Random projection in dimensionality reduction: applications to image and text data

By Ella Bingham, Heikki Mannila. 2001

1,581 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Lei Zhang
2. Ming-Hsuan Yang
3. Michael W. Mahoney
4. Francis R. Bach
5. David P. Woodruff
6. Yi Ma
7. David Dapeng Zhang
8. Ping Li

In Computer Vision and Pattern Recognition

1. Luc Van Gool
2. Ming-Hsuan Yang
3. Dacheng Tao
4. Xiaogang Wang
5. Yi Yang
6. Lei Zhang
7. Jitendra Malik
8. Andrew Zisserman

Citations in the corpus

• Robust Face Recognition via Sparse Representation (2009, methodology): “Random projection has been previously studied as a general dimensionality-reduction method for numerous clustering problems [47], [48], [49], as well as for learning nonlinear manifolds [50], [51].”
• Locality Preserving Projections (2003, neutral): “Many manifold learning and dimensionality reduction techniques [3][4][13][37][38][45] have been applied to discover such a manifold for document representation and indexing.”
• Time-series clustering - A decade review (2015, methodology): “The methods in this group are Wavelets [ 85 ] : HAAR , DAUBECHIES , Coeiflets , Symlets , Discrete Wavelet Transform ( DWT ) , spectral Cheby - shev Polynomials [ 99 ] , spectral DFT [ 20 ] , Random Mappings [ 100 ] , Piecewise Aggregate Approximation ( PAA ) [ 24 ] , Statistical Models , Time - ser”
• The Algorithm Design Manual (2020, result): “Both theoretical [IM04] and empirical [BM01] results indicate that this method preserves distances quite nicely.”
• Random Projection for High Dimensional Data Clustering: A Cluster Ensemble Approach (2003, methodology): “In this paper we investigate how a relatively new transformation method, random projection (Papadimitriou et al., 1998; Kaski, 1998; Achlioptas, 2001; Bingham & Mannila, 2001), can best be used to improve the clustering result for high dimensional data.”
• Permutation Search Methods are Efficient, Yet Faster Search is Possible (2015, background): “Classic random projections are known to preserve inner products and distance values [5].”
• Retrieval-Augmented Convolutional Neural Networks for Improved Robustness against Adversarial Examples (2018, methodology): “…engine based on locality-sensitive hashing (LSH; see, e.g., Datar et al., 2004) with a reduced feature dimension using random projection (see, e.g., Bingham & Mannila, 2001, and references therein), as the sizes of candidate sets D (cid:48) in the experiments contain approximately 1M or less…”
• Text Classification Algorithms: A Survey (2019, background): “et or high dimension feature spaces. Texts and documents, especially with weighted feature extraction, generate a huge number of features. Many researchers have applied random projection to text data [83,84] for text mining, text classification, and dimensionality reduction. In this section, we revie”
• Learning Feature Engineering for Classification (2017, background): “Hence, Random Projection [Bingham and Mannila, 2001] for dimensionality reduction is not applicable.”
• Approximate nearest neighbors and the fast Johnson-Lindenstrauss transform (2006, background): “[7] Bingham, E., Mannila, H. Random projection in dimensionality reduction: applications to image and text data, Knowledge Discovery and Data Mining (2001), 245 250.”
• Revisiting the Nystrom Method for Improved Large-scale Machine Learning (2013, methodology): “summarized in the recent monograph of Mahoney [46] and the recent review article of Halko, Martinsson, and Tropp [32]. Here, we note that, on the empirical side, both random projection methods (e.g., [12, 26, 61] and [6]) and random sampling methods (e.g., [54, 48]) have been used in applications fo”
• TOPSIG: topology preserving document signatures (2011, methodology): “Although strictly speaking an orthogonal projection is ideal, nearly orthogonal vectors can be used and have been found to perform similarly [3].”
• Subspace clustering for high dimensional data: a review (2004, methodology): “With such datasets, random searching becomes a viable heuristic method and has been used with many of the aforementioned criteria [1; 12; 29].”
• An Analysis of Random Projection for Changeable and Privacy-Preserving Biometric Verification (2010, methodology): “Other applications of RP for dimensionality reduction include face recognition [32], image and text data processing [33] and clustering [34], and learning of mixture of Gaussian [35].”