Titlebook: Elements of Dimensionality Reduction and Manifold Learning; Benyamin Ghojogh,Mark Crowley,Ali Ghodsi Textbook 2023 The Editor(s) (if appli

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Background on KernelsIn functional analysis—a field of mathematics—there are various spaces of either data points or functions. For example, the Euclidean space is a subset of the Hilbert space, while the Hilbert space itself is a subset of the Banach space. The Hilbert space is a space of functions and its dimensionality is often considered to be high.

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Fisher Discriminant AnalysisFisher Discriminant Analysis (FDA) attempts to find a subspace that separates the classes as much as possible, while the data also become as spread as possible.

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Locally Linear EmbeddingLocally Linear Embedding (LLE) is a nonlinear spectral dimensionality reduction method that can be used for manifold embedding and feature extraction.

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Laplacian-Based Dimensionality ReductionSpectral dimensionality reduction methods deal with the graph and geometry of data and usually reduce to an eigenvalue or generalized eigenvalue problem (see Chap. .).

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Probabilistic Metric LearningIt was mentioned in Chap. . that metric learning can be divided into three types of learning—spectral, probabilistic and deep metric learning.