Distance-based linear discriminant analysis for interval-valued data

Ramos-Guajardo, Ana Belén; Grzegorzewski, Przemysław

doi:10.1016/j.ins.2016.08.068

Cited by 27 publications

(12 citation statements)

References 37 publications

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“…A predominant approach to handle interval‐valued data as an entire entity, which can be found in the literature, especially associated with the linear regression analysis for interval‐valued data, classification or hypotheses testing, is sometimes called the distance‐based methodology . Its usefulness results from many theoretical and practical reasons summarized in .…”

Section: Nonparametric Tests In the Ontic Perspectivementioning

confidence: 99%

“…3,4 Interval-valued data that appear in different contexts drew the attention of many researchers. Various problems concerning interval-valued data in regression analysis, [5][6][7][8][9] time series, 10 principal component analysis, 11,12 correlation analysis, 13,14 classification, 9,[15][16][17][18][19][20][21] clustering, 22,23 analysis of variance, 24 and hypothesis testing [25][26][27][28][29][30][31][32][33] have been deeply studied in the literature.…”

Section: Introductionmentioning

confidence: 99%

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The sign test and the signed‐rank test for interval‐valued data

Grzegorzewski

Śpiewak

2019

Int J Intell Syst

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Two versions of the generalized sign test and the signed‐rank test for interval‐valued data (both for one‐sample and paired two‐sample problem) are proposed. These two versions correspond to different possible views on the interval outcomes of the experiment—either the epistemic or the ontic one. Each view yields its own approach to data analysis which results in different test construction and the way of carrying on the statistical inference.

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Section: Nonparametric Tests In the Ontic Perspectivementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The sign test and the signed‐rank test for interval‐valued data

Grzegorzewski

Śpiewak

2019

Int J Intell Syst

Self Cite

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“…The researches on IVD in recent years are mainly focusing on clustering analysis [9], regression analysis [10], principal component analysis [11]- [14] and discriminant analysis [15]- [23], less on classification tasks. Typical classification methods cannot fit for processing IVD directly because they do not address the inherent uncertainty of IVD.…”

Section: Introductionmentioning

confidence: 99%

An Interval-Valued Data Classification Method Based on the Unified Representation Frame

Qi¹,

Guo²,

Artem³

et al. 2020

IEEE Access

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Interval-valued data (IVD) is a kind of data where each feature is an interval. The midpoint and boundary are the two commonly used methods for representing IVD. However, their structure information (such as location, size) may be incomplete because only midpoint or endpoint is adopted which will lead to poor results of data processing. To better depict the structural information of IVD, a unified representation frame (URF) for IVD is proposed. It not only takes into account the size and location information, but the relationship between them as well. This frame can also represent the midpoint and boundary methods in a unified way. Besides, symmetrical uncertainty (SU) is adopted to measure the relationship between features and classes quantitatively, and irrelevant features will be eliminated based on SU. The proposed URF_ SU is applied in some traditional classifiers like LIBSVM, CART Tree and KNN. The experimental results on synthetic and real-world datasets demonstrate that the proposed approach is more effective than other representation methods of IVD in classification tasks. INDEX TERMS Interval-valued data, unified representation frame, symmetrical uncertainty, feature selection.

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“…Interval data appear when dealing with different experimental studies involving ranges, fluctuations, subjective perceptions, censored and grouped data, among others (see, for instance, [2,8,13,14,17,18,23,24,28]).…”

Section: Introductionmentioning

confidence: 99%

“…Random intervals have been shown to be suitable in different settings. Regarding classification and discriminant analysis for interval data different works has been developed in [8,24,28,32], to mention only a few. In addition, the problem of interval data in regression analysis has been tackled, for instance, in [4,5,10,9,29].…”

Section: Introductionmentioning

confidence: 99%

Testing the degree of overlap for the expected value of random intervals

Ramos-Guajardo

González‐Rodríguez

Colubi

2020

International Journal of Approximate Reasoning

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Some hypothesis tests for analyzing the degree of overlap between the expected value of random intervals are provided. For this purpose, a suitable measure to quantify the overlapping grade between intervals is considered on the basis of the Szymkiewicz-Simpson coefficient defined for general sets. It can be seen as a kind of likeness index to measure the mutual information between two intervals. On one hand, an estimator for the proposed degree of overlap between intervals is provided and its strong consistency is analyzed. On the other hand, two tests are also proposed in this framework: a one-sample test to examine the degree of overlap between the expected value of a random interval and a given interval, and a two-sample test to check the degree of overlap between the expected value of two random intervals. To solve such hypothesis tests, two statistics are suggested and their limit distributions are studied by considering both asymptotic and bootstrap techniques. Their power has been also explored by means of local alternatives. In addition, some simulation studies are carried out to investigate the behavior of the proposed approaches. Finally, the performance of the tests is also reported in a real-life application.

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Distance-based linear discriminant analysis for interval-valued data

Cited by 27 publications

References 37 publications

The sign test and the signed‐rank test for interval‐valued data

The sign test and the signed‐rank test for interval‐valued data

An Interval-Valued Data Classification Method Based on the Unified Representation Frame

Testing the degree of overlap for the expected value of random intervals

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