Random projection and orthonormality for lossy image compression

Amador, José J.

doi:10.1016/j.imavis.2006.05.018

Cited by 16 publications

(6 citation statements)

References 31 publications

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“…A good starting point for developing a random factor model is the random projection method (see, e.g, Bingham and Mannila (2001); Vempala (2005)) that consists of a projection of data to a lower-dimensional space by a random matrix. The random projection method has been used, e.g., to reduce the complexity of the data for classification purposes (Kohonen et al (2000)), for structure-preserving perturbation of confidential data in scientific applications (Liu et al, 2006), for data compression (Bingham and Mannila, 2001), for compression of images (Amador, 2007), and in the design of approximation algorithms (Blum, 2006). The random projection allows one to reduce dimensionality of the investigated problem, often substantially, while preserving the structure of the problem.…”

Section: Choice Of Factorsmentioning

confidence: 99%

“…The random projection consists of a projection of data to a lower-dimensional space by a random matrix. The random projection method has been used, e.g., to reduce the complexity of the data for classification purposes [27], for structure-preserving perturbation of confidential data in scientific applications [28], for data compression [25], for compression of images [29], and in the design of approximation algorithms [30].…”

Section: Introductionmentioning

confidence: 99%

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Random selection of factors preserves the correlation structure in a linear factor model to a high degree

Tanskanen¹,

Lukkarinen

Vatanen³

2018

PLoS ONE

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In a very high-dimensional vector space, two randomly-chosen vectors are almost orthogonal with high probability. Starting from this observation, we develop a statistical factor model, the random factor model, in which factors are chosen stochastically based on the random projection method. Randomness of factors has the consequence that correlation and covariance matrices are well preserved in a linear factor representation. It also enables derivation of probabilistic bounds for the accuracy of the random factor representation of time-series, their cross-correlations and covariances. As an application, we analyze reproduction of time-series and their cross-correlation coefficients in the well-diversified Russell 3,000 equity index.

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Section: Choice Of Factorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Random selection of factors preserves the correlation structure in a linear factor model to a high degree

Tanskanen¹,

Lukkarinen

Vatanen³

2018

PLoS ONE

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“…It states that distances between points are approximately preserved, if they are projected randomly onto a lower-dimensional subspace. The mathematical formulation and proofs of this lemma are given in References [8,25,26].…”

Section: Random Projectionmentioning

confidence: 99%

“…Several successful applications of RP are reported, such as for information retrieval in text documents [4][5][6], for the recognition of handwritten text [7], for (hyper-spectral) image compression [8,9] or face recognition [10], and indexing of audio documents [11]. These results indicate that RP preserves distances and has a performance similar to e.g.…”

Section: Introductionmentioning

confidence: 96%

Random projection experiments with chemometric data

Вармуза

Filzmoser

Liebmann

2010

Journal of Chemometrics

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a Random projection (RP) is a linear method for the projection of high-dimensional data onto a lower dimensional space. RP uses projection vectors (loading vectors) that consist of random numbers taken from a symmetric distribution with zero mean; many successful applications have been reported for high-dimensional data sets. The basic ideas of RP are presented, and tested with artificial data, data from chemoinformatics and from chemometrics. RP's potential in dimensionality reduction is investigated by a subsequent cluster analysis, classification or calibration, and is compared to PCA as a reference method. RP allowed drastic reduction in data size and computing time, while preserving the performance quality. Successful applications are shown in structure similarity searches (53 478 chemical structures characterized by 1233 binary substructure descriptors) and in classification of mutagenicity (6506 chemical structures characterized by 1455 molecular descriptors). Only in calibration tasks with low-dimensional data as in many chemical applications, RP showed limited performance. For special applications in chemometrics with very large data sets and/or severe restrictions for hardware and software resources, RP is a promising method.

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“…Bingham and Manilla (2001) have used RP to show that projecting high-dimensional data onto a lower dimensional subspace does not distort data significantly. Extending upon Bingham and Manilla (2001) and Amador (2007) has provided a paradigm where sinusoidal kernels and RP are successful in providing compression and recovery of images. In a most recent investigation, Varmuza et al (2010) have proved that RP is a promising method for special applications in chemometrics with very large datasets and severe restrictions for hardware and software resources.…”

Section: Introductionmentioning

confidence: 99%

Reducing data dimensionality using random projections and fuzzy k‐means clustering

Cherukuri

2011

International Journal of Intelligent Computing and Cybernetics

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Purpose -The purpose of this paper is to introduce a new hybrid method for reducing dimensionality of high dimensional data. Design/methodology/approach -Literature on dimensionality reduction (DR) witnesses the research efforts that combine random projections (RP) and singular value decomposition (SVD) so as to derive the benefit of both of these methods. However, SVD is well known for its computational complexity. Clustering under the notion of concept decomposition is proved to be less computationally complex than SVD and useful for DR. The method proposed in this paper combines RP and fuzzy k-means clustering (FKM) for reducing dimensionality of the data. Findings -The proposed RP-FKM is computationally less complex than SVD, RP-SVD. On the image data, the proposed RP-FKM has produced less amount of distortion when compared with RP. The proposed RP-FKM provides better text retrieval results when compared with conventional RP and performs similar to RP-SVD. For the text retrieval task, superiority of SVD over other DR methods noted here is in good agreement with the analysis reported by Moravec. Originality/value -The hybrid method proposed in this paper, combining RP and FKM, is new. Experimental results indicate that the proposed method is useful for reducing dimensionality of high-dimensional data such as images, text, etc.

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Random projection and orthonormality for lossy image compression

Cited by 16 publications

References 31 publications

Random selection of factors preserves the correlation structure in a linear factor model to a high degree

Random selection of factors preserves the correlation structure in a linear factor model to a high degree

Random projection experiments with chemometric data

Reducing data dimensionality using random projections and fuzzy k‐means clustering

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