Data Sets In High-dimensional Spaces Research Articles

Research on Topic Evolution Path Recognition Based on LDA2vec Symmetry Model

Topic extraction and evolution analysis became a research hotspot in the academic community due to its ability to reveal the development trend of a certain field and discover the evolution law of topic content in different development stages of the field. However, current research methods still face challenges, such as inaccurate topic recognition and unclear evolution paths, which can seriously compromise the comprehensiveness and accuracy of the analysis. To address the problem, the paper proposes a topic evolution path recognition method based on the LDA2vec symmetry model. Under given conditions, both the LDA and Word2vec used in the model conform to the structural symmetry of their datasets in high-dimensional space, and the fused LDA2vec method improves the accuracy of the analysis results. Firstly, we recognize the topics based on the LDA model, which uses Gibbs symmetric sampling and obeys the symmetric Dirichlet distribution to ensure data convergence. Secondly, Word2vec is used to learn the contextual information of the topic words in the document collection, and the words in the corpus are projected as vectors in the high-dimensional space so that the computed pairs of words with similar semantics have symmetry in the hyperplane of the high-dimensional space. Subsequently, the word vector is used as a weight, and the LDA topic word probability value is weighted to generate a new topic vector. Thirdly, the vector similarity index is employed to calculate the semantic similarity among topics at adjacent stages, and evolution paths that directly reflect the topic relationships are constructed. Finally, an empirical study is conducted in the field of data security to demonstrate the effectiveness of the proposed approach for topic evolution analysis. The results show that the proposed approach can accurately recognize the topic content and construct clear evolution paths, which contribute to the comprehensive and accurate analysis of topic evolution in a specific research field.

Joint Label Inference and Discriminant Embedding.

Graph-based learning in semisupervised models provides an effective tool for modeling big data sets in high-dimensional spaces. It has been useful for propagating a small set of initial labels to a large set of unlabeled data. Thus, it meets the requirements of many emerging applications. However, in real-world applications, the scarcity of labeled data can negatively affect the performance of the semisupervised method. In this article, we present a new framework for semisupervised learning called joint label inference and discriminant embedding for soft label inference and linear feature extraction. The proposed criterion and its associated optimization algorithm take advantage of both labeled and unlabeled data samples in order to estimate the discriminant transformation. This type of criterion should allow learning more discriminant semisupervised models. Nine public image data sets are used in the experiments and method comparisons. These experimental results show that the performance of the proposed method is superior to that of many advanced semisupervised graph-based algorithms.

CFRP Impact Damage Inspection Based on Manifold Learning Using Ultrasonic Induced Thermography

Impact damage, caused by low-energy impact, is inevitable during the whole life time of carbon fiber reinforced plastic (CFRP) material. However, the barely visible impact damage (BVID) is difficult to be detected by visual methods. Ultrasonic thermography (UT) is an emerging nondestructive testing technique that visualizes damage in thermal images captured by an infrared (IR) camera when the material is stimulated by ultrasound. However, noise and blurry edges around the high-temperature areas may cause confusion and lead to unreliable results in the thermal images of UT test. In this paper, an impact damage inspection method is proposed based on manifold learning for the CFRP material. Low-power ultrasonic excitation is used for this UT. The IR image sequences are processed as datasets in high-dimensional space. These datasets are reduced to lower dimensions by manifold learning to find the intrinsic structure in the two-dimensional manifold. Each dimension of the embedding manifold correlates highly with one degree of freedom underlying the original pixel: steady and random components. The steady component, which reflects the temperature rise caused by damage, is used for VID and BVID detection. The experimental system was set up, and CFRP plate specimens with different impact damage were tested. All the impact damage could be detected and shown in reconstructed static image with little noise. The proposed method using image sequences could provide a visualized, reliable, and effective impact damage inspection and localization means for CFRP material during manufacturing and in service.

Hybrid Visualization of the Medical Images Data Sets

This paper presents new method to visualize medical images data sets by using the properties of continuity and trustworthy dimensional reduction methods. Continuity and trustworthy dimensional reduction methods are well-known promising nonlinear methods are used to visualize different data sets, as medical images. However, their visualizations face the problem of false colors which lead the specialist to make wrong analysis of patient status. To overcomes these errors, we will combine these two methods in one to generate hybrid method has continuity and trustworthiness properties. The proposed method produces best visualization by perfect preserving the corresponding color distances between visualization and original data sets in high-dimensional space. The application of hybrid method shows it is interested for visualizing medical images data sets. It has been compared with the continuity methods (as Isomap) and the trustworthy method (as curvilinear distance analysis (CDA)). The results proves the efficiency of of the proposed method in visualizing medical images data sets, where the false colors in the visualization are overcome as well as possible. The experiments shows the hybrid visualization has more chances to discover the true colors of the medical images data sets.

Self-Aligning Manifolds for Matching Disparate Medical Image Datasets.

Manifold alignment can be used to reduce the dimensionality of multiple medical image datasets into a single globally consistent low-dimensional space. This may be desirable in a wide variety of problems, from fusion of different imaging modalities for Alzheimer's disease classification to 4DMR reconstruction from 2D MR slices. Unfortunately, most existing manifold alignment techniques require either a set of prior correspondences or comparability between the datasets in high-dimensional space, which is often not possible. We propose a novel technique for the 'self-alignment' of manifolds (SAM) from multiple dissimilar imaging datasets without prior correspondences or inter-dataset image comparisons. We quantitatively evaluate the method on 4DMR reconstruction from realistic, synthetic sagittal 2D MR slices from 6 volunteers and real data from 4 volunteers. Additionally, we demonstrate the technique for the compounding of two free breathing 3D ultrasound views from one volunteer. The proposed method performs significantly better for 4DMR reconstruction than state-of-the-art image-based techniques.

A sparse nearest mean classifier for high dimensional multi-class problems

The analysis of small datasets in high dimensional spaces is inherently difficult. For two-class classification problems there are a few methods that are able to face the so-called curse of dimensionality. However, for multi-class sparsely sampled datasets there are hardly any specific methods. In this paper, we propose four multi-class classifier alternatives that effectively deal with this type of data. Moreover, these methods implicitly select a feature subset optimized for class separation. Accordingly, they are especially interesting for domains where an explanation of the problem in terms of the original features is desired. In the experiments, we applied the proposed methods to an MDMA powders dataset, where the problem was to recognize the production process. It turns out that the proposed multi-class classifiers perform well, while the few utilized features correspond to known MDMA synthesis ingredients. In addition, to show the general applicability of the methods, we applied them to several other sparse datasets, ranging from bioinformatics to chemometrics datasets having as few as tens of samples in tens to even thousands of dimensions and three to four classes. The proposed methods had the best average performance, while very few dimensions were effectively utilized.

Supervised locally linear embedding with probability-based distance for classification

We present a novel dimension reduction method for classification based on probability-based distance and the technique of locally linear embedding (LLE). Logistic Discrimination (LD) is adopted for estimating the probability distribution as well as for classification on the reduced data. Different from the supervised locally linear embedding (SLLE) that is only used for the dimension reduction of training data, our probability-based locally linear embedding (PLLE) can be applied on both training and testing data. Five microarray data sets in high-dimensional spaces, the IRIS data, and a real set of handwritten digits are experimented. The numerical results show the proposed methodology performs better, compared with the LD classifiers applied on the lower-dimensional embedding coordinates computed by LLE or SLLE.

NIPALSTREE: A New Hierarchical Clustering Approach for Large Compound Libraries and Its Application to Virtual Screening

A hierarchical clustering algorithm--NIPALSTREE--was developed that is able to analyze large data sets in high-dimensional space. The result can be displayed as a dendrogram. At each tree level the algorithm projects a data set via principle component analysis onto one dimension. The data set is sorted according to this one dimension and split at the median position. To avoid distortion of clusters at the median position, the algorithm identifies a potentially more suited split point left or right of the median. The procedure is recursively applied on the resulting subsets until the maximal distance between cluster members exceeds a user-defined threshold. The approach was validated in a retrospective screening study for angiotensin converting enzyme (ACE) inhibitors. The resulting clusters were assessed for their purity and enrichment in actives belonging to this ligand class. Enrichment was observed in individual branches of the dendrogram. In further retrospective virtual screening studies employing the MDL Drug Data Report (MDDR), COBRA, and the SPECS catalog, NIPALSTREE was compared with the hierarchical k-means clustering approach. Results show that both algorithms can be used in the context of virtual screening. Intersecting the result lists obtained with both algorithms improved enrichment factors while losing only few chemotypes.

Clustering High Dimensional Massive Scientific Datasets

Many scientific applications can benefit from an efficient clustering algorithm of massively large high dimensional datasets. However most of the developed algorithms are impractical to use when the amount of data is very large. Given N objects each defined by an M-dimensional feature vector, any clustering technique for handling very large datasets in high dimensional space should run in time O(MN) at best, and O(MN log N) in the worst case, using no more than O(MN) storage, for it to be practical. We introduce a hybrid algorithm, called HyCeltyc, for clustering massively large high dimensional datasets in O(MN) time which is linear in the size of the data. HyCeltyc, which stands for Hybrid Cell Density Clustering method, combines a cell-density based algorithm with a hierarchical agglomerative method to identify clusters in linear time. The main steps of the algorithm involve sampling, dimensionality reduction, selection of significant features on which to cluster the data and a grid-based clustering algorihm that is linear in the data size.

Approximate single linkage cluster analysis of large data sets in high-dimensional spaces

Motivated by a real-world data set of more than 40 000 observations, we consider single linkage clustering of large data sets in high-dimensional spaces. In this particular case, the data we consider are observations in the space of one-dimensional submanifolds of Euclidean space. This data set is so large that the individual observations cannot each be inspected. A goal of the analysis is to produce a partial ordering of the data so that a useful inspection of selected observations can take place. An essential step is construction of a metric on the objects in this high-dimensional space that can be computed fairly quickly. The size of the problem makes the running time of Prim's algorithm (the fastest available algorithm for finding a minimal spanning tree of a complete graph) prohibitive. We have developed several methods which approximate the single linkage tree. We report the result of applying our approximations to the data set.