Data dimensionality estimation methods: a survey

Camastra, Francesco

doi:10.1016/s0031-3203(03)00176-6

Cited by 236 publications

(174 citation statements)

References 68 publications

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“…(14)) and percentil75 (Eq. (15)) are used accordingly to their implementation in Camastra (2003). According to the Fig.…”

Section: Descriptors Based On First Order Statisticsmentioning

confidence: 99%

“…The fractal dimension has found a number of applications in various data analysis studies (Camastra, 2003;Rozza et al, 2012) and, particularly, in image analysis Backes and Bruno, 2012;Bruno et al, 2008). Actually, as stated in Mandelbrot (1983) and Falconer (2003), natural objects cannot be well described using Euclidean geometry but using persistent self-repeating patterns, like those present in fractal objects.…”

Section: Volumetric Fractal Dimensionmentioning

confidence: 99%

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Gabor wavelets combined with volumetric fractal dimension applied to texture analysis

Zuñiga

Florindo

Bruno

2014

Pattern Recognition Letters

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a b s t r a c tTexture analysis and classification remain as one of the biggest challenges for the field of computer vision and pattern recognition. On this matter, Gabor wavelets has proven to be a useful technique to characterize distinctive texture patterns. However, most of the approaches used to extract descriptors of the Gabor magnitude space usually fail in representing adequately the richness of detail present into a unique feature vector. In this paper, we propose a new method to enhance the Gabor wavelets process extracting a fractal signature of the magnitude spaces. Each signature is reduced using a canonical analysis function and concatenated to form the final feature vector. Experiments were conducted on several texture image databases to prove the power and effectiveness of the proposed method. Results obtained shown that this method outperforms other early proposed method, creating a more reliable technique for texture feature extraction.

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“…(14)) and percentil75 (Eq. (15)) are used accordingly to their implementation in Camastra (2003). According to the Fig.…”

Section: Descriptors Based On First Order Statisticsmentioning

confidence: 99%

Section: Volumetric Fractal Dimensionmentioning

confidence: 99%

Gabor wavelets combined with volumetric fractal dimension applied to texture analysis

Zuñiga

Florindo

Bruno

2014

Pattern Recognition Letters

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“…One of the most important arbitrarily assumed parameters is the reduced space dimension . It can be fixed initially using one of the methods for estimating a hidden dimension [37], or by taking a value resulting from other requirements, for example = 2 or = 3 to enable a suitable visualization of the investigated data set. It is worth remembering that the procedure applied earlier for generating an initial solution with the fixed parameter = − , creates a solution which does not always have a dimensionality identical to the assumed (as mentioned in the previous section).…”

Section: Comments and Suggestionsmentioning

confidence: 99%

Reduction of Dimension and Size of Data Set by Parallel Fast Simulated Annealing

Kulczycki

Łukasik

2014

Studies in Computational Intelligence

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Abstract.A universal method of dimension and sample size reduction, designed for exploratory data analysis procedures, constitutes the subject of this paper. The dimension is reduced by applying linear transformation, with the requirement that it has the least possible influence on the respective locations of sample elements. For this purpose an original version of the heuristic Parallel Fast Simulated Annealing method was used. In addition, those elements which change the location significantly as a result of the transformation, may be eliminated or assigned smaller weights for further analysis. As well as reducing the sample size, this also improves the quality of the applied methodology of knowledge extraction. Experimental research confirmed the usefulness of the procedure worked out in a broad range of problems of exploratory data analysis such as clustering, classification, identification of outliers and others.

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“…A central issue in dimension reduction is choosing a sensible number of dimensions to be retained. We refer to [10] for a review on this topic. Two kind of approaches have been proposed in the last decades for intrinsic dimension estimation.…”

Section: Introductionmentioning

confidence: 99%

Intrinsic dimension estimation by maximum likelihood in isotropic probabilistic PCA

Bouveyron

Celeux

Girard³

2011

Pattern Recognition Letters

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A central issue in dimension reduction is choosing a sensible number of dimensions to be retained. This work demonstrates the surprising result of the asymptotic consistency of the maximum likelihood criterion for determining the intrinsic dimension of a dataset in an isotropic version of Probabilistic Principal Component Analysis (PPCA). Numerical experiments on simulated and real datasets show that the maximum likelihood criterion can actually be used in practice and outperforms existing intrinsic dimension selection criteria in various situations. This paper exhibits and outlines the limits of the maximum likelihood criterion. It leads to recommend the use of the AIC criterion in specific situations. A useful application of this work would be the automatic selection of intrinsic dimensions in mixtures of isotropic PPCA for classification.

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Data dimensionality estimation methods: a survey

Cited by 236 publications

References 68 publications

Gabor wavelets combined with volumetric fractal dimension applied to texture analysis

Gabor wavelets combined with volumetric fractal dimension applied to texture analysis

Reduction of Dimension and Size of Data Set by Parallel Fast Simulated Annealing

Intrinsic dimension estimation by maximum likelihood in isotropic probabilistic PCA

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