Manifold alignment with Schroedinger eigenmaps

2016 ◽  
Author(s):  
Juan E. Johnson ◽  
Charles M. Bachmann ◽  
Nathan D. Cahill
Keyword(s):  
Manifold Alignment

Manifold Alignment

2011 ◽  
pp. 95-120 ◽  
Author(s):  
Chang Wang ◽  
Peter Krafft ◽  
Sridhar Mahadevan
Keyword(s):  
Manifold Alignment

scholarly journals Concept Discovery for The Interpretation of Landscape Scenicness

2020 ◽  
Vol 2 (4) ◽  
pp. 397-413
Author(s):  
Pim Arendsen ◽  
Diego Marcos ◽  
Devis Tuia
Keyword(s):  
Vector Spaces ◽  
Large Set ◽  
Feature Representations ◽  
The United Kingdom ◽  
New Concepts ◽  
Manifold Alignment ◽  
Semantic Concepts ◽  
Visual Concepts ◽  
Alignment Technique ◽  
Concept Activation

In this paper, we study how to extract visual concepts to understand landscape scenicness. Using visual feature representations from a Convolutional Neural Network (CNN), we learn a number of Concept Activation Vectors (CAV) aligned with semantic concepts from ancillary datasets. These concepts represent objects, attributes or scene categories that describe outdoor images. We then use these CAVs to study their impact on the (crowdsourced) perception of beauty of landscapes in the United Kingdom. Finally, we deploy a technique to explore new concepts beyond those initially available in the ancillary dataset: Using a semi-supervised manifold alignment technique, we align the CNN image representation to a large set of word embeddings, therefore giving access to entire dictionaries of concepts. This allows us to obtain a list of new concept candidates to improve our understanding of the elements that contribute the most to the perception of scenicness. We do this without the need for any additional data by leveraging the commonalities in the visual and word vector spaces. Our results suggest that new and potentially useful concepts can be discovered by leveraging neighbourhood structures in the word vector spaces.

scholarly journals Semi-Supervised Manifold Alignment Using Parallel Deep Autoencoders

Algorithms ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 186
Author(s):  
Fayeem Aziz ◽  
Aaron S.W. Wong ◽  
Stephan Chalup
Keyword(s):  
Manifold Learning ◽  
Network Architecture ◽  
Image Data ◽  
High Dimensional ◽  
Double Pendulum ◽  
Manifold Alignment ◽  
Series Of Experiments ◽  
Underlying Manifold ◽  
Low Dimensional ◽  
Pendulum Dynamics

The aim of manifold learning is to extract low-dimensional manifolds from high-dimensional data. Manifold alignment is a variant of manifold learning that uses two or more datasets that are assumed to represent different high-dimensional representations of the same underlying manifold. Manifold alignment can be successful in detecting latent manifolds in cases where one version of the data alone is not sufficient to extract and establish a stable low-dimensional representation. The present study proposes a parallel deep autoencoder neural network architecture for manifold alignment and conducts a series of experiments using a protein-folding benchmark dataset and a suite of new datasets generated by simulating double-pendulum dynamics with underlying manifolds of dimensions 2, 3 and 4. The dimensionality and topological complexity of these latent manifolds are above those occurring in most previous studies. Our experimental results demonstrate that the parallel deep autoencoder performs in most cases better than the tested traditional methods of semi-supervised manifold alignment. We also show that the parallel deep autoencoder can process datasets of different input domains by aligning the manifolds extracted from kinematics parameters with those obtained from corresponding image data.

A Bayesian nonparametric semi-supervised model for integration of multiple single-cell experiments

2020 ◽  
Author(s):  
Archit Verma ◽  
Barbara Engelhardt
Keyword(s):  
Single Cell ◽  
Latent Variable ◽  
Environmental Variability ◽  
Simulated Data ◽  
Joint Analysis ◽  
Variable Model ◽  
Manifold Alignment ◽  
Multiple Data Sets ◽  
Sequencing Platforms ◽  
Low Dimensional

Joint analysis of multiple single cell RNA-sequencing (scRNA-seq) data is confounded by technical batch effects across experiments, biological or environmental variability across cells, and different capture processes across sequencing platforms. Manifold alignment is a principled, effective tool for integrating multiple data sets and controlling for confounding factors. We demonstrate that the semi-supervised t-distributed Gaussian process latent variable model (sstGPLVM), which projects the data onto a mixture of fixed and latent dimensions, can learn a unified low-dimensional embedding for multiple single cell experiments with minimal assumptions. We show the efficacy of the model as compared with state-of-the-art methods for single cell data integration on simulated data, pancreas cells from four sequencing technologies, induced pluripotent stem cells from male and female donors, and mouse brain cells from both spatial seqFISH+ and traditional scRNA-seq.Code and data is available at https://github.com/architverma1/sc-manifold-alignment

scholarly journals Fuzzy Granule Manifold Alignment Preserving Local Topology

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 178695-178705
Author(s):  
Wei Li ◽  
Jianwu Xue ◽  
Yumin Chen ◽  
Xuebai Zhang ◽  
Chao Tang ◽  
...  
Keyword(s):  
Manifold Alignment ◽  
Local Topology
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