Dimensionality Reduction: A Comparative Review

By L. V. D. van der Maaten, Eric O. Postma, Jaap van den Herik. 2008

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Citations in the corpus

Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMAP, and PaCMAP for Data Visualization (2020, methodology): “…methods that focus on preserving local structure are t-SNE (van der Maaten and Hinton, 2008), LargeVis (Tang et al., 2016), and UMAP (McInnes et al., 2018) (see van der Maaten et al., 2009; Bellet et al., 2013; Belkina et al., 2019, for a survey of these methods and how to tune their parameters).”
A Survey on Metric Learning for Feature Vectors and Structured Data (2013, methodology): “These methods aim at capturing or preserving some properties of the original data (such as the variance or local distance measurements) in the low-dimensional representation.10 The interested reader may refer to the surveys by Fodor (2002) and van der Maaten et al. (2009).”
Automatic Classification of Cellular Expression by Nonlinear Stochastic Embedding (ACCENSE) (2013, background): “That PCA finds the most optimal representation within the set of possible linear projections of the data is, however, also an important limitation––a linear projection may be too restrictive to yield accurate representations (10).”
Will the Pedestrian Cross? A Study on Pedestrian Path Prediction (2014, unknown): “[20] for an overview of techniques).”
Visualizing structure and transitions in high-dimensional biological data (2019, background): “Previous work has focused on preserving pairwise distances or local neighborhoods 5,22,23 .”
Dimensionality of object representations in monkey inferotemporal cortex (2014, methodology): “There are newer algorithms for dealing with such nonlinear manifolds, such as isometric feature mapping (ISOMAP) (Tenenbaum, de Silva, & Langford, 2000) and locally linear embedding (LLE) (Roweis & Saul, 2000), among others (see review by van der Maaten et al. (2009)).”
A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials (2017, background): “Thus, these local methods can fail to capture the global pattern, especially when the data manifold contains a noisy signal [304,310].”
Mel Frequency Cepstral Coefficient and its Applications: A Review (2022, methodology): “For this purpose, many approaches have been developed to reduce dimensionality [1].”
Linear dimensionality reduction: survey, insights, and generalizations (2014, methodology): “A concise introduction to nonlinear manifold methods is given in Zhao et al. (2007), an extensive comparative review is Van der Maaten et al. (2009), and a probabilistic perspective on many spectral methods is given in Lawrence (2012).”
Dimensionality Reduction via Matrix Factorization for Predictive Modeling from Large, Sparse Behavioral Data (2015, methodology): “…type of dimensionality reduction (focusing on standard linear DR through SVD, which is the most popular and was found to outperform other methods in (van der Maaten et al. 2009)); or the various ways to use DR (factors-as-features vs. matrix reconstruction, as is used in collaborative ﬁltering).”
Deep learning of feature representation with multiple instance learning for medical image analysis (2014, methodology): “Due to the enormous dimension length, PCA was performed to compress the dimension of the DNN features to 1000 dimensions, and following experiments were carried out on reduced feature.”