scholarly journals A Fusion Scheme of Local Manifold Learning Methods

10.5772/66303 ◽  
2017 ◽  
Author(s):  
Xianglei Xing ◽  
Kejun Wang ◽  
Weixing Feng
Keyword(s):  
Manifold Learning ◽  
Learning Methods ◽  
Fusion Scheme

Learning Manifolds

2012 ◽  
pp. 374-402
Author(s):  
Diana Mateus ◽  
Christian Wachinger ◽  
Selen Atasoy ◽  
Loren Schwarz ◽  
Nassir Navab
Keyword(s):  
Manifold Learning ◽  
Domain Knowledge ◽  
Dimensional Space ◽  
Human Motion ◽  
Motion Modeling ◽  
Learning Methods ◽  
Data Representations ◽  
Non Linear ◽  
Data Points ◽  
Low Dimensional

Computer aided diagnosis is often confronted with processing and analyzing high dimensional data. One alternative to deal with such data is dimensionality reduction. This chapter focuses on manifold learning methods to create low dimensional data representations adapted to a given application. From pairwise non-linear relations between neighboring data-points, manifold learning algorithms first approximate the low dimensional manifold where data lives with a graph; then, they find a non-linear map to embed this graph into a low dimensional space. Since the explicit pairwise relations and the neighborhood system can be designed according to the application, manifold learning methods are very flexible and allow easy incorporation of domain knowledge. The authors describe different assumptions and design elements that are crucial to building successful low dimensional data representations with manifold learning for a variety of applications. In particular, they discuss examples for visualization, clustering, classification, registration, and human-motion modeling.

Fusion of Local Manifold Learning Methods

2015 ◽  
Vol 22 (4) ◽  
pp. 395-399 ◽  
Author(s):  
Xianglei Xing ◽  
Kejun Wang ◽  
Zhuowen Lv ◽  
Yu Zhou ◽  
Sidan Du
Keyword(s):  
Manifold Learning ◽  
Learning Methods

scholarly journals Learning Geographical Manifolds: A Kernel Trick for Geographical Machine Learning

2019 ◽  
Author(s):  
Levi John Wolf ◽  
Elijah Knaap
Keyword(s):  
Machine Learning ◽  
Dimension Reduction ◽  
Manifold Learning ◽  
Learning Algorithms ◽  
Machine Learning Algorithms ◽  
Dimensional Structure ◽  
Geographic Scale ◽  
Learning Methods ◽  
Machine Learning Methods ◽  
Non Linear

Dimension reduction is one of the oldest concerns in geographical analysis. Despite significant, longstanding attention in geographical problems, recent advances in non-linear techniques for dimension reduction, called manifold learning, have not been adopted in classic data-intensive geographical problems. More generally, machine learning methods for geographical problems often focus more on applying standard machine learning algorithms to geographic data, rather than applying true "spatially-correlated learning," in the words of Kohonen. As such, we suggest a general way to incentivize geographical learning in machine learning algorithms, and link it to many past methods that introduced geography into statistical techniques. We develop a specific instance of this by specifying two geographical variants of Isomap, a non-linear dimension reduction, or "manifold learning," technique. We also provide a method for assessing what is added by incorporating geography and estimate the manifold's intrinsic geographic scale. To illustrate the concepts and provide interpretable results, we conducting a dimension reduction on geographical and high-dimensional structure of social and economic data on Brooklyn, New York. Overall, this paper's main endeavor--defining and explaining a way to "geographize" many machine learning methods--yields interesting and novel results for manifold learning the estimation of intrinsic geographical scale in unsupervised learning.

scholarly journals A Geometric Perspective on Functional Outlier Detection

Stats ◽  
2021 ◽  
Vol 4 (4) ◽  
pp. 971-1011
Author(s):  
Moritz Herrmann ◽  
Fabian Scheipl
Keyword(s):  
Outlier Detection ◽  
Manifold Learning ◽  
Functional Data ◽  
Detection Methods ◽  
Tabular Data ◽  
Learning Methods ◽  
Full Generality ◽  
Theoretical Understanding ◽  
Vector Valued ◽  
Practical Feasibility

We consider functional outlier detection from a geometric perspective, specifically: for functional datasets drawn from a functional manifold, which is defined by the data’s modes of variation in shape, translation, and phase. Based on this manifold, we developed a conceptualization of functional outlier detection that is more widely applicable and realistic than previously proposed taxonomies. Our theoretical and experimental analyses demonstrated several important advantages of this perspective: it considerably improves theoretical understanding and allows describing and analyzing complex functional outlier scenarios consistently and in full generality, by differentiating between structurally anomalous outlier data that are off-manifold and distributionally outlying data that are on-manifold, but at its margins. This improves the practical feasibility of functional outlier detection: we show that simple manifold-learning methods can be used to reliably infer and visualize the geometric structure of functional datasets. We also show that standard outlier-detection methods requiring tabular data inputs can be applied to functional data very successfully by simply using their vector-valued representations learned from manifold learning methods as the input features. Our experiments on synthetic and real datasets demonstrated that this approach leads to outlier detection performances at least on par with existing functional-data-specific methods in a large variety of settings, without the highly specialized, complex methodology and narrow domain of application these methods often entail.

Manifold Learning Methods for Visualization and Browsing of Drum Machine Samples

2021 ◽  
Vol 69 (1/2) ◽  
pp. 40-53
Author(s):  
Jordie Shier ◽  
Kirk McNally ◽  
George Tzanetakis ◽  
Ky Grace Brooks
Keyword(s):  
Manifold Learning ◽  
Learning Methods
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