Combining Unsupervised and Supervised Approaches to Feature Selection for Multivariate Signal Compression

Eruhimov, Victor; Martyanov, Vladimir; Raulefs, Peter; Tuv, Eugene

doi:10.1007/11875581_58

Cited by 4 publications

(4 citation statements)

References 7 publications

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“…We briefly position our work in the context of other similar approaches in the area. The majority of datacompression techniques for sequential data use the same set of low-energy coefficients whether using Fourier [7,8], Wavelets [9,10] or Chebyshev polynomials [13] as the orthogonal basis for representation and compression. Using the same set of orthogonal coefficients has several advantages: a) it is straightforward to compare the respective coefficients; b) space partitioning and indexing structures (such as R-trees) can be directly used on the compressed data; c) there is no need to store also the indices (position) of the basis functions to which the stored coefficients correspond.…”

Section: Related Workmentioning

confidence: 99%

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Compressive mining: fast and optimal data mining in the compressed domain

2014

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Real-world data typically contain repeated and periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.). However, distance estimation when the data are represented using different sets of coefficients is still a largely unexplored area. This work studies the optimization problems related to obtaining the tightest lower/upper bound on Euclidean distances when each data object is potentially compressed using a different set of orthonormal coefficients. Our technique leads to tighter distance estimates, which translates into more accurate search, learning and mining operations directly in the compressed domain.We formulate the problem of estimating lower/upper distance bounds as an optimization problem. We establish the properties of optimal solutions, and leverage the theoretical analysis to develop a fast algorithm to obtain an exact solution to the problem. The suggested solution provides the tightest estimation of the L 2 -norm or the correlation. We show that typical data-analysis operations, such as k-NN search or k-Means clustering, can operate more accurately using the proposed compression and distance reconstruction technique. We compare it with many other prevalent compression and reconstruction techniques, including random projections and PCA-based techniques. We highlight a surprising result, namely that when the data are highly sparse in some basis, our technique may even outperform PCA-based compression.The contributions of this work are generic as our methodology is applicable to any sequential or highdimensional data as well as to any orthogonal data transformation used for the underlying data compression scheme.

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Section: Related Workmentioning

confidence: 99%

“…3 for an example). The bulk of related work on compression and distance estimation used the same sets of coefficients for all objects [7,8,9,10]. This simplified the distance estima- tion in the compressed domain.…”

Section: Introductionmentioning

confidence: 99%

Compressive mining: fast and optimal data mining in the compressed domain

2014

View full text Add to dashboard Cite

show abstract

“…The majority of data compression techniques for sequential data use the same set of low-energy coefficients whether using Fourier [6,7], Wavelets [8,9] or Chebyshev polynomials [10] as the orthogonal basis for representation and compression. Using the same set of orthogonal coefficients has several advantages: a) it is immediate to compare the respective coefficients, b) spacepartitioning indexing structures (such as R-trees) can be directly used on the compressed data, and c) there is no need to store also the indices of the basis functions that the stored coefficients correspond to.…”

Section: Related Workmentioning

confidence: 99%

Optimal Distance Estimation Between Compressed Data Series

Freris¹,

Vlachos²,

Kozat

2012

Proceedings of the 2012 SIAM International Conference on Data Mining

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Most real-world data contain repeated or periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate complete orthogonal basis (e.g., Fourier, Wavelets, Karhunen-Loève expansion or Principal Components).In the face of ever increasing data repositories and given that most mining operations are distance-based, it is vital to perform accurate distance estimation directly on the compressed data. However, distance estimation when the data are represented using different sets of coefficients is still a largely unexplored area. This work studies the optimization problems related to obtaining the tightest lower/upper bound on the distance based on the available information. In particular, we consider the problem where a distinct set of coefficients is maintained for each sequence, and the L2-norm of the compression error is recorded. We establish the properties of optimal solutions, and leverage the theoretical analysis to develop a fast algorithm to obtain an exact solution to the problem. The suggested solution provides the tightest provable estimation of the L2-norm or the correlation, and executes at least two order of magnitudes faster than a numerical solution based on convex optimization. The contributions of this work extend beyond the purview of periodic data, as our methods are applicable to any sequential or high-dimensional data as well as to any orthogonal data transformation used for the underlying data compression scheme.

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“…Researchers have studied series compression in the context of many different applications (Box, Jenkins, and Reinsel 2008;Montgomery, Jennings, and Kulahci 2008;Cryer and Chan 2009), from the analysis of financial data (Fu, Chung, Luk, and Ng 2008;Dorr and Denton 2009) to distributed monitoring systems (Di, Jin, Li, Tie, and Chen 2007) and manufacturing applications (Eruhimov, Martyanov, Raulefs, and Tuv 2006). In particular, they have considered various feature sets for compressing series and measuring similarity between them.…”

Section: Introductionmentioning

confidence: 99%

Compression of time series by extracting major extrema

Fink

Gandhi

2010

Journal of Experimental & Theoretical Artificial Intelligen

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We formalise the notion of important extrema of a time series, that is, its major minima and maxima; analyse the basic mathematical properties of important extrema; and apply these results to the problem of time-series compression. First, we define the numeric importance levels of extrema in a series, and present algorithms for identifying major extrema and computing their importances. Then, we give a procedure for fast lossy compression of a time series at a given rate, by extracting its most important minima and maxima, and discarding the other points.

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Combining Unsupervised and Supervised Approaches to Feature Selection for Multivariate Signal Compression

Cited by 4 publications

References 7 publications

Compressive mining: fast and optimal data mining in the compressed domain

Compressive mining: fast and optimal data mining in the compressed domain

Optimal Distance Estimation Between Compressed Data Series

Compression of time series by extracting major extrema

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