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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Journal of the Indonesian Mathematical Society Kalbiscientia Jurnal Sains dan Teknologi
Rahmat Sagara
Department of Mathematics Education - Sampoerna School of Education
Civil Engineering, Building, Construction & Architecture Computer Science & IT Industrial & Manufacturing Engineering Mathematics Mechanical Engineering

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THE NEW NOTION DISTANCE OF CONTENT BASED IMAGE RETRIEVAL (CBIR) Herwindiati, Dyah E.; Isa, Sani M.; Sagara, Rahmat
Journal of the Indonesian Mathematical Society Volume 16 Number 1 (April 2010)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.16.1.31.51-67

Abstract

This paper proposes a new notion distance on the CBIR process whichis derived from the measure of multivariate dispersion called vector variance (VV).The minimum vector variance (MVV) estimator is robust estimator having the highbreakdown point. The CBIR is a retrieval technique using the visual informationby retrieving collections of digital images. The process of retrieval is carried outby measuring the similarity between query image and the image in the databasethrough similarity measure. Distance is a metric often used as similarity measureon CBIR. The query image is relevant to an image in the database if the value ofsimilarity measure is 'small'. This means that a good CBIR retrieval system mustbe supported by an accurate similarity measure. The classical distance is generatedfrom the arithmetic mean which is vulnerable to the masking e®ect. The appearanceof extreme data causes the in°ation of deviation of the arithmetic mean, this impliesthe distance between the extreme data or the outlier becomes closer than it supposedto be. In the end of section we discuss the high performance of the MVV robustdistance to CBIR process.DOI : http://dx.doi.org/10.22342/jims.16.1.31.51-67
Sebuah Telaah Elips dan Lingkaran Melalui Sebuah Pendekatan Aljabar Matriks Sagara, Rahmat
CAUCHY Vol 1, No 2 (2010): CAUCHY
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (136.652 KB) | DOI: 10.18860/ca.v1i2.1709

Abstract

In this article, ellipse and circle will be learnt in depth via matrix algebra approach. The discussion of the both is started from their classic definition continued by surveying ellipse in matrix form. During the survey, some properties about ellipse will be explained and also, the procedure in drawing the figures can be obtained geometrically using some aspect in geometry: rotation and translation. At the end of the discussion, the new definition of the figures is deduced. Both of them are defined as” a set of points in a plane that are the same distance from a fixed point” but in different point of view about the ‘distance’. The ‘distance’ in the definition is derived from different norm definition. The difference lies on the positive definite matrix used in the norm definition. Base on the new definition, we’ll have the conclusion that circle is a special type of ellipse.
Pengembangan Bagan Kendali 3 Sigma Berbasis Simulasi Untuk Pengawasan Variabilitas Proses Multivariat Sagara, Rahmat; Umam, Khoirul
KALBISCIENTIA Jurnal Sains dan Teknologi Vol. 6 No. 2 (2019): Sains dan Teknologi
Publisher : Institut Teknologi dan Bisnis Kalbis

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Abstract

This article describes a method in developing control charts for generalized variance as a quality statistics in terms of process variability through simulation. Mathematical equation that maps sample size n and number of quality variables p onto constant multiplier of standard deviation K is obtained thorough least square method using simulated data. The constant K for a certain n and p is used for control charts with the upper control limits of UCL=μ+Kσ where μ and σ are the mean and the standard deviation of the generalized variance, respectively. The simulation of finding the constant K is used with the constraint of 3 sigma paradigm.
Co-Authors Dyah E. Herwindiati Khoirul Umam Sani M. Isa