Isomap Method Research Articles

Extraction of molecular information from experimental data on liquids using manifold learning

This study proposes that microscopic information can be extracted from experimental data on liquid substances using a manifold learning technique. Here, 98 liquid substances could be classified based on their functional groups by applying the isomap method, a manifold learning technique, to nine thermal properties of the substances. Moreover, information related to their intermolecular interactions, which could be divided into the contributions of van der Waals and polar interactions, molecular weight, and number of carbon atoms could be extracted by the proposed method. This study could guide future research on the utilization of manifold learning techniques in liquid-substance characterization and development.

Research on WPD and DBSCAN-L-ISOMAP for circuit fault feature extraction

Abstract To solve the problem of feature extraction in electronic circuits due to the nonstationary and nonlinear characteristics of fault signals, a fault feature extraction method for electronic circuits is proposed, which combines wavelet packet analysis and an improved landmark ISOMAP mapping algorithm. The wavelet packet technology is used to decompose and reconstruct the fault feature signals at multiple levels. The extracted wavelet entropy is used to construct the feature vector matrix. The density-based spatial clustering of applications with noise (DBSCAN) clustering algorithm is used to calculate and screen the landmark points. The improved landmark ISOMAP is used to embed the high-dimensional fault feature parameter set into the low-dimensional eigenspace, extract the low-dimensional and sensitive fault feature subset, and apply the support vector machine to identify the fault. The fault diagnosis experiment of the three-phase VIENNA rectifier shows that compared with the principal component analysis method, the traditional ISOMAP method, and the landmark ISOMAP method, the landmark ISOMAP method based on DBSCAN clustering algorithm extracts the fault signal characteristics of electronic equipment more easily.

A Mechatronics System based on Feature Selection and AI for IoT Intrusion Detection Applications

In today's rapid development of the Internet, people's daily lives have become easier, but on the other hand, people's privacy is also faced with potential threats if necessary,security measures are not taken. To detect or stop cyberattacks in this area, network intrusion detection systems (IDS) can be equipped with machine learning algorithms to improve accuracy and speed. Recent research on intrusion and anomaly detection has shown that machine learning (ML) algorithms are widely used to detect maliciousweb traffic, using neural networks to learn models to visualize the sequence of connections between computers on a network. By analyzing and selecting the correct features, dense attacks can be detected more accurately, ultimately reducing misclassification rates and improving accuracy. In this study, we propose a Teacher-Student Feature Selection (TSFS) method that first uses the Isomap method to extract and select features in low dimensions and the best display, and then performs classification. The artificial neural MLP-Net for classification is used to minimize diagnostic errors. Although the teacher-student scheme is not new, to our knowledge, this is the first time this scheme has been used to select features in an intruder alert system. The proposed method can be used to select monitored and unmonitored features. The method is evaluated on different datasets and compared with the state-of-the-art feature selection methods available. The results show that the method performs better in classification, clustering, and error detection. Furthermore, experimental evaluations show that the method is less sensitive to parameter selection.

Visualizing big data via a mixture of PARAMAP and Isomap

Dimension reduction strives to represent higher dimensional data by a lower-dimensional structure. A famous approach by Carroll called Parametric Mapping or PARAMAP (Shepard & Carroll, 1966) works by iterative minimization of a loss function measuring the smoothness or continuity of the mapping from the lower dimensional representation to the original data. The algorithm was revitalized with essential modifications (Akkucuk & Carroll, 2006). Even though the algorithm was modified, it still needed to make a large number of randomly generated starts. In this paper we discuss the use of a variant of the Isomap method (Tenenbaum et al., 2000) to obtain a starting framework to replace the random starts. The core set of landmark points are selected by a special procedure akin to selection of seeds for the k-means algorithm. These core set of landmark points are used to create a rational start for running the PARAMAP algorithm only once but effectively reach a global minimum. Since Isomap is faster and less inclined to local optimum problems than PARAMAP, and the iterative process involved in adding new points to the configuration will be less time consuming (since only one starting configuration is used), we believe the resulting method should be better suited to deal with large data sets, and more prone to obtain an acceptable solution in realistic time.

Automatic Crop Classification in Northeastern China by Improved Nonlinear Dimensionality Reduction for Satellite Image Time Series

Accurate and timely information on the spatial distribution of crops is of great significance to precision agriculture and food security. Many cropland mapping methods using satellite image time series are based on expert knowledge to extract phenological features to identify crops. It is still a challenge to automatically obtain meaningful features from time-series data for crop classification. In this study, we developed an automated method based on satellite image time series to map the spatial distribution of three major crops including maize, rice, and soybean in northeastern China. The core method used is the nonlinear dimensionality reduction technique. However, the existing nonlinear dimensionality reduction technique cannot handle missing data, and it is not designed for subsequent classification tasks. Therefore, the nonlinear dimensionality reduction algorithm Landmark–Isometric feature mapping (L–ISOMAP) is improved. The advantage of the improved L–ISOMAP is that it does not need to reconstruct time series for missing data, and it can automatically obtain meaningful featured metrics for classification. The improved L–ISOMAP was applied to Landsat 8 full-band time-series data during the crop-growing season in the three northeastern provinces of China; then, the dimensionality reduction bands were inputted into a random forest classifier to complete a crop distribution map. The results show that the area of crops mapped is consistent with official statistics. The 2015 crop distribution map was evaluated through the collected reference dataset, and the overall classification accuracy and Kappa index were 83.68% and 0.7519, respectively. The geographical characteristics of major crops in three provinces in northeast China were analyzed. This study demonstrated that the improved L–ISOMAP method can be used to automatically extract features for crop classification. For future work, there is great potential for applying automatic mapping algorithms to other data or classification tasks.

Outlier Mining Methods Based on Graph Structure Analysis

Outlier detection in high-dimensional datasets is a fundamental and challenging problem across disciplines that has also practical implications, as removing outliers from the training set improves the performance of machine learning algorithms. While many outlier mining algorithms have been proposed in the literature, they tend to be valid or efficient for specific types of datasets (time series, images, videos, etc.). Here we propose two methods that can be applied to generic datasets, as long as there is a meaningful measure of distance between pairs of elements of the dataset. Both methods start by defining a graph, where the nodes are the elements of the dataset, and the links have associated weights that are the distances between the nodes. Then, the first method assigns an outlier score based on the percolation (i.e., the fragmentation) of the graph. The second method uses the popular IsoMap nonlinear dimensionality reduction algorithm, and assigns an outlier score by comparing the geodesic distances with the distances in the reduced space. We test these algorithms on real and synthetic datasets and show that they either outperform, or perform on par with other popular outlier detection methods. A main advantage of the percolation method is that is parameter free and therefore, it does not require any training; on the other hand, the IsoMap method has two integer number parameters, and when they are appropriately selected, the method performs similar to or better than all the other methods tested.

An improved Isomap method for manifold learning

PurposeIsometric feature mapping (Isomap) is a very popular manifold learning method and is widely used in dimensionality reduction and data visualization. The most time-consuming step in Isomap is to compute the shortest paths between all pairs of data points based on a neighbourhood graph. The classical Isomap (C-Isomap) is very slow, due to the use of Floyd’s algorithm to compute the shortest paths. The purpose of this paper is to speed up Isomap.Design/methodology/approachThrough theoretical analysis, it is found that the neighbourhood graph in Isomap is sparse. In this case, the Dijkstra’s algorithm with Fibonacci heap (Fib-Dij) is faster than Floyd’s algorithm. In this paper, an improved Isomap method based on Fib-Dij is proposed. By using Fib-Dij to replace Floyd’s algorithm, an improved Isomap method is presented in this paper.FindingsUsing the S-curve, the Swiss-roll, the Frey face database, the mixed national institute of standards and technology database of handwritten digits and a face image database, the performance of the proposed method is compared with C-Isomap, showing the consistency with C-Isomap and marked improvements in terms of the high speed. Simulations also demonstrate that Fib-Dij reduces the computation time of the shortest paths from O(N3) to O(N2lgN).Research limitations/implicationsDue to the limitations of the computer, the sizes of the data sets in this paper are all smaller than 3,000. Therefore, researchers are encouraged to test the proposed algorithm on larger data sets.Originality/valueThe new method based on Fib-Dij can greatly improve the speed of Isomap.

An Image Retrieval Method Based on Manifold Learning with Scale-Invariant Feature Control

Aiming at the problem of the traditional dimensionality reduction methods cannot recover the inherent structure, and Scale Invariant Feature Transform(SIFT)achieving low precision when reinstating images, an Image Retrieval Method Based on Manifold Learning with Scale-Invariant Feature is proposed. It aims to find low-dimensional compact representations of high-dimensional observation data and explores the inherent low and intrinsic dimension of data. The feature extraction method-SIFT and the adaptive ISOMAP method are combined and conducted experiments on the ORL face image dataset. This paper analyzes and discusses the problem of effects of the neighborhood parameter and the intrinsic dimension size on the face image recognition.

Large-scale quantitative analysis of neurons via morphological structures by Fast Automatically Structural Tracing Algorithm (FAST)

Quantitative analysis of neurons is a very important issue in neural science especially after numerous three-dimensional neural images in Drosophila brains were taken from confocal laser scanning microscope [1]. However, analyzing these messy data is mostly by human being with some semi-automatic software packages so far. Not only the task is very labor intensive but also the result is susceptible to errors and usually lacks objectivity. Therefore, fast and accurate analyzing tools are crucial and very desirable. Recently, we developed a computational algorithm, FAST (Fast Automatically Structural Tracing algorithm), which can trace neurons and get characteristic quantities of neuron fibers from their morphology in a very efficient way. These characteristic quantities (called SIs, Structural Indexes) are, for example, number of branch points, number of end points, cross section area of fibers, branch angle of fibers, distribution of fiber length, curvature of fibers, and innervation in neuropils, etc. After structural indexes of neuron fibers were obtained, isomap [2] and modularity [3] methods are applied to classify neurons without depending on human intervention. The isomap method can defined the similarity between neurons by geodesic paths in a high-dimensional manifold as well as the modularity method can find the best community structure of classification by optimization, i.e., to maximize the intra module connections as many as possible and to minimize the inter module connections as few as possible. With these tools, large-scale neural morphological structures, their annotations as well as quantified characteristics, and neural classifications can be facilely and reliably retrieved as useful data for computational neuroscience. Figure 1 A schematic diagram for innervation table and classification results of local neurons in olfactory system of Drosophila.

Visualization of graphical data in a user-specified 2D space using a weighted Isomap method

We present a visualization system for exploring the high-dimensional graphical data, such as textures or 3D models, in 2D space using the dimensionality reduction method. To arrange high-dimensional data in a meaningful 2D space, we develop a novel semi-supervised dimensionality reduction method that can embed data of high dimension in a user-defined 2D coordinate system that is meaningful in terms of the properties of the data. This is achieved by modifying the Isomap method by weighting the data so that the resulting coordinates have no degeneracies and are orthogonal.

Metadynamics in the conformational space nonlinearly dimensionally reduced by Isomap

Atomic motions in molecules are not linear. This infers that nonlinear dimensionality reduction methods can outperform linear ones in analysis of collective atomic motions. In addition, nonlinear collective motions can be used as potentially efficient guides for biased simulation techniques. Here we present a simulation with a bias potential acting in the directions of collective motions determined by a nonlinear dimensionality reduction method. Ad hoc generated conformations of trans,trans-1,2,4-trifluorocyclooctane were analyzed by Isomap method to map these 72-dimensional coordinates to three dimensions, as described by Brown and co-workers [J. Chem. Phys. 129, 064118 (2008)]. Metadynamics employing the three-dimensional embeddings as collective variables was applied to explore all relevant conformations of the studied system and to calculate its conformational free energy surface. The method sampled all relevant conformations (boat, boat-chair, and crown) and corresponding transition structures inaccessible by an unbiased simulation. This scheme allows to use essentially any parameter of the system as a collective variable in biased simulations. Moreover, the scheme we used for mapping out-of-sample conformations from the 72D to 3D space can be used as a general purpose mapping for dimensionality reduction, beyond the context of molecular modeling.

Geodesic distances in the maximum likelihood estimator of intrinsic dimensionality

While analyzing multidimensional data, we often have to reduce their dimensionality so that to preserve as much information on the analyzed data set as possible. To this end, it is reasonable to find out the intrinsic dimensionality of the data. In this paper, two techniques for the intrinsic dimensionality are analyzed and compared, i.e., the maximum likelihood estimator (MLE) and ISOMAP method. We also propose the way how to get good estimates of the intrinsic dimensionality by the MLE method.

Application of Isomap Method in Prediction of Protein Quaternary Structure

A new method for the prediction of protein quaternary structure is constructed based on Isomap (Isometric feature mapping) algorithm, which is a manifold learning-based data mining method. DC (Dipeptide Composition) is used as sequence encoding scheme for the construction of decision system. A DR (Dimensionality Reduction) algorithm, the so-called Isomap is introduced to reduce the decision system, which can be used to classify new objects. The results thus obtained in predicting the quaternary structure of proteins are quite encouraging.

Analyzing the main trade-offs in multiobjective radiation therapy treatment planning databases

Multiobjective radiotherapy planning aims to capture all clinically relevant trade-offs between the various planning goals. This is accomplished by calculating a representative set of Pareto optimal solutions and storing them in a database. The structure of these representative Pareto sets is still not fully investigated. We propose two methods for a systematic analysis of multiobjective databases: principal component analysis and the isomap method. Both methods are able to extract the key trade-offs from a database and provide information which can lead to a better understanding of the clinical case and intensity-modulated radiation therapy planning in general.

Sequential nonlinear manifold learning

The computation of compact and meaningful representations of high dimensional sensor data has recently been addressed through the development of Nonlinear Dimensional Reduction (NLDR) algorithms. The numerical implementation of spectral NLDR techniques typically leads to a symmetric eigenvalue problem that is solved by traditional batch eigensolution algorithms. The application of such algorithms in real-time systems necessitates the development of sequential algorithms that perform feature extraction online. This paper presents an efficient online NLDR scheme, Sequential-Isomap, based on incremental singular value decomposition (SVD) and the Isomap method. Example simulations demonstrate the validity and significant potential of this technique in real-time applications such as autonomous systems.

Robust kernel Isomap

Isomap is one of widely used low-dimensional embedding methods, where geodesic distances on a weighted graph are incorporated with the classical scaling (metric multidimensional scaling). In this paper we pay our attention to two critical issues that were not considered in Isomap, such as: (1) generalization property (projection property); (2) topological stability. Then we present a robust kernel Isomap method, armed with such two properties. We present a method which relates the Isomap to Mercer kernel machines, so that the generalization property naturally emerges, through kernel principal component analysis. For topological stability, we investigate the network flow in a graph, providing a method for eliminating critical outliers. The useful behavior of the robust kernel Isomap is confirmed through numerical experiments with several data sets.