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목적: 본 논문은 저가화장품 기업의 시장경쟁력 향상과 효과적인 의사결정을 위한 정보를 제공하고자 한다. 경쟁시장에서 소 비자들에게 상대적으로 저평가되어 있는 특정 저가화장품 기업의 벤치마킹을 통해 시장경쟁력 강화를 위한 positioning map과 repositioning map 전략에 대한 연구를 실시하였다. 방법: 본 연구를 수행하기 위한 자료 수집은 2017년 3월 20일부터 4월 21일 까지 진행되었다. 저가화장품을 사용한 경험이 있는 성인 여성을 대상으로 편의 표집하였으며, 배포한 총 300부 중 22부의 부적 합한 설문지를 제외하고 278부를 회수하여 최종 자료로 사용하였다. 수집된 자료는 SPSS 통계 프로그램을 사용하여 빈도 분석과 biplot 분석을 실시하였으며, analytic hierarchy process (AHP) 통계 프로그램을 사용하여 쌍대비교 분석도 실시하였다. 결과: 미 샤 화장품 브랜드를 대상으로 벤치마킹 하여 repositioning한 결과 미샤 화장품 브랜드의 시장 점유율이 2위로 상승하여 시장경쟁 력 1위인 이니스프리 화장품 브랜드와 차이는 7.2%가 나는 것으로 파악되었다. 현재의 positioning에서 미샤의 점유율은 20.20% 이었으나 repositioning 후의 점유율은 27.76%가 되어 7.56%만큼 점유율이 증가하는 것을 알 수 있었다. 결론: 시장경쟁력 강화를 위한 repositioning 전략에 관한 연구는 가장 시장경쟁 우위가 있는 평가요소를 대상으로 벤치마킹 하여 특정 저가화장품 브랜드를 repositioning함으로써 저가화장품 기업의 한정적인 자원배분 문제에 효율적인 해결 방안을 제시해 줄 수 있는 것으로 기대할 수 있다.

Purpose: This study was performed to provide low-cost cosmetic companies with useful information to enhance their market competitiveness and decision making. We used a positioning map to demonstrate how repositioning the map strategy could enhance market competitiveness via benchmarking of a specific low-cost cosmetics brand which was relatively underestimated in the market. Methods: The data for this study were collected from March 20 to April 21, 2017. Adult women with histories of low-cost cosmetics use were recruited via convenience sampling. We distributed 300 questionnaires; 22 questionnaires with inadequate responses were excluded and 278 questionnaires were used as the final data, which were analyzed by frequency and biplot analyses using the SPSS statistical program. In addition, the analytic hierarchy process (AHP) statistical program was used to perform a pairwise comparison analysis. Results: When the MISSHA cosmetic brand was benchmarked and repositioned, its market share increased to second highest. There was a 7.2% difference from the innisfree cosmetic brand, which occupied the first place in market competitiveness. In the current positioning, MISSHA's market share was 20.2%, but its market share after repositioning was 27.76%, which reveals that its market share increased by 7.56%. Conclusion: The repositioning strategy for strengthening market competitiveness can act as an efficient problem solving method for allocation of restricted resources by repositioning. We were able to reposition a specific low-cost cosmetic brand through benchmarking, using evaluation factors of the market’s most competitive low-cost cosmetic brand.

目的: 本文为提高低价化妆品企业的市场竞争力和有效决策提供了有益的信息，通过在竞争市场消费者们相对 低评价的特定低价化妆品企业的标杆管理来强化市场竞争，对于定位图，再定位图战略进行了研究。方法: 资 料收集从2017年3月20日开始到4月21日为止。以具有低价化妆品使用经验的成年女性为对象，随机抽样并 分发调查文卷，从300份调查问卷中，除去不合格的22份以外，剩下的278份回收并用来做撰写论文的最终材 料。结果: 以谜尚化妆品品牌为对象进行了标杆管理和重新定位，结果显示: 谜尚化妆品品牌的市场份额上升至 第二名，且与市场竞争力最强的悦诗风吟化妆品品牌相差7.2％。在目前的定位中，谜尚化妆品的市场份额为 20.20％，但重新定位后的市场份额为27.76％，这表明市场份额增长了7.56％。结论: 为了强化市场竞争力， 关于重新定位战略的研究，以市场竞争优势最高的评价要素为对象进行标杆管理，通过重新定位特定低价化妆 品品牌，提出对低价化妆品企业的限定性资源分配问题提出有效的解决方案。

In this paper, for competitive advantage in a rapidly change fast-food market. Analysis techniques bioplot was used for optimum proportioning strategies and repositioning strategy of fastfood outlet. McDonald was found to be the most highly competitive markets, but Lotteria was shown to the third. Lotteria with a 20.57% market share is not a good strategy, to avoid competition with a 34.59% market share of McDonald. Run by repositioning strategy that benchmark five evaluation factors, market share increased by 29.96%, and has risen to second. Biplot analysis for limited companies of resource allocation problems, and give efficient problem solving methods.

일반적으로 타이어 제조공학에 있어서 측정되는 자료는 여러개의 설계인자와 성능 특성치가 사용된 다변량 자료행렬로 주어지는데, 이러한 자료행렬의 중요한 특성중의 하나는 각 반응값들이 서로 다른 것들과 높은 상관관곌르 가질 수 있다는 것이다. 따라서 본 연구는 이러한 복잡한 성격을 갖는 자료행렬의 분석에 적합한 biplot 작성의 수학적 이론을 알아보고, 또한 각 변수들의 구조적 특성 및 내재한 상호 관련성을 다변량 분산분석 biplot과 다반응치 희귀모형 biplot을 이용하여 포괄적으로 고찰하였다.

It is essential in modern industry that quality and procuctivity are improved continuously. To accomplish this purpose, quality control must be maintained in all parts of a company. Recently, some tire manufacture companies are beginning to show interest in quality control. They have tried to achive some results through the statistical analysis for the experimental data which has accumulated up to now and then they strive to determine the structural relationship between the design factors in tire construction and tire performance characteristics. The measurement data obtained from the construction engineering is given in multivariate form owing to the various properties found in tire design components as wll as in performance. Also it may be existed the relationship among the multimple response variables. Thus we proposes the use of the biplot graphical display as an analytic tool of data matrices with complex respects. The proposed biplots are also availalbe to understand both the underlying structure of the data and the roles played by the different components. In particular, we consider the matter of how best to use the biplots in the maltivariate analysis of variance and multiple response data. Finally we apply this method to analyze the actual data.

Ranked data are widely used in the area of social sciences, for instance in polls and preference surveys, in which a number of objects (or stimuli) are evaluted and ranked by a panel of judges (or subject) according to their preference. We propose a graphical method for ranked data by quantifying objects and judges. In a plot for judges, the interpoint distances can be interpreted as Spearman or Kendall distance between two rankings given by respective judges. Similarly, we also construct a plot for objects with a sensible relationship to the previous plot for judges.

When a pair of rankings arrives simultaneously, it might not be natural to condition on one part of paired rankings or on the other part of paired rankings. Such simultaneously paired rankings need symmetric approach.In this study, we propose biplot for simultaneously paired rankings data, based on quantification. The biplot, originated from Gabriel (1971), is such a nice graphical tool that subjects(observations) as well as objects(variables) can be plotted to show off mutual relationships. And we also propose a procedure for the within-pair difference in simul- taneously paired rankings.

Biplot is a graphical display of the rows and columns of an n${\times}$p data matrix. In particular, Gabriel (1995) suggested the MANOVA biplot using singular value decomposition (SVD) with the averages of response variables according to treatment groups. But his biplot may cause wrong results by disregarding them when there exist covariate effects. In this paper, we will provide the MANCOA biplot based on the SVD with the parameter estimates for MANCOVA model when there exist covariate effects.

We consider support vector machines(SVM) to predict Y with p numerical variables $X_1$, ${\ldots}$, $X_p$. This paper aims to build a biplot of p explanatory variables, in which the first dimension indicates the direction of SVM classification and/or regression fits. We use the geometric scheme of kernel principal component analysis adapted to map n observations on the two-dimensional projection plane of which one axis is determined by a SVM model a priori.

Canonical correlation analysis is a multivariate technique for identifying and quantifying the statistical relationship between two sets of variables. Like most multivariate techniques, the main objective of canonical correlation analysis is to reduce the dimensionality of the dataset. It would be particularly useful if high dimensional data can be represented in a low dimensional space. In this study, we will construct statistical graphs for paired sets of multivariate data. Specifically, plots of the observations as well as the variables are proposed. We discuss the geometric interpretation and goodness-of-fit of the proposed plots. We also provide a numerical example.

Simple canonical correlation biplot is a graphical method to investigate two sets of variables and observations in simple canonical correlation analysis. If we consider the set of covariate variables that linearly affects two sets of variables, we can apply the partial canonical correlation biplot in partial canonical correlation analysis that removes the linear effect of the set of covariate variables on two sets of variables. On the other hand, we consider the set of covariate variables that linearly affect one set of variables but not the other. In this case, if we apply the simple or partial canonical correlation biplot, we cannot clearly interpret other two sets of variables. Therefore, in this study, we will apply the semi-partial canonical correlation analysis of Timm (2002) and remove the linear effect of the set of covariate variables on one set of variables but not the other. And we suggest the semi-partial canonical correlation biplot for interpreting the semi-partial canonical correlation analysis. In addition, we will compare shapes and shape the variabilities of the simple, partial and semi-partial canonical correlation biplots using a procrustes analysis.

반응표면분석에서 다반응값의 최적화 문제는 다반응값 최적화 문제보다 복잡하다. 이런 다반응값 문제에서 반응변수들이나 설명변수 상호간의 곤계나 중요성 등을 평가하는 것은 중요하다. 이러한 평가를 위하여 biplot가 유용한 그림도구로 쓰일 수 있다.

반응표면분석에서 다반응값의 최적화 문제는 단반응값 최적화문제보다 복잡하다. 이런 다반응값 문제에서 반응변수들이나 설명변수 상호간의 관계나 중요성 등을 평가하는 것은 중요하다. 이러한 평가를 위하여 biplot를 이용할 수 있는데, 1차 회귀모형이 적합치 않은 경 우, 2차 회귀모형을 위한 순차적 실험계획을 이용하여 2차 회귀 모형에 대응되는 biplot를 그려 선형 및 비선형효과를 알 수 없게 된다.

The analysis of data from a multiresponse experiment requires careful consideration of the multivariate nature of the data. In a multiresponse sitation, the optimization problem is more complex than in the single response case. The biplot is a graphical tool which make the analyst to understand the correlation of the response variables, the relation of the response variables arid the explanatory variables and the relative importance of the explanatory variables. In case of good fitting of the first order model, we can draw the biplot with the first order experimental design. Otherwise, we can make the biplot with the second order experimental design by adding other experimental points.

Biplots are the multivariate analogue of scatter plots. They are useful for giving a graphical description of the data matrix, for detecting patterns and for displaying results found by more formal methods of analysis. Nevertheless, when some values are missing in data matrix, most biplots are not directly applicable. In particular, we are interested in the shape variability of principal component biplot which is the most popular in biplots with missing values. For this, we estimate the missing data using the EM algorithm and mean imputation according to missing rates. Even though we estimate missing values of biplot of incomplete data, we have different shapes of biplots according to the imputation methods and missing rates. Therefore we propose a RMS(root mean square) for measuring and comparing the shape variability between the original biplots and the estimated biplots.

In the genetic association study of complex diseases, we may obtain several continuous phenotypes which are correlated to each other. The purpose of the analysis is to identify the relationship between genetic polymorphism and multiple phenotypes. Performing univariate analysis separately for each phenotype is common, but it has limitations in detecting pleiotropic genes. Its performance tends to deteriorate in the multiple testing problems. In this study, we suggest to employ a canonical correlation biplot (CCB) and a semi-partial canonical correlation biplot (SPCCB) as the multivariate approaches. The CCB summarizes the correlation between linear composites for phenotypes and genotypes. Also, it produces three kinds of graphs which are able to catch the relationship between genotypes, between phenotypes and ultimately between genotypes and phenotypes at a glance. SPCCB is an extension of the CCB by permitting covariates. We show the results of these methods by applying them to a sample genetic data as an illustration.

The AMMI (additive main effects and multiplicative interaction) and GGE (genotype main effect and genotype by environment interaction) biplot which were accounted for a substantial part of total sum of square in the analysis of variance suggested to be more appropriate models for explaining G $\times$ E interaction. The grain yield of total ten sesame genotypes was significantly affected by environment which explained 61% of total variation, whereas genotype and genotype x environment interaction (G $\times$ E) were explained 16%, 24% respectively. From the results of experiment, three genotypes Miryang49, Koppoom and Ansan were unstable, whereas other three genotypes Kyeongbuk18, Miryang50 and Kanghuk which were shorter projections to AEA ordinate were relatively stable over the environments. Yangbak which was closeness to the mean yield and short projection of the genotype marker lines was regarded as genotype indicating good performance with stability. Ansan, Miryang48 and Yangbaek showed the best performance in the environments of Naju, Suwon, Iksan and Andong. Similarly, genotype Miyrang47 exhibited the best performance in the environments of Chuncheon and Miryang. Andong is the closest to the ideal environment, and therefore, is the most desirable among eight environments.

범주형자료의 분석을 위한 통계적 기법으로 로그선형모형이나 로지스틱모형과 같은 모형을 이용한 분석기법과 행렬도와 같은 모형무관기법이 있다. 본 논문에서는 명목형 다항반응 로지스틱회귀모형의 차원축소된 공간인 차원에서의 표현과 이 모형이 적용될 수 있는 분할표자료에 대하여 행렬도를 이용하여 탐색적으로 분석이 가능함을 보이고 있다. 특히, 명목형 다항반응 로지스틱회귀모형에서의 설명변수와 반응변수간의 독립성을 행렬도를 활용하여 진단할 수 있음을 보였다. 즉, 모형무관기법의 행렬도를 통해 설명변수와 기준범주에 대한 다른 반응범주의 상대적 비율과의 대응관계가 나타나지 않을 경우 설명변수와 반응변수간의 독립성이 만족된다고 판단할 수 있으며 대응관계가 나타날 경우 이들 변수간의 독립성이 만족되지 않는다고 판단할 수 있다.

It is well known that there are two statistical techniques for the categorical data analysis. One is a technique using the model such as log-linear models or logistic models and the other is a model-free technique such as the biplot. In this paper, we show the -dimensional representation of multinominal logistic regression model and biplot analysis of this model.

행렬도는 자료행렬의 행과 열을 한 그림에 동시에 나타내어 다변량 자료의 결과 해석에 많은 이점을 주는 그림도구이다. Gabriel(1981)은 다변량 분산분석에서 주어진 변량 자료로부터 각 처리별 변수들의 평균값을 구하여 행렬도의 입력자료로 사용하고, 대수적으로는 비정칙값분해(singular value decomposition, SVD)를 하는 다변량 분산분석 행렬도(MANOVA biplot)를 제안했다. 그러나 이는 계산 과정이 복잡하고 실제 적용에서 해석상 안정적이지 못하다. 본 소고에서는 자료로부터 다변량 분산분석 모형의 계수행렬값을 추정하고 이것의 비정칙값 분해를 하여 행렬도분석을 하는 또 다른 다변량 분산분석 행렬도를 제안하려 한다.

Biplot is a graphical display of the rows and columns of an data matrix. In particular, Gabriel(1981) suggested a MANOVA biplot using singular value decomposition (SVD) with the averages of response variables according to treatment groups. But this biplot has a complicated calculation of algorithm and sometimes is not stable for interpretation of MANOVA model. In this paper, to overcome these problems, we will provide the biplot based on the SVD with the estimated parameter matrix in MANOVA.

행렬도(biplot)는 이원표 자료행렬(two-way data matrix)의 행과 열을 한 그림에 동시에 나타내는 탐색적 방법으로, 복잡한 다변량 분석 결과를 보다 쉽게 파악할 수 있는 장점이 있다. 특히 주성분인자 행렬도(principal component factor biplot; PCFB)는 인자분석을 통해서 변수들 간의 상호의존 구조를 탐색하기 위한 시각적 도구이다. 자료에 따라 잠재된 변수들이 독립(independent)이고 비가우시안(non-Gaussian) 분포를 가진다는 사전 정보가 있을 때, Jutten과 Herault (1991)가 제안한 독립성분분석(independent component analysis)을 이용한다. 이 경우 주성분법을 이용한 인자분석을 적용하면 원래 변수들의 상호 관계를 잘못 해석할 수도 있다. 따라서 본 논문에서는 자료에 따라 잠재된 변수들이 독립이고 비가우시안 분포를 가진다는 사전 정보가 있을 때, 독립성분분석을 응용하여 원래 변수들 간의 상호 관계를 기하학적으로 살펴볼 수 있는 시각적 도구인 독립성분 행렬도(independent component biplot; ICB)를 제안하려 한다.

Biplot is a useful graphical method to simultaneously explore the rows and columns of a two-way data matrix. In particular, principal component factor biplot is a graphical method to describe the interrelationship among many variables in terms of a few underlying but unobservable random variables called factors. If we consider the unobservable variables (which are mutually independent and also non-Gaussian), we can apply the independent component analysis decomposing a mixture of non-Gaussian in its independent components. In this case, if we apply the principal component factor analysis, we cannot clearly describe the interrelationship among many variables. Therefore, in this study, we apply the independent component analysis of Jutten and Herault (1991) decomposing a mixture of non-Gaussian in its independent components. We suggest an independent component biplot to interpret the independent component analysis graphically.

본 연구는 두 변수군의 관계가 공변량의 영향으로 왜곡될 수 있는 상황을 정확히 분석하기 위해, 기존 방법론을 확장한 이편정준상관분석을 이용하여 이를 시각화하기 위한 이편정준상관 행렬도를 제안하였다. 이는 두 변수군 모두에서 동일한 공변량을 제거하는 편정준상관이나 한 변수군에서만 제거하는 준편정준상관과 달리, 두 변수군 각각에 서로 다른 공변량을 독립적으로 제거함으로써 보다 왜곡 없는 정준상관 구조를 시각화하는 기법이다. 제안된 행렬도의 실증적 유용성을 검증하고자 2025년 기준 상위 50명의 경륜 선수 자료를 활용하였으며, 경기기록요인에서는 체격요인의 효과를, 기술요인에서는 개인특성요인의 효과를 제거하였다. 또한 기존의 정준상관 및 준편정준상관 행렬도와의 비교 분석을 수행하고, 프로크러스티즈 분석을 통해 행렬도 간의 형상 변동 차이를 검증하였다. 연구 결과, 경기기록요인과 기술요인 변수군은 각각 체격 및 개인특성이라는 서로 다른 공변량 변수군에 의해 구조적 왜곡이 발생하고 있음이 확인되었다. 특히 프로크러스티즈 통계량을 통해 양측의 공변량 변수군을 독립적으로 통제한 이편정준상관 행렬도가 자료의 구조를 가장 명확하게 반영하고 있음을 확인하였다. 결론적으로 본 연구는 다차원적 변수군 간의 복합적인 관계를 분석함에 있어 기존 방법론의 한계를 극복하고, 공변량 구조의 비대칭성을 반영할 수 있는 새로운 시각화 도구를 제안했다는 점에서 중요한 방법론적 의의를 지닌다.

To accurately analyze situations where the relationship between two sets of variables can be distorted by the influence of covariates, this study proposes a bi-partial canonical correlation biplot(BPCCB) based on bi-partial canonical correlation analysis. Unlike partial canonical correlation, which removes the same covariates from both sets of variables, or semi-partial canonical correlation, which removes them from only one set of variables, the proposed technique that visualizes a more distortion-free canonical correlation structure by independently removing different covariates from each of the two sets of variables. To test the empirical effectiveness of the BPCCB, data from the top 50 cycle racing riders in 2025 were analyzed. The analysis independently controlled for physique factors within race record factors and individual characteristic factors within skill factors. In addition, a comparative analysis was performed against the CCB and SPCCB, and the differences in shape variation among the biplots were verified through Procrustes analysis. The results confirmed that structural distortions occurred in both race record and skill factors, caused by distinct sets of covariates: physique and individual characteristics, respectively. In particular, Procrustes statistics confirmed that the BPCCB, which independently controls for sets of covariates on both sides, reflects the data structure most clearly without distortion. In conclusion, this study holds significant methodological implications by overcoming the limitations of existing approaches in analyzing complex relationships among multidimensional sets of variables and proposing a new visualization tool that reflects the asymmetry of covariate structures.

본 연구에서는 2004년 대한테니스협회(KTA)에 등록된 랭킹 100위권 이내의 남자선수 50명에 대한 공변량요인인 체격요인변수군의 체력요인변수군과 기초기술요인변수군에 모두 미치는 각 효과를 제거한 PCCB와 단지 체력요인변수군에서만 미치는 공변량요인 효과를 제거한 Choi, Choi(2012)의 SPCCB를 서로 비교하였다. 이미 Choi, Choi(2012)는 GCCB, PCCB 그리고 SCCB의 결과를 서로 비교하고 있다. 보다 구체적으로 두 행렬도의 차이점을 살펴보기 위하여 Choi, Choi (2010)에서와 같이 분석 대상인 테니스 선수를 전체선수, 상위랭킹과 하위랭킹 별로 고려하였다. 특히, 공변량인 체격요인변수군의 영향력이 상위랭킹선수와 하위랭킹선수에 따른 두 변수군에 대한 PCCB와 SPCCB에서 형상변동 차이를 프로크러스티즈 분석을 활용한 비교를 통하여 분명하게 보이는 것과는 매우 대조적으로 전체선수들 비교에서는 별 차이를 보이지 않아 랭킹별 비교가 필요함을 보여주었다.

The semi-partial canonical correlation biplot (SPCCB) is a two-dimensional graphical display for interpreting the semi-partial canonical correlation analysis that removed the linear effect of the set of covariate variables on one set of variables but not the other. Recently, Choi, Choi (2012) investigated the relationship between physical fitness and basic skill factors of KTA tennis players using the partial canonical correlation biplot (PCCB) that removed the linear effect of physique factors to be the set of covariate variables on two physical fitness and basic skill factors. However, we can recognize that physique factors is the set of covariate variables effecting on just only physical fitness but not basic skill factors. In this study, since Choi, Choi (2012) had compared G (generalized) CCB, PCCB and S (simple) CCB, we will investigate the relationship between physical fitness and basic skill factors of KTA tennis players using SPCCB and compare PCCB and SPCCB. We compare shapes and shape variabilities for these biplots using a procrustes analysis.