Add to ORKGSUMMARY We consider an alignment algorithm for reconstructing global coordinates of a given data set from coordinates constructed for data points in small local neighborhoods through computing a spectral subspace of an alignment matrix. We show that, under certain conditions, the null space of the alignment matrix recovers global coordinates even when local point sets have different dimensions. This result generalizes a previous analysis to allow alignment of local coordinates of mixed dimensions. We also extend this result to the setting of a semi-supervised learning problem and we present several examples to illustrate our results
Past decades, numerous spectral analysis based algorithms have been proposed for dimensionality redu...
Abstract. Fisher’s linear discriminant analysis (LDA), one of the most popular dimensionality reduct...
Many unsupervised algorithms for nonlinear dimensionality reduction, such as locally linear embeddin...
The goal of dimensionality reduction or manifold learning for a given set of high-dimensional data p...
AbstractThis paper presents a spectral analysis for an alignment matrix that arises in reconstructio...
We present a new manifold learning algorithm called Local Orthogonality Preserving Alignment (LOPA)....
Abstract—Over the past few decades, dimensionality reduction has been widely exploited in computer v...
Over the past few decades, dimensionality reduction has been widely exploited in computer vision and...
Spectral analysis-based dimensionality reduction algorithms are important and have been popularly ap...
Manifold learning has been demonstrated as an effective way to represent intrinsic geometrical struc...
Manifold learning has been demonstrated as an effective way to represent intrinsic geometrical struc...
The problem of nonlinear dimensionality reduction is considered. We focus on problems where prior in...
AbstractWe consider the performance of Local Tangent Space Alignment (Zhang & Zha [1]), one of sever...
High dimensional data is usually produced by the source that only enjoys a limited number of degrees...
© Springer Science+Business Media New York 2013. Dozens of manifold learning-based dimensionality re...
Past decades, numerous spectral analysis based algorithms have been proposed for dimensionality redu...
Abstract. Fisher’s linear discriminant analysis (LDA), one of the most popular dimensionality reduct...
Many unsupervised algorithms for nonlinear dimensionality reduction, such as locally linear embeddin...
The goal of dimensionality reduction or manifold learning for a given set of high-dimensional data p...
AbstractThis paper presents a spectral analysis for an alignment matrix that arises in reconstructio...
We present a new manifold learning algorithm called Local Orthogonality Preserving Alignment (LOPA)....
Abstract—Over the past few decades, dimensionality reduction has been widely exploited in computer v...
Over the past few decades, dimensionality reduction has been widely exploited in computer vision and...
Spectral analysis-based dimensionality reduction algorithms are important and have been popularly ap...
Manifold learning has been demonstrated as an effective way to represent intrinsic geometrical struc...
Manifold learning has been demonstrated as an effective way to represent intrinsic geometrical struc...
The problem of nonlinear dimensionality reduction is considered. We focus on problems where prior in...
AbstractWe consider the performance of Local Tangent Space Alignment (Zhang & Zha [1]), one of sever...
High dimensional data is usually produced by the source that only enjoys a limited number of degrees...
© Springer Science+Business Media New York 2013. Dozens of manifold learning-based dimensionality re...
Past decades, numerous spectral analysis based algorithms have been proposed for dimensionality redu...
Abstract. Fisher’s linear discriminant analysis (LDA), one of the most popular dimensionality reduct...
Many unsupervised algorithms for nonlinear dimensionality reduction, such as locally linear embeddin...