scispace - formally typeset
Search or ask a question
Journal ArticleDOI

A Hybrid Methodology For On-Line Process Monitoring

TL;DR: A hybrid strategy of using locally linear embedding for nonlinear dimensionality reduction of high dimensional data and support vector machines for classification of the resultant features is proposed as a robust methodology for process monitoring.
Abstract: A hybrid strategy of using (i) locally linear embedding for nonlinear dimensionality reduction of high dimensional data and (ii) support vector machines for classification of the resultant features is proposed as a robust methodology for process monitoring. Illustrative examples substantiate the methodology vis-a-vis current practice.
Citations
More filters
Book ChapterDOI
18 Dec 2007
TL;DR: A novel methodology for online fault diagnosis with Dynamic Time Warping has been suggested and its performance has been investigated using two simulated case studies using a warping window constraint and a Lower Bounding measure.
Abstract: Owing to the superiority of Dynamic Time Warping as a similarity measure of time series, it can become an effective tool for fault diagnosis in chemical process plants. However, direct application of Dynamic Time Warping can be computationally inefficient, given the complexity involved. In this work we have tackled this problem by employing a warping window constraint and a Lower Bounding measure. A novel methodology for online fault diagnosis with Dynamic Time Warping has been suggested and its performance has been investigated using two simulated case studies.

4 citations

References
More filters
Journal ArticleDOI
22 Dec 2000-Science
TL;DR: Locally linear embedding (LLE) is introduced, an unsupervised learning algorithm that computes low-dimensional, neighborhood-preserving embeddings of high-dimensional inputs that learns the global structure of nonlinear manifolds.
Abstract: Many areas of science depend on exploratory data analysis and visualization. The need to analyze large amounts of multivariate data raises the fundamental problem of dimensionality reduction: how to discover compact representations of high-dimensional data. Here, we introduce locally linear embedding (LLE), an unsupervised learning algorithm that computes low-dimensional, neighborhood-preserving embeddings of high-dimensional inputs. Unlike clustering methods for local dimensionality reduction, LLE maps its inputs into a single global coordinate system of lower dimensionality, and its optimizations do not involve local minima. By exploiting the local symmetries of linear reconstructions, LLE is able to learn the global structure of nonlinear manifolds, such as those generated by images of faces or documents of text.

15,106 citations


"A Hybrid Methodology For On-Line Pr..." refers background in this paper

  • ...Local approaches such as locally linear embedding (LLE) (Roweis and Saul, 2000), Laplacian eigenmaps (Belkin and Niyogi, 2002) attempt to preserve the local geometry of the data; essentially, they seek to map nearby points on the manifold to nearby points in the low-dimensional representation....

    [...]

Journal ArticleDOI
22 Dec 2000-Science
TL;DR: An approach to solving dimensionality reduction problems that uses easily measured local metric information to learn the underlying global geometry of a data set and efficiently computes a globally optimal solution, and is guaranteed to converge asymptotically to the true structure.
Abstract: Scientists working with large volumes of high-dimensional data, such as global climate patterns, stellar spectra, or human gene distributions, regularly confront the problem of dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. The human brain confronts the same problem in everyday perception, extracting from its high-dimensional sensory inputs-30,000 auditory nerve fibers or 10(6) optic nerve fibers-a manageably small number of perceptually relevant features. Here we describe an approach to solving dimensionality reduction problems that uses easily measured local metric information to learn the underlying global geometry of a data set. Unlike classical techniques such as principal component analysis (PCA) and multidimensional scaling (MDS), our approach is capable of discovering the nonlinear degrees of freedom that underlie complex natural observations, such as human handwriting or images of a face under different viewing conditions. In contrast to previous algorithms for nonlinear dimensionality reduction, ours efficiently computes a globally optimal solution, and, for an important class of data manifolds, is guaranteed to converge asymptotically to the true structure.

13,652 citations


"A Hybrid Methodology For On-Line Pr..." refers methods in this paper

  • ...Global approaches such as Isomap (Tenenbaum et al., 2000) attempts to preserve geometry at all scales, mapping nearby points on the manifold to nearby points in low-dimensional space, and faraway points to faraway points....

    [...]

Journal ArticleDOI
TL;DR: The objective of this review paper is to summarize and compare some of the well-known methods used in various stages of a pattern recognition system and identify research topics and applications which are at the forefront of this exciting and challenging field.
Abstract: The primary goal of pattern recognition is supervised or unsupervised classification. Among the various frameworks in which pattern recognition has been traditionally formulated, the statistical approach has been most intensively studied and used in practice. More recently, neural network techniques and methods imported from statistical learning theory have been receiving increasing attention. The design of a recognition system requires careful attention to the following issues: definition of pattern classes, sensing environment, pattern representation, feature extraction and selection, cluster analysis, classifier design and learning, selection of training and test samples, and performance evaluation. In spite of almost 50 years of research and development in this field, the general problem of recognizing complex patterns with arbitrary orientation, location, and scale remains unsolved. New and emerging applications, such as data mining, web searching, retrieval of multimedia data, face recognition, and cursive handwriting recognition, require robust and efficient pattern recognition techniques. The objective of this review paper is to summarize and compare some of the well-known methods used in various stages of a pattern recognition system and identify research topics and applications which are at the forefront of this exciting and challenging field.

6,527 citations

Proceedings Article
03 Jan 2001
TL;DR: The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering.
Abstract: Drawing on the correspondence between the graph Laplacian, the Laplace-Beltrami operator on a manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in a higher dimensional space. The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering. Several applications are considered.

4,557 citations

Journal ArticleDOI
TL;DR: An algorithm for the analysis of multivariate data is presented along with some experimental results that is based upon a point mapping of N L-dimensional vectors from the L-space to a lower-dimensional space such that the inherent data "structure" is approximately preserved.
Abstract: An algorithm for the analysis of multivariate data is presented along with some experimental results. The algorithm is based upon a point mapping of N L-dimensional vectors from the L-space to a lower-dimensional space such that the inherent data "structure" is approximately preserved.

3,460 citations


"A Hybrid Methodology For On-Line Pr..." refers background or methods in this paper

  • ...They include: non-linear PCA (Malthouse, 1998), multi-dimensional scaling (MDS) (Borg and Groenen,1997), Sammon mapping (Sammon, 1969), singular value decomposition (SVD), self-organizing map (SOM) (Kohonen, 1995), generative topographic mapping (Bishop et al.,1998), principal curves and surfaces…...

    [...]

  • ...Consequently they cannot accommodate new data points (Sammon, 1969; Mao and Jain, 1995) and the entire procedure has to be repeated from start using all data points....

    [...]