Nonlinear Dimensionality Reduction: Advanced Techniques for Enhancing Data Representation in Robotic Systems

· Robotics Science 42권 · One Billion Knowledgeable
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1: Nonlinear dimensionality reduction: Explore foundational concepts and the importance of reducing highdimensional data for easier analysis.

2: Linear map: Introduces the basics of linear mapping and its role in reducing data dimensionality in machine learning.


3: Support vector machine: Learn how support vector machines apply dimensionality reduction in classification tasks and pattern recognition.


4: Principal component analysis: Delve into PCA's technique for transforming data into a set of linearly uncorrelated variables.


5: Isometry: Examine how isometric techniques preserve distances between points while reducing data dimensions.


6: Dimensionality reduction: Understand the broader scope of dimensionality reduction and its applications in various fields.


7: Semidefinite embedding: Study semidefinite programming and its connection to dimensionality reduction methods.


8: Kernel method: Discover the power of kernel methods in handling nonlinear relationships in data reduction.


9: Kernel principal component analysis: Explore KPCA’s capability to perform dimensionality reduction in a highdimensional feature space.


10: Numerical continuation: Learn how numerical continuation techniques assist in understanding highdimensional systems.


11: Spectral clustering: Understand how spectral clustering leverages dimensionality reduction to group similar data points.


12: Isomap: A look at Isomap, a technique that combines multidimensional scaling with geodesic distances for dimensionality reduction.


13: Johnson–Lindenstrauss lemma: Delve into the mathematics of the JohnsonLindenstrauss lemma, which ensures dimensionality reduction maintains geometric properties.


14: LinearnonlinearPoisson cascade model: Study how this model integrates linear and nonlinear methods in dimensionality reduction.


15: Manifold alignment: Learn about manifold alignment and its importance in aligning data from different domains in dimensionality reduction.


16: Diffusion map: Understand how diffusion maps use the diffusion process for dimensionality reduction in complex datasets.


17: Tdistributed stochastic neighbor embedding: Explore tSNE's ability to reduce dimensionality while preserving local structures in data.


18: Kernel embedding of distributions: Study how kernel embedding allows for dimensionality reduction on distributions, not just datasets.


19: Random projection: A practical approach to dimensionality reduction that relies on random projections for fast computation.


20: Manifold regularization: Learn about manifold regularization techniques and their impact on learning from highdimensional data.


21: Empirical dynamic modeling: Discover how empirical dynamic modeling aids in dimensionality reduction through time series data analysis.

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