithm is able to exactly recover parameters of some image manifolds, including those generated by translations or dilations of a fixed generating measure. Additionally, we show that a discrete version of the algorithm retrieves parameters from manifolds generated from discrete measures by providing a theoretical bridge to transfer recovery results from functional data to discrete data. Testing of the proposed algorithms on various image data manifolds shows that Wassmap yields good embeddings compared with other global and local techniques.

Classifying FRB spectrograms using nonlinear dimensionality reduction techniques

ABSTRACT Fast radio bursts (FRBs) are mysterious astronomical phenomena, and it is still uncertain whether they consist of multiple types. In this study, we use two nonlinear dimensionality reduction algorithms – Uniform Manifold Approximation and Projection (UMAP) and t-distributed stochastic neighbour embedding (t-SNE) – to differentiate repeaters from apparently non-repeaters in FRBs. Based on the first Canadian Hydrogen Intensity Mapping Experiment (CHIME) FRB catalogue, these two methods are applied to standardized parameter data and image data from a sample of 594 sub-bursts and 535 FRBs, respectively. Both methods are able to differentiate repeaters from apparently non-repeaters. The UMAP algorithm using image data produces more accurate results and is a more model-independent method. Our result shows that in general repeater clusters tend to be narrowband, which implies a difference in burst morphology between repeaters and apparently non-repeaters. We also compared our UMAP predictions with the CHIME/FRB discovery of six new repeaters, the performance was generally good except for one outlier. Finally, we highlight the need for a larger and more complete sample of FRBs.

Reducing the Dimensionality of SPD Matrices with Neural Networks in BCI

In brain–computer interface (BCI)-based motor imagery, the symmetric positive definite (SPD) covariance matrices of electroencephalogram (EEG) signals with discriminative information features lie on a Riemannian manifold, which is currently attracting increasing attention. Under a Riemannian manifold perspective, we propose a non-linear dimensionality reduction algorithm based on neural networks to construct a more discriminative low-dimensional SPD manifold. To this end, we design a novel non-linear shrinkage layer to modify the extreme eigenvalues of the SPD matrix properly, then combine the traditional bilinear mapping to non-linearly reduce the dimensionality of SPD matrices from manifold to manifold. Further, we build the SPD manifold network on a Siamese architecture which can learn the similarity metric from the data. Subsequently, the effective signal classification method named minimum distance to Riemannian mean (MDRM) can be implemented directly on the low-dimensional manifold. Finally, a regularization layer is proposed to perform subject-to-subject transfer by exploiting the geometric relationships of multi-subject. Numerical experiments for synthetic data and EEG signal datasets indicate the effectiveness of the proposed manifold network.

A Novel Approach to Decision-Making on Diagnosing Oncological Diseases Using Machine Learning Classifiers Based on Datasets Combining Known and/or New Generated Features of a Different Nature

This paper deals with the problem of diagnosing oncological diseases based on blood protein markers. The goal of the study is to develop a novel approach in decision-making on diagnosing oncological diseases based on blood protein markers by generating datasets that include various combinations of features: both known features corresponding to blood protein markers and new features generated with the help of mathematical tools, particularly with the involvement of the non-linear dimensionality reduction algorithm UMAP, formulas for various entropies and fractal dimensions. These datasets were used to develop a group of multiclass kNN and SVM classifiers using oversampling algorithms to solve the problem of class imbalance in the dataset, which is typical for medical diagnostics problems. The results of the experimental studies confirmed the feasibility of using the UMAP algorithm and approximation entropy, as well as Katz and Higuchi fractal dimensions to generate new features based on blood protein markers. Various combinations of these features can be used to expand the set of features from the original dataset in order to improve the quality of the received classification solutions for diagnosing oncological diseases. The best kNN and SVM classifiers were developed based on the original dataset augmented respectively with a feature based on the approximation entropy and features based on the UMAP algorithm and the approximation entropy. At the same time, the average values of the metric MacroF1-score used to assess the quality of classifiers during cross-validation increased by 16.138% and 4.219%, respectively, compared to the average values of this metric in the case when the original dataset was used in the development of classifiers of the same name.

Measure of Similarity between GMMs Based on Geometry-Aware Dimensionality Reduction

Gaussian Mixture Models (GMMs) are used in many traditional expert systems and modern artificial intelligence tasks such as automatic speech recognition, image recognition and retrieval, pattern recognition, speaker recognition and verification, financial forecasting applications and others, as simple statistical representations of underlying data. Those representations typically require many high-dimensional GMM components that consume large computing resources and increase computation time. On the other hand, real-time applications require computationally efficient algorithms and for that reason, various GMM similarity measures and dimensionality reduction techniques have been examined to reduce the computational complexity. In this paper, a novel GMM similarity measure is proposed. The measure is based on a recently presented nonlinear geometry-aware dimensionality reduction algorithm for the manifold of Symmetric Positive Definite (SPD) matrices. The algorithm is applied over SPD representations of the original data. The local neighborhood information from the original high-dimensional parameter space is preserved by preserving distance to the local mean. Instead of dealing with high-dimensional parameter space, the method operates on much lower-dimensional space of transformed parameters. Resolving the distance between such representations is reduced to calculating the distance among lower-dimensional matrices. The method was tested within a texture recognition task where superior state-of-the-art performance in terms of the trade-off between recognition accuracy and computational complexity has been achieved in comparison with all baseline GMM similarity measures.

Hierarchical unimodal processing within the primary somatosensory cortex during a bimodal detection task

Do sensory cortices process more than one sensory modality?To answer these questions, scientists have generated a wide variety of studies at distinct space-time scales in different animal models, and often shown contradictory conclusions. Some conclude that this process occurs in early sensory cortices, but others that this occurs in areas central to sensory cortices. Here, we sought to determine whether sensory neurons process and encode physical stimulus properties of different modalities (tactile and acoustic). Forthis, we designed a bimodal detection task where the senses of touch and hearing compete from trial to trial. Two Rhesus monkeys performed this novel task, while neural activity was recorded in areas 3b and 1 of the primary somatosensory cortex (S1). Weanalyzed neurons' coding properties and variability, organizing them by their receptive field's position relative to the stimulation zone. Our results indicate that neurons of areas 3b and 1 are unimodal, encoding only the tactile modality in both the firing rate and variability. Moreover, we found that neurons in area 3b carried more information about the periodic stimulus structure than those in area 1, possessed lower response and coding latencies, and had a lower intrinsic time scale. In sum, these differences reveal a hidden processing-based hierarchy. Finally, using a powerful nonlinear dimensionality reduction algorithm, we show that the activity from areas 3b and 1 can be separated, establishing a clear division in the functionality of these two subareas of S1.

Application of adaptive Laplacian Eigenmaps in near infrared spectral modeling

Laplacian Eigenmaps is a nonlinear dimensionality reduction algorithm based on graph theory. The algorithm adopted the Gaussian function to measure the affinity between a pair of points in the adjacency graph. However, the scaling parameter σ in the Gaussian function is a hyper-parameter tuned empirically. Once the value of σ is determined and fixed, the weight between two points depends wholly on the Euclidian distance between them, which is not suitable for multi-scale sample sets. To optimize the weight between two points in the adjacency graph and make the weight reflect the scale information of different sample sets, an adaptive LE improved algorithm is used in this paper. Considering the influence of adjacent sample points and multi-scale data, the Euclidean distance between the k-th nearest sample point to sample point xi is used as the local scaling parameter σi of xi, instead of using a single scaling parameter σ. The efficiency of the algorithm is testified by applying on two public near-infrared data sets. LE-SVR and ALE-SVR models are established after LE and ALE dimension reduction of SNV preprocessed data sets. Compared with the LE-SVR model, the R2 and RPD of the ALE-SVR model established on the two data sets are improved, while RMSE is decreased, indicating that the prediction effect and stability of the regression model are established by the ALE algorithm are better than that of the traditional LE algorithm. Experiments show that the ALE algorithm can achieve a better dimensionality reduction effect than the LE algorithm.