Experiments with Random Projection

By Sanjoy Dasgupta. Conference on Uncertainty in Artificial Intelligence, 2000

440 citations recorded by the source corpus.

Recent theoretical work has identified random projection as a promising dimensionality reduction technique for learning mixtures of Gaussians. Here we summarize these results and illustrate them by a wide variety of experiments on synthetic and real data.

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Citations in the corpus

Place Recognition with ConvNet Landmarks: Viewpoint-Robust, Condition-Robust, Training-Free (2015, methodology): “We leverage this lemma and apply a Gaussian Random Projection [9, 2] to transfer the original features to a space of much lower dimension.”
Random Projection, Margins, Kernels, and Feature-Selection (2005, methodology): “Theoretical results for some algorithms of this form are given in [AV99], and experimental results are given in [FM03, GBN05, Das00 ].”
Random projection in dimensionality reduction: applications to image and text data (2001, methodology): “Dasgupta [6, 7] has used random projections in learning high-dimensional Gaussian mixture models.”
Multicategory Proximal Support Vector Machine Classifiers (2005, methodology): “The RSVM approach can be interpreted as a random projection approach [10].”
A survey of dimensionality reduction techniques (2014, background): “Alternatively, random mapping [Kaski1998, Dasgupta2000, Bingham2001] solves this problem by choosing zero ‐ mean random vectors as the “interesting” directions onto which project the original observations (this amounts to simply taking a random matrix W whose columns are normalized to have unit…”
Coding for Random Projections (2013, methodology): “1 Introduction The method of random projections has become popular for larg e-scale machine learning applications such as classification, regression, matrix factorization, sing ular value decomposition, near neighbor search, bioinformatics, and more [22, 6, 1, 3, 10, 18, 11, 24, 7, 16, 25].”
Random projection-based multiplicative data perturbation for privacy preserving distributed data mining (2006, background): “In [ 71 ], the author has studied random projections in learning high-dimensional Gaussian mixture models.”
Feature Extraction by Non-Parametric Mutual Information Maximization (2003, methodology): “A similar strategy has been used to learn GMMs in high dimensional spaces (Dasgupta, 2000).”
Locality Preserving Projections (2003, unknown): “random projection [19], informed projection [18], region-based PCA [48], etc.”
Toward a Quantitative Survey of Dimension Reduction Techniques (2019, methodology): “Finally, Xie et al. [24] survey DR techniques based on the Random Projection (RP) method [25].”
Automatically characterizing large scale program behavior (2002, methodology): “For this work we choose to use random linear projection [5] to create a new low-dimensional space into which we project the data.”
Continual Learning in Practice (2019, background): “An alternative approach of random projections shows that it sufﬁces to use (a slightly larger number of) random vectors [22, 23].”
An Analysis of Random Projection for Changeable and Privacy-Preserving Biometric Verification (2010, methodology): “Each entry of R is independent and identically distributed (i.i.d.) according to a Gaussian distribution of mean zero and variance 1/N , rij ∼ N(0, 1/N), i = 1, . . . , N , j = 1, . . . ,M .”
Using the Triangle Inequality to Accelerate k-Means (2003, background): “The overhead of the g and U data structures will be much smaller with a C implementation than with the Matlab implementation used name cardinality dimensionality description birch 100000 2 10 by 10 grid of Gaussian clusters, DS1 in (Zhang et al., 1996) covtype 150000 54 remote soil cover measurement”
Random Projection for High Dimensional Data Clustering: A Cluster Ensemble Approach (2003, background): “Recently, Dasgupta (2000) showed that random projection can change the shape of highly eccentric clusters to be more spherical.”
Using Topic Modeling Methods for Short-Text Data: A Comparative Analysis (2020, methodology): “…of R n that could capture as much of the dataset’s variation as possible; speciﬁcally, given data S = { x 1 , ... , x m }, we would ﬁnd the linear projection to R d as in Equation 1, proposed by Dasgupta (2000): where χ ∗ i is the projection of a point χ i and µ ∗ is the mean of the projected data.”