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Nonlinear Dimensionality Reduction by Locally Linear Inlaying
IEEE Transactions on Neural Networks, 2009High-dimensional data is involved in many fields of information processing. However, sometimes, the intrinsic structures of these data can be described by a few degrees of freedom. To discover these degrees of freedom or the low-dimensional nonlinear manifold underlying a high-dimensional space, many manifold learning algorithms have been proposed ...
Yuexian Hou +4 more
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Incremental nonlinear dimensionality reduction by manifold learning
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006Understanding the structure of multidimensional patterns, especially in unsupervised cases, is of fundamental importance in data mining, pattern recognition, and machine learning. Several algorithms have been proposed to analyze the structure of high-dimensional data based on the notion of manifold learning.
Martin H. C. Law, Anil K. Jain 0001
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Locally Adaptive Nonlinear Dimensionality Reduction
2006Popular nonlinear dimensionality reduction algorithms, e.g., SIE and Isomap suffer a difficulty in common: global neighborhood parameters often fail in tackling data sets with high variation in local manifold. To improve the availability of nonlinear dimensionality reduction algorithms in the field of machine learning, an adaptive neighbors selection ...
Yuexian Hou, Hongmin Yang, Pilian He
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Some aspects of nonlinear dimensionality reduction
Computational StatisticszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liwen Wang +3 more
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Dimensional reduction in nonlinear filtering
Nonlinearity, 2010The theory of nonlinear filtering forms the framework of many data assimilation problems. When the rates of change of different variables differ by orders of magnitude, efficient data assimilation can be accomplished by constructing nonlinear filtering equations for the coarse-grained signal.
J H Park +2 more
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Nonlinear Discriminative Dimensionality Reduction of Multiple Datasets
2018 52nd Asilomar Conference on Signals, Systems, and Computers, 2018Dimensionality reduction (DR) is critical to many machine learning and signal processing tasks involving high-dimensional large-scale data. Standard DR tools such as principal component analysis (PCA) deal with a single dataset at a time. In diverse practical settings however, one is often tasked with learning the discriminant subspace such that one ...
Jia Chen 0002 +2 more
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DISCRIMINATIVE NONLINEAR DIMENSIONALITY REDUCTION FOR IMPROVED CLASSIFICATION
International Journal of Neural Systems, 1994Multi-Layer Perceptron (MLP) neural networks have been used extensively for classification tasks. Typically, the MLP network is trained explicitly to produce the correct classification as its output. For speech recognition, however, several investigators have recently experimented with an indirect approach: a unique MLP predictive network is trained ...
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Supervised nonlinear dimensionality reduction by Neighbor Retrieval
2009 IEEE International Conference on Acoustics, Speech and Signal Processing, 2009Many recent works have combined two machine learning topics, learning of supervised distance metrics and manifold embedding methods, into supervised nonlinear dimensionality reduction methods. We show that a combination of an early metric learning method and a recent unsupervised dimensionality reduction method empirically outperforms previous methods.
Jaakko Peltonen +2 more
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Nonlinear dimensionality reduction and data visualization: A review
International Journal of Automation and Computing, 2007Dimensionality reduction and data visualization are useful and important processes in pattern recognition. Many techniques have been developed in the recent years. The self-organizing map (SOM) can be an efficient method for this purpose. This paper reviews recent advances in this area and related approaches such as multidimensional scaling (MDS ...
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An Explicit Sparse Mapping for Nonlinear Dimensionality Reduction
2014A disadvantage of most nonlinear dimensionality reduction methods is that there are no explicit mappings to project high-dimensional features into low-dimensional representation space. Previously, some methods have been proposed to provide explicit mappings for nonlinear dimensionality reduction methods. Nevertheless, a disadvantage of these methods is
Ying Xia +3 more
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