• The Korean Journal of Applied Statistics
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• v.19 no.3
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• pp.431-445
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• 2006

In this paper we review some methods for analyzing functional data and illustrate real application of functional data analysis. Representing methods for functional data by using basis function, analyzing functional variation by functional principal component analysis and functional linear models are reviewed. For a real application, we use temperature and precipitation data measured in Korea from the January of 1970 to the May of 2004. We apply functional principal component analysis for each data and test the significance of regional division done by using shining hours. We also estimate functional regression model for temperature and precipitation.

• The Korean Journal of Applied Statistics
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• v.28 no.5
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• pp.885-893
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• 2015

It is important to improve the forecasting accuracy of one-year-ahead seasonal factors in order to produce seasonally adjusted series of the following year. In this paper, seasonal factors of 8 monthly Korean economic time series are examined and forecast based on the functional principal component regression. One-year-ahead forecasts of seasonal factors from the functional principal component regression are compared with other forecasting methods based on mean absolute error (MAE) and mean absolute percentage error (MAPE). Forecasting seasonal factors via the functional principal component regression performs better than other comparable methods.

• The Korean Journal of Applied Statistics
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• v.30 no.1
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• pp.135-145
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• 2017

Principal component analysis (PCA) describes the variation of multivariate data in terms of a set of uncorrelated variables. Since each principal component is a linear combination of all variables and the loadings are typically non-zero, it is difficult to interpret the derived principal components. Sparse principal component analysis (SPCA) is a specialized technique using the elastic net penalty function to produce sparse loadings in principal component analysis. When data are structured by groups of variables, it is desirable to select variables in a grouped manner. In this paper, we propose a new PCA method to improve variable selection performance when variables are grouped, which not only selects important groups but also removes unimportant variables within identified groups. To incorporate group information into model fitting, we consider a hierarchical lasso penalty instead of the elastic net penalty in SPCA. Real data analyses demonstrate the performance and usefulness of the proposed method.

• Proceedings of the Korea Water Resources Association Conference
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• 2005.05b
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• pp.119-122
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• 2005

정규식생지수는 일반적으로 식생의 활력도를 나타나는 지표로서 널리 사용되고 있다. 최근에는 정규식생지수가 특정지역의 강우량과 온도의 계절 및 경년변화와 어떤 상관관계를 가지며 기후변화는 식생지수에 어떠한 영향을 미치는지 등에 관한 연구가 활발히 수행되고 있다. 본 연구에서는 1981년부터 2001년까지의 NOAA/AVHRR 영상으로부터 계산된 남한지역 정규식생지수의 주성분 분석을 통해 자료의 공간변화패턴을 분석하고 경험적 직교함수를 이용하여 시간적 변화 양상을 파악하였다. 분석결과 정규식생지수의 공간변화도는 첫 주성분에 의하여 약 $60\%$ 정도 설명되어지며 첫 주성분은 남한지역의 지형 자료 패턴을 따르고 두 번째 주성분은 전체 변화도의 약 $17\%$를 나타내며 강한 남북기울기를 보여주는 것은 계절변화와 상관한 위도변화에 따른 정규식생지수의 변화를 나타낸다. 그리고 소양강댐 및 안동댐 유역의 정규식생지수, 강우량 및 유입량 상관관계 분석 결과 정규식생지수의 계절변화와 경년변화는 강우량의 변화에 그리 민감하지 않은 것으로 나타났다.

• Proceedings of the Korea Water Resources Association Conference
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• 2017.05a
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• pp.154-154
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• 2017

전 세계적인 기후변동과 기후변화의 영향으로 대규모 인명 및 재산피해를 유발하는 자연재난의 빈도와 강도가 증가하고 있다. 이렇게 변화하는 상황에서 효율적인 대책을 수립하기 위해서는 재해에 노출된 특성을 지역적 특성과 함께 고려하여 지역별로 재해에 위험한 정도를 평가하는 것이 선행되어지고, 재난 피해 발생전에 피해 지역 및 범위를 예측하는 것이 필요하다고 판단된다. 따라서 본 연구에서는 국내 자연재난 피해의 65% 이상을 차지하는 호우피해를 대상으로 PSR(Pressure-State-Response) 구조를 이용하여 호우피해위험지수(Heavy rain Damage Risk Index, HDRI)를 제안하여 호우 위험도를 평가하고자하였다. 또한 도출된 지역별 위험등급에 따른 호우피해 예측함수를 개발하여 재해발생 전에 개략적인 피해의 범위를 예측하고자 하였다. 먼저 지역별 호우 위험도 평가를 위해 압력지표, 현상지표, 대책지표를 구축하고, 주성분분석을 이용하여 평가지표를 결정하였다. 결정된 평가지표를 동일한 가중치를 부여하여 호우피해위험지수를 도출하였다. 분석결과, 경기도 31개 지자체 중에서 가장 안전한 1등급인 지자체는 15개의 지자체로 나타났으며, 2등급인 지자체는 7개, 3등급인 지자체는 9개로 분류되었다. 지자체별 호우 위험도 등급에 따라서 재해기간별 총강우량, 재해일수, 선행강우량(1~5일), 지속시간별 최대강우량(1~24시간) 등의 자료를 설명변수로 구축하였고, 다중회귀모형과 주성분분석을 활용하여 예측함수를 개발하였다. 등급별 호우피해 예측함수는 N-RMSE가 12~18%로 호우피해를 적절하게 예측하는 것으로 평가되었다. 본 연구를 통해 지자체별 호우피해위험도 등급을 파악 할 수 있으며, 평가된 호우피해위험도 등급별로 호우피해 예측함수 개발을 통해 사전에 호우피해 발생 및 규모를 파악할 수 있게 되었다. 따라서 본 연구의 결과는 각 지자체 및 관련 부처에서 효과적인 방재체계를 수립하는데 있어 기초자료로 활용될 수 있을 것으로 판단된다.

• Journal of KIISE:Software and Applications
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• v.31 no.3
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• pp.361-368
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• 2004

The purpose of this study is to propose a new on-line nonlinear PCA(OL-NPCA) method for a nonlinear feature extraction from the incremental data. Kernel PCA(KPCA) is widely used for nonlinear feature extraction, however, it has been pointed out that KPCA has the following problems. First, applying KPCA to N patterns requires storing and finding the eigenvectors of a N${\times}$N kernel matrix, which is infeasible for a large number of data N. Second problem is that in order to update the eigenvectors with an another data, the whole eigenspace should be recomputed. OL-NPCA overcomes these problems by incremental eigenspace update method with a feature mapping function. According to the experimental results, which comes from applying OL-NPCA to a toy and a large data problem, OL-NPCA shows following advantages. First, OL-NPCA is more efficient in memory requirement than KPCA. Second advantage is that OL-NPCA is comparable in performance to KPCA. Furthermore, performance of OL-NPCA can be easily improved by re-learning the data.

• The Korean Journal of Applied Statistics
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• v.32 no.4
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• pp.607-618
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• 2019

A new and interesting task in statistics is to effectively analyze functional data that frequently comes from advances in modern science and technology in areas such as meteorology and biomedical sciences. Functional linear regression with scalar response is a popular functional data analysis technique and it is often a common problem to determine a functional association if a functional predictor variable affects the scalar response in the models. Recently, Kong et al. (Journal of Nonparametric Statistics, 28, 813-838, 2016) established classical testing methods for this based on functional principal component analysis (of the functional predictor), that is, the resulting eigenfunctions (as a basis). However, the eigenbasis functions are not generally suitable for regression purpose because they are only concerned with the variability of the functional predictor, not the functional association of interest in testing problems. Additionally, eigenfunctions are to be estimated from data so that estimation errors might be involved in the performance of testing procedures. To circumvent these issues, we propose a testing method based on fixed basis such as B-splines and show that it works well via simulations. It is also illustrated via simulated and real data examples that the proposed testing method provides more effective and intuitive results due to the localization properties of B-splines.

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.6
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• pp.735-740
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• 2012

In this paper, we introduce design methodologies of polynomial radial basis function neural network classifier with the aid of Principal Component Analysis(PCA) and Linear Discriminant Analysis(LDA). By minimizing the information loss of given data, Feature data is obtained through preprocessing of PCA and LDA and then this data is used as input data of RBFNNs. The hidden layer of RBFNNs is built up by Fuzzy C-Mean(FCM) clustering algorithm instead of receptive fields and linear polynomial function is used as connection weights between hidden and output layer. In order to design optimized classifier, the structural and parametric values such as the number of eigenvectors of PCA and LDA, and fuzzification coefficient of FCM algorithm are optimized by Artificial Bee Colony(ABC) optimization algorithm. The proposed classifier is applied to some machine learning datasets and its result is compared with some other classifiers.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.6
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• pp.642-653
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• 2008

This study deals with modeling of head-related transfer functions(HRTFs) using principal components analysis(PCA) in the time and frequency domains. Four PCA models based on head-related impulse responses(HRIRs), complex-valued HRTFs, augmented HRTFs, and log-magnitudes of HRTFs are investigated. The objective of this study is to compare modeling performances of the PCA models in the least-squares sense and to show the theoretical relationship between the PCA models. In terms of the number of principal components needed for modeling, the PCA model based on HRIR or augmented HRTFs showed more efficient modeling performance than the PCA model based on complex-valued HRTFs. The PCA model based on HRIRs in the time domain and that based on augmented HRTFs in the frequency domain are shown to be theoretically equivalent. Modeling performance of the PCA model based on log-magnitudes of HRTFs cannot be compared with that of other PCA models because the PCA model deals with log-scaled magnitude components only, whereas the other PCA models consider both magnitude and phase components in linear scale.

• The Korean Journal of Applied Statistics
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• v.30 no.3
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• pp.311-321
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• 2017

Principal component analysis is a popular statistical method to reduce the dimension of the high dimensional climate data and to extract meaningful climate patterns. Based on the principal component analysis, we can further apply a regression approach for the linear prediction of future climate, termed as principal component regression (PCR). In this paper, we develop a new PCR method based on the regularized principal component analysis for spatial data proposed by Wang and Huang (2016) to account spatial feature of the climate data. We apply the proposed method to temperature prediction in the East Asia region and compare the result with conventional PCR results.