Detection of maize seed germination rate based on improved locally linear embedding

Dimension reduction has become an important tool for dealing with high dimensional data. Locally linear embedding (LLE) is a nonlinear dimension reduction method which can preserve local configurations of nearest neighbors. However, finding the nearest neighbors requires the definition of a distance measure, which is a critical step in LLE. In this paper, the Rank-order distance measure is used to substitute the traditional Euclidean distance measure in order to find better nearest neighbor candidates for preserving local configurations of the manifolds. The Rank-order distance between the data points is calculated using their neighbors’ ranking orders, and is shown to be able to improve the clustering of high dimensional data. The proposed method is called Rank-order based LLE (RLLE). The RLLE method is evaluated by comparing with the original LLE, ISO-LLE and IED-LLE on two handwritten datasets. It is shown that the effectiveness of a distance measure in the LLE method is closely related to whether it can be used to find good nearest neighbors. The experimental results show that the proposed RLLE method can improve the process of dimension reduction effectively, and C-index is another good candidate for evaluating the dimension reduction results.

Statistical methods have been getting constant development since 1970s. However, the statistical methods of the big data are no longer restricted with these methods which are listed in the textbook. This paper mainly demonstrates the Discrimination Analysis of Multivariate Statistical Analysis, Linear Dimensionality Reduction and Nonlinear Dimensionality Reduction Method under the circumstances of the wide range of applications of high-dimensional data. This paper includes three parts. To begin with, the paper illustrates a developing trend from the data to the high-dimensional. Meanwhile, it analyzes the impacts of the high-dimensional data on discriminate analysis methods. The second part represents the necessity of the dimensionality reduction studies in the era of the high-dimensional data overflowing. Then, the paper focuses on introducing the main methods of the linear dimensionality reduction. In addition, this paper covers the basic idea of the nonlinear dimensionality reduction. Moreover, it systematically analyzes the breakthrough of the traditional methods. Furthermore, it chronologically demonstrates the developing trend of the dimensionality reduction method. The final part shows a comprehensive and systematic conclusion to the whole essay and describes a developing prospect of the dimension reduction methods in the future. The purpose of this essay is to design a framework of a performance system which is subject to the characteristics of China High-tech enterprises. It based on the analysing the principles and significance of the performance system of High-tech enterprises. The framework will promote the standardize management of High-tech enterprises of China.

Dimensionality reduction is an unsupervised learning task aimed at creating a low-dimensional summary and/or extracting the most salient features of a dataset. Principal component analysis is a linear dimensionality reduction method in the sense that each principal component is a linear combination of the input variables. To allow features that are nonlinear functions of the input variables, many nonlinear dimensionality reduction (NLDR) methods have been proposed. In this article, we propose novel NLDR methods based on bottleneck deep autoencoders. Our contributions are 2-fold: (1) We introduce a monotonicity constraint into bottleneck deep autoencoders for estimating a single nonlinear component and propose two methods for fitting the model. (2) We propose a new, forward stepwise deep learning architecture for estimating multiple nonlinear components. The former helps extract interpretable, monotone components when the assumption of monotonicity holds, and the latter helps evaluate reconstruction errors in the original data space for a range of components. We conduct numerical studies to compare different model fitting methods and use two real data examples from the studies of human immune responses to HIV to illustrate the proposed methods. Supplementary materials for this article are available online.

This paper carries on research surrounding the influences produced by dimensionality reduction on machine learning classification effect. Firstly, paper constructs the analysis architecture of data dimension reduction classification, combines the two different unsupervised dimension reduction methods, locally linear embedding (LLE) and principal component analysis (PCA) with the five machine learning classification methods: Gradient Boosting Decision Tree (GBDT), Random Forest, Support Vector Machine (SVM), K-Nearest Neighbor (KNN) and Logistic Regression. And then uses the handwritten digital identification dataset to analyze the classification performance of these five classification methods on different dimension datasets by different dimensionality reduction methods. The analysis shows that using the appropriate dimensionality reduction method for dimensionality reduction classification can effectively improve the classification accuracy; the dimensionality reduction classification effect of non-linear dimensionality reduction method is generally better than the linear dimensionality reduction method; different machine learning classification algorithms have significant differences in the sensitivity of dimensions.

Locally linear embedding (LLE) is a method for nonlinear dimensionality reduction, which calculates a low dimensional embedding with the property that nearby points in the high dimensional space remain nearby and similarly co-located with respect to one another in the low dimensional space [1]. LLE algorithm needs to set up a free parameter, the number of nearest neighbors k . This parameter has a strong influence in the transformation. In this paper is proposed a cost function that quantifies the quality of the embedding results and computes an appropriate k . Quality measure is tested on artificial and real-world data sets, which allow us to visually confirm whether the embedding was correctly calculated.

Recent advances in the analysis of high-dimensional signal data have triggered an increasing interest in geometry-based methods for nonlinear dimensionality reduction (NDR). In many applications, high-dimensional datasets typically contain redundant information, and NDR methods are important for an efficient analysis of their properties. During the last few years, concepts from differential geometry were used to create a new range of NDR methods. In the construction of such geometry-based strategies, a natural question is to understand their interaction with classical and modern signal processing tools (convolution transforms, Fourier analysis, wavelet functions). In particular, an important task is the analysis of the incurred geometrical deformation when applying signal transforms to the elements of a dataset. In this paper, we propose the concepts of modulation maps and modulation manifolds for the construction of particular datasets relevant in signal processing and NDR. We consider numerical methods for analyzing geometrical properties of the modulation manifolds, with a particular focus on their scalar and mean curvature. In our numerical examples, we apply the resulting geometry-based analysis to simple test cases, where we present geometrical and topological effects of relevance in manifold learning.

Spike sorting is one of the cornerstones of extracellular electrophysiology. By leveraging advanced signal processing and data analysis techniques, spike sorting makes it possible to detect, isolate, and map single neuron spiking activity from both in vivo and in vitro extracellular electrophysiological recordings. A crucial step of any spike sorting pipeline is to reduce the dimensionality of the recorded spike waveform data. Reducing the dimensionality of the processed data is a near-universal practice, fundamentally motivated by the use of clustering algorithms responsible to detect, isolate, and sort the recorded putative neurons. In this paper, we propose and illustrate on both synthetic and experimental data that employing the nonlinear dimensionality reduction technique Uniform Manifold Approximation and Projection (UMAP) can drastically improve the performance, efficiency, robustness, and scalability of spike sorting pipelines without increasing their computational cost. We show how replacing the linear or ad hoc, expert-defined, supervised nonlinear dimensionality reduction methods commonly used in spike sorting pipelines by the unsupervised, mathematically grounded, nonlinear dimensionality reduction method provided by UMAP drastically increases the number of correctly sorted neurons, makes the identification of quieter, seldom spiking neurons more reliable, enables deeper and more precise explorations and analysis of the neural code, and paves new ways toward more efficient and end-to-end automatable spike sorting pipelines of large-scale extracellular neural recording as those produced by high-density multielectrode arrays.

Variable selection based on locally linear embedding mapping for near-infrared spectral analysis

Divergent Projection Analysis for Unsupervised Dimensionality Reduction

One of the most effective ways to reduce the computational complexity of nonlinear dimensionality reduction is hierarchical partitioning of the space with the subsequent approximation of calculations. In this paper, the efficiency of two approaches to space partitioning, the partitioning of input and output spaces, is analyzed. In addition, a method for nonlinear dimensionality reduction is proposed. It is based on construction of a partitioning tree of the input multidimensional space and an iterative procedure of the gradient descent with the approximation carried out on the nodes of the constructed space partitioning tree. In the method proposed, the relative position of the corrected objects and partitioning tree nodes in both input and output spaces is taken into account in the approximation. The method developed was analyzed based on publicly available datasets.

In researches and experiments, we often work with large volumes of high-dimensional data and regularly confront the problem of dimensionality reduction. Some Non-Linear Dimensionality Reduction (NLDR) methods have been developed for unsupervised datasets. As for supervised datasets, there is a newly developed method called SIsomap, which is capable of discovering structures that underlie complex natural observations. However, SIsomap is limited from the fact that it doesn’t provide an explicit mapping from original space to embedded space, and thus can’t be applied to classification. To solve this problem, we apply neural network to learning that mapping and then to classify. We test our method on a real world dataset. To prove the effectiveness of our method, we also compare it with a related classification method, Extended Isomap. Experiments show that our proposed method has satisfactory performance.

Visible-NIR spectral characterization and grade inversion modelling study of the Derni copper deposit

A new quality assessment criterion for nonlinear dimensionality reduction

Broadband acoustic resonance dissolution spectroscopy (BARDS) has been recently introduced as a low-cost method for the analysis of powdered materials. In this study, ten Iranian natural table salts, each separated into five particle size fractions, were analyzed with BARDS. The compositions and crystalline structure of samples were investigated with inductively coupled plasma optical emission spectroscopy, flame photometry, and X-ray diffraction methods. Moreover, different linear and nonlinear dimensionality reduction methods were used to visualize the ten salt types. The analyses revealed the presence of halite, sylvite, and anhydrite in the rock salts, and halite, bischofite, and periclase in the sea salts. Subjecting bubble volume spectra to nonlinear dimensionality reduction using the t-distributed stochastic neighbor embedding algorithm, the salts were clearly distinguished in a two-dimensional space with the distances and positions relative to their composition, crystalline structure, and particle morphology. The results of this study provide a roadmap toward unraveling the underlying mechanisms behind the BARDS spectra for further applications in characterizing natural edible salts.

BIOT: Explaining multidimensional nonlinear MDS embeddings using the Best Interpretable Orthogonal Transformation