• Communications for Statistical Applications and Methods
• /
• 제31권2호
• /
• pp.179-189
• /
• 2024

In multivariate regression with a high-dimensional response Y ∈ ℝ^r and a relatively low-dimensional predictor X ∈ ℝ^p (where r ≥ 2), the statistical analysis of such data presents significant challenges due to the exponential increase in the number of parameters as the dimension of the response grows. Most existing dimension reduction techniques primarily focus on reducing the dimension of the predictors (X), not the dimension of the response variable (Y). Yoo and Cook (2008) introduced a response dimension reduction method that preserves information about the conditional mean E(Y | X). Building upon this foundational work, Yoo (2018) proposed two semi-parametric methods, principal response reduction (PRR) and principal fitted response reduction (PFRR), then expanded these methods to unstructured principal fitted response reduction (UPFRR) (Yoo, 2019). This paper reviews these four response dimension reduction methodologies mentioned above. In addition, it introduces the implementation of the mbrdr package in R. The mbrdr is a unique tool in the R community, as it is specifically designed for response dimension reduction, setting it apart from existing dimension reduction packages that focus solely on predictors.

• Communications for Statistical Applications and Methods
• /
• 제22권2호
• /
• pp.173-180
• /
• 2015

We propose a selection procedure of principal components in principal component regression. Our method selects principal components using variable selection procedures instead of a small subset of major principal components in principal component regression. Our procedure consists of two steps to improve estimation and prediction. First, we reduce the number of principal components using the conventional principal component regression to yield the set of candidate principal components and then select principal components among the candidate set using sparse regression techniques. The performance of our proposals is demonstrated numerically and compared with the typical dimension reduction approaches (including principal component regression and partial least square regression) using synthetic and real datasets.

• Communications for Statistical Applications and Methods
• /
• 제29권6호
• /
• pp.721-733
• /
• 2022

In this paper we compare parameter estimation by Grassmann manifold optimization and sequential candidate set algorithm in a structured principal fitted component (PFC) model. The structured PFC model extends the form of the covariance matrix of a random error to relieve the limits that occur due to too simple form of the matrix. However, unlike other PFC models, structured PFC model does not have a closed form for parameter estimation in dimension reduction which signals the need of numerical computation. The numerical computation can be done through Grassmann manifold optimization and sequential candidate set algorithm. We conducted numerical studies to compare the two methods by computing the results of sequential dimension testing and trace correlation values where we can compare the performance in determining dimension and estimating the basis. We could conclude that Grassmann manifold optimization outperforms sequential candidate set algorithm in dimension determination, while sequential candidate set algorithm is better in basis estimation when conducting dimension reduction. We also applied the methods in real data which derived the same result.

• Communications for Statistical Applications and Methods
• /
• 제31권2호
• /
• pp.235-246
• /
• 2024

In high-dimensional data analysis, sufficient dimension reduction (SDR) has been considered as an attractive tool for reducing the dimensionality of predictors while preserving regression information. The principal support vector machine (PSVM) (Li et al., 2011) offers a unified approach for both linear and nonlinear SDR. This article comprehensively explores a variety of SDR methods based on the PSVM, which we call principal machines (PM) for SDR. The PM achieves SDR by solving a sequence of convex optimizations akin to popular supervised learning methods, such as the support vector machine, logistic regression, and quantile regression, to name a few. This makes the PM straightforward to handle and extend in both theoretical and computational aspects, as we will see throughout this article.

• 한국산업융합학회 논문집
• /
• 제5권1호
• /
• pp.33-38
• /
• 2002

This paper proposes an efficient method for improving the performance of polynomial adaline using the dimension reduction of independent variables. The adaptive principal component analysis is applied for reducing the dimension by extracting efficiently the features of the given independent variables. It can be solved the problems due to high dimensional input data in the polynomial adaline that the principal component analysis converts input data into set of statistically independent features. The proposed polynomial adaline has been applied to classify the patterns. The simulation results shows that the proposed polynomial adaline has better performances of the classification for test patterns, in comparison with those using the conventional polynomial adaline. Also, it is affected less by the scope of the smoothing factor.

• 한국지리정보학회지
• /
• 제7권4호
• /
• pp.24-33
• /
• 2004

원격탐사(remote sensing) 기술의 비약적인 발전과 함께 위성 영상데이터의 분광대역수가 급속히 증가하고 있다. 대역수의 증가로 영상데이터량이 급격히 증가하게 되고, 이에 따라 이들 데이터를 처리하기 위해서는 처리속도가 빠른 영상처리 기술이 필요하게 되었다. 분광 대역 수를 줄여 빠르게 처리하는 한가지 방법으로 널리 사용되고 있는 것이 주성분 변환법이다. 본 논문에서는 주성분 변환법에 대한 처리과정에 대해 논하였으며, 위성 영상데이터를 주성분 변환한 결과인 주성분 영상데이터를 분석하였다. 분석결과 실험 영상데이터의 경우, 3개의 주성분($PC_1$, $PC_2$, $PC_3$)의 누적 백분율 분산 값이 99.1%로 이는 3개의 주성분이 거의 대부분의 정보를 가지고 있음을 알 수 있었다. 3개의 주성분 영상데이터만을 사용한다면 데이터 저장을 위한 메모리 용량이나 데이터 전송시간 및 처리시간을 크게 감소시킬 수 있다. 또한 본 논문에서는 주성분 영상데이터를 최대유사분류법과 신경회로망을 이용한 다층 퍼셉트론 분류법으로 분류하고 결과를 평가한 후, 주성분 변환법이 갖는 차원축소 효과를 분석하였다. 분석결과 주성분 3개를 사용한 분류결과와 주성분 6개를 사용한 분류결과간의 분류정답률이 크게 차이가 나지 않았다. 이는 분류에 사용하는 영상데이터 수를 6개 차원에서 3개 차원으로 줄여도 비슷한 분류성능을 얻을 수 있음을 확인할 수 있었다.

• 정보처리학회논문지B
• /
• 제15B권4호
• /
• pp.285-292
• /
• 2008

색상 히스토그램은 영상의 색상 특징을 표현하기 위한 특징 벡터로 빈번히 사용되지만, 고차원의 특징 벡터를 생성하므로 효율성의 면에서 한계점을 갖고 있다. 본 논문에서는 주어진 차량 영상의 색상 히스토그램에 PCA (principal components analysis) 기법을 적용하여 특징 벡터의 차원을 축소시키는 방법을 제안한다. 차원이 축소된 특징 벡터들에 대해서는 SVM (support vector machine) 기법을 적용하여 차량 색상을 인식하기 위해 사용한다. 특징 벡터의 차원을 1/32로 축소한 결과, 차원이 축소되기 이전의 특징 벡터와 비교하여 약 1.42%의 미소한 차이로 색상 인식 성공률이 감소하였다. 또한, 색상 인식의 수행 시간은 1/31로 단축됨으로써 효율적으로 색상 인식을 수행할 수 있었다.

• Journal of the Korean Statistical Society
• /
• 제25권1호
• /
• pp.49-66
• /
• 1996

The singular value decomposition is one of the most useful methods in the area of matrix computation. It gives dimension reduction which is the centeral idea in many multivariate analyses. But this method is not resistant, i.e., it is very sensitive to small changes in the input data. In this article, we derive the resistant version of singular value decomposition for principal component analysis. And we give its statistical applications to biplot which is similar to principal component analysis in aspects of the dimension reduction of an n x p data matrix. Therefore, we derive the resistant principal component analysis and biplot based on the resistant singular value decomposition. They provide graphical multivariate data analyses relatively little influenced by outlying observations.

• Communications for Statistical Applications and Methods
• /
• 제19권4호
• /
• pp.559-569
• /
• 2012

Compositional data consist of compositions that are non-negative vectors of proportions with the unit-sum constraint. In disciplines such as petrology and archaeometry, it is fundamental to statistically analyze this type of data. Aitchison (1983) introduced a log-contrast principal component analysis that involves logratio transformed data, as a dimension-reduction technique to understand and interpret the structure of compositional data. However, the analysis is not usable when zero values are present in the data. In this paper, we introduce 4 possible methods to reduce the dimension of compositional data with zero values. Two real data sets are analyzed using the methods and the obtained results are compared.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• 제12권1호
• /
• pp.1-5
• /
• 2012

Data reduction has been used widely in data mining for convenient analysis. Principal component analysis (PCA) and factor analysis (FA) methods are popular techniques. The PCA and FA reduce the number of variables to avoid the curse of dimensionality. The curse of dimensionality is to increase the computing time exponentially in proportion to the number of variables. So, many methods have been published for dimension reduction. Also, data augmentation is another approach to analyze data efficiently. Support vector machine (SVM) algorithm is a representative technique for dimension augmentation. The SVM maps original data to a feature space with high dimension to get the optimal decision plane. Both data reduction and augmentation have been used to solve diverse problems in data analysis. In this paper, we compare the strengths and weaknesses of dimension reduction and augmentation for classification and propose a classification method using data reduction for classification. We will carry out experiments for comparative studies to verify the performance of this research.