|
Tangent space learning and generalization
Xiaofei HE, Binbin LIN
Front Elect Electr Eng Chin. 2011, 6 (1): 27-42.
https://doi.org/10.1007/s11460-011-0124-4
Manifold learning has attracted considerable attention over the last decade, in which exploring the geometry and topology of the manifold is the central problem. Tangent space is a fundamental tool in discovering the geometry of the manifold. In this paper, we will first review canonical manifold learning techniques and then discuss two fundamental problems in tangent space learning. One is how to estimate the tangent space from random samples, and the other is how to generalize tangent space to ambient space. Previous studies in tangent space learning have mainly focused on how to fit tangent space, and one has to solve a global equation for obtaining the tangent spaces. Unlike these approaches, we introduce a novel method, called persistent tangent space learning (PTSL), which estimates the tangent space at each local neighborhood while ensuring that the tangent spaces vary smoothly on the manifold. Tangent space can be viewed as a point on Grassmann manifold. Inspired from the statistics on Grassmann manifold, we use intrinsic sample total variance to measure the variation of estimated tangent spaces at a single point, and thus, the generalization problem can be solved by estimating the intrinsic sample mean on Grassmann manifold. We validate our methods by various experimental results both on synthetic and real data.
References |
Related Articles |
Metrics
|
|
Advances in adaptive nonlinear manifolds and dimensionality reduction
Hujun YIN
Front Elect Electr Eng Chin. 2011, 6 (1): 72-85.
https://doi.org/10.1007/s11460-011-0131-5
Recent decades have witnessed a much increased demand for advanced, effective and efficient methods and tools for analyzing, understanding and dealing with data of increasingly complex, high dimensionality and large volume. Whether it is in biology, neuroscience, modern medicine and social sciences or in engineering and computer vision, data are being sampled, collected and cumulated in an unprecedented speed. It is no longer a trivial task to analyze huge amounts of high dimensional data. A systematic, automated way of interpreting data and representing them has become a great challenge facing almost all fields and research in this emerging area has flourished. Several lines of research have embarked on this timely challenge and tremendous progresses and advances have been made recently. Traditional and linear methods are being extended or enhanced in order to meet the new challenges. This paper elaborates on these recent advances and discusses various state-of-the-art algorithms proposed from statistics, geometry and adaptive neural networks. The developments mainly follow three lines: multidimensional scaling, eigen-decomposition as well as principal manifolds. Neural approaches and adaptive or incremental methods are also reviewed. In the first line, traditional multidimensional scaling (MDS) has been extended not only to be more adaptive such as neural scale, curvilinear component analysis (CCA) and visualization induced self-organizing map (ViSOM) for online learning, but also to be more local scaling such as Isomap for enhanced flexibility for nonlinear data sets. The second line extends linear principal component analysis (PCA) and has attracted a huge amount of interest and enjoyed flourishing advances with methods like kernel PCA (KPCA), locally linear embedding (LLE) and Laplacian eigenmap. The advantage is obvious: a nonlinear problem is transformed into a linear one and a unique solution can then be sought. The third line starts with the nonlinear principal curve and surface and links up with adaptive neural network approaches such as self-organizing map (SOM) and ViSOM. Many of these frameworks have been further improved and enhanced for incremental learning and mapping function generalization. This paper discusses these recent advances and their connections. Their application issues and implementation matters will also be briefly enlightened and commented on.
References |
Related Articles |
Metrics
|
|
Codimensional matrix pairing perspective of BYY harmony learning: hierarchy of bilinear systems, joint decomposition of data-covariance, and applications of network biology
Lei XU
Front Elect Electr Eng Chin. 2011, 6 (1): 86-119.
https://doi.org/10.1007/s11460-011-0135-1
One paper in a preceding issue of this journal has introduced the Bayesian Ying-Yang (BYY) harmony learning from a perspective of problem solving, parameter learning, and model selection. In a complementary role, the paper provides further insights from another perspective that a co-dimensional matrix pair (shortly co-dim matrix pair) forms a building unit and a hierarchy of such building units sets up the BYY system. The BYY harmony learning is re-examined via exploring the nature of a co-dim matrix pair, which leads to improved learning performance with refined model selection criteria and a modified mechanism that coordinates automatic model selection and sparse learning. Besides updating typical algorithms of factor analysis (FA), binary FA (BFA), binary matrix factorization (BMF), and nonnegative matrix factorization (NMF) to share such a mechanism, we are also led to (a) a new parametrization that embeds a de-noise nature to Gaussian mixture and local FA (LFA); (b) an alternative formulation of graph Laplacian based linear manifold learning; (c) a codecomposition of data and covariance for learning regularization and data integration; and (d) a co-dim matrix pair based generalization of temporal FA and state space model. Moreover, with help of a co-dim matrix pair in Hadamard product, we are led to a semi-supervised formation for regression analysis and a semi-blind learning formation for temporal FA and state space model. Furthermore, we address that these advances provide with new tools for network biology studies, including learning transcriptional regulatory, Protein-Protein Interaction network alignment, and network integration.
References |
Related Articles |
Metrics
|
|
Processing real-world imagery with FACADE-based approaches
Dewen HU, Zongtan ZHOU, Zhengzhi WANG
Front Elect Electr Eng Chin. 2011, 6 (1): 120-136.
https://doi.org/10.1007/s11460-011-0133-3
This paper considers the processing of realworld imagery in the so-called Form-And-Color-And-DEpth (FACADE) framework, which features some superior mechanisms of the human vision system (HVS). FACADE framework was originally proposed by Grossberg et al. as an integrative model of the HVS to illustrate the possible procedures for visual perception of shape (the boundary contour), surface (luminance and color), and binocular depth. As a simplified, reasonable and mathematically full-fledged approach to the HVS, we saw FACADE as a promising infrastructure through which to construct a powerful image processing engine. However, in our attempts to use the approach in its original modality, to deal with real-world imagery, we found it to be inefficient and non-robust. After re-introducing the model hierarchy and illustrating the involved cell dynamics of the FACADE framework, this paper reveals the crucial issues that lead to the deficiency and accordingly present our substitutive solutions by incorporating the mechanisms of anisotropic spatial- and diffusive orientational-competition to make the HVS-featured model efficient and robust. A computer system based on the improved FACADE engine has been implemented and tested not only with illustrative images to highlight the model characteristics, but also with some real-world imagery in both monocular and binocular situations, thereby demonstrating the ability of the FACADE-based image processing approach featuring the HVS.
References |
Related Articles |
Metrics
|
|
Addiction as a dynamical rationality disorder
Hava T. SIEGELMANN
Front Elect Electr Eng Chin. 2011, 6 (1): 151-158.
https://doi.org/10.1007/s11460-011-0134-2
Addiction is frequently modeled as a behavioral disorder resulting from the internal battle between two subsystems: one model describes slow planning versus fast habitual action; another, hot versus cold modes. In another model, one subsystem pushes the individual toward substance abuse, while the other tries to pull him away. These models all describe one side winning over the other at each point of confrontation, represented as a simple binary switch: on or off, win or lose. We propose however, an alternative model, in which opposing systems work in parallel, tipping toward one subsystem or the other, in greater or lesser degree, based on a continuous rationality factor. Our approach results in a dynamical system that qualitatively emulates seeking behavior, cessation, and relapse—enabling the accurate description of a process that can lead to recovery. As an adjunct to the model, we are in the process of creating an associated, interactive website that will enable addicts to journal their thoughts, emotions and actions on a daily basis. The site is not only a potentially rich source of data for our model, but will in its primary function aid addicts to individually identify parameters affecting their decisions and behavior.
References |
Related Articles |
Metrics
|
15 articles
|