• Communications for Statistical Applications and Methods
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• v.31 no.2
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• pp.179-189
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• 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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.2
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• pp.522-539
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• 2021

In order to solve the problems of the existing audio fingerprint method when extracting audio fingerprints from long speech segments, such as too large fingerprint dimension, poor robustness, and low retrieval accuracy and efficiency, a robust audio fingerprint retrieval method based on feature dimension reduction and feature combination is proposed. Firstly, the Mel-frequency cepstral coefficient (MFCC) and linear prediction cepstrum coefficient (LPCC) of the original speech are extracted respectively, and the MFCC feature matrix and LPCC feature matrix are combined. Secondly, the feature dimension reduction method based on information entropy is used for column dimension reduction, and the feature matrix after dimension reduction is used for row dimension reduction based on energy feature dimension reduction method. Finally, the audio fingerprint is constructed by using the feature combination matrix after dimension reduction. When speech's user retrieval, the normalized Hamming distance algorithm is used for matching retrieval. Experiment results show that the proposed method has smaller audio fingerprint dimension and better robustness for long speech segments, and has higher retrieval efficiency while maintaining a higher recall rate and precision rate.

• Communications for Statistical Applications and Methods
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• v.23 no.2
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• pp.93-103
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• 2016

In the paper, we discuss dimension reduction of predictors ${\mathbf{X}}{\in}{{\mathbb{R}}^p}$ in a regression of $Y{\mid}{\mathbf{X}}$ with a notion of sufficiency that is called sufficient dimension reduction. In sufficient dimension reduction, the original predictors ${\mathbf{X}}$ are replaced by its lower-dimensional linear projection without loss of information on selected aspects of the conditional distribution. Depending on the aspects, the central subspace, the central mean subspace and the central $k^{th}$-moment subspace are defined and investigated as primary interests. Then the relationships among the three subspaces and the changes in the three subspaces for non-singular transformation of ${\mathbf{X}}$ are studied. We discuss the two conditions to guarantee the existence of the three subspaces that constrain the marginal distribution of ${\mathbf{X}}$ and the conditional distribution of $Y{\mid}{\mathbf{X}}$. A general approach to estimate them is also introduced along with an explanation for conditions commonly assumed in most sufficient dimension reduction methodologies.

• The Korean Journal of Applied Statistics
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• v.23 no.5
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• pp.977-985
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• 2010

In this paper, we propose an approach to conduct partial sufficient dimension reduction with heavily unbalanced categorical predictors. For this, we consider integrated categorical predictors and investigate certain conditions that the integrated categorical predictor is fully informative to partial sufficient dimension reduction. For illustration, the proposed approach is implemented on optimal partial sliced inverse regression in simulation and data analysis.

• KIPS Transactions on Software and Data Engineering
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• v.5 no.8
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• pp.361-368
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• 2016

While dimension reduction methods on high dimensional data have been widely studied, research on dimension reduction methods for high dimensional streaming data with concept drift is limited. In this paper, we review incremental dimension reduction methods and propose a method to apply dimension reduction efficiently in order to improve classification performance on high dimensional streaming data with concept drift.

• Communications for Statistical Applications and Methods
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• v.23 no.2
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• pp.105-117
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• 2016

In the paper, as a sequence of the first tutorial, we discuss sufficient dimension reduction methodologies used to estimate central subspace (sliced inverse regression, sliced average variance estimation), central mean subspace (ordinary least square, principal Hessian direction, iterative Hessian transformation), and central $k^{th}$-moment subspace (covariance method). Large-sample tests to determine the structural dimensions of the three target subspaces are well derived in most of the methodologies; however, a permutation test (which does not require large-sample distributions) is introduced. The test can be applied to the methodologies discussed in the paper. Theoretical relationships among the sufficient dimension reduction methodologies are also investigated and real data analysis is presented for illustration purposes. A seeded dimension reduction approach is then introduced for the methodologies to apply to large p small n regressions.

• Communications for Statistical Applications and Methods
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• v.31 no.2
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• pp.213-234
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• 2024

In recent decades, increasing research attention has been directed toward predicting the price of stocks in financial markets using deep learning methods. For instance, recurrent neural network (RNN) is known to be competitive for datasets with time-series data. Long short term memory (LSTM) further improves RNN by providing an alternative approach to the gradient loss problem. LSTM has its own advantage in predictive accuracy by retaining memory for a longer time. In this paper, we combine both supervised and unsupervised dimension reduction methods with LSTM to enhance the forecasting performance and refer to this as a dimension reduction based LSTM (DR-LSTM) approach. For a supervised dimension reduction method, we use methods such as sliced inverse regression (SIR), sparse SIR, and kernel SIR. Furthermore, principal component analysis (PCA), sparse PCA, and kernel PCA are used as unsupervised dimension reduction methods. Using datasets of real stock market index (S&P 500, STOXX Europe 600, and KOSPI), we present a comparative study on predictive accuracy between six DR-LSTM methods and time series modeling.

• Communications for Statistical Applications and Methods
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• v.28 no.3
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• pp.267-279
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• 2021

A regression with multi-dimensional responses is quite common nowadays in the so-called big data era. In such regression, to relieve the curse of dimension due to high-dimension of responses, the dimension reduction of predictors is essential in analysis. Sufficient dimension reduction provides effective tools for the reduction, but there are few sufficient dimension reduction methodologies for multivariate regression. To fill this gap, we newly propose two fused slice-based inverse regression methods. The proposed approaches are robust to the numbers of clusters or slices and improve the estimation results over existing methods by fusing many kernel matrices. Numerical studies are presented and are compared with existing methods. Real data analysis confirms practical usefulness of the proposed methods.

• Communications for Statistical Applications and Methods
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• v.26 no.5
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• pp.519-526
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• 2019

Response dimension reduction in a sufficient dimension reduction (SDR) context has been widely ignored until Yoo and Cook (Computational Statistics and Data Analysis, 53, 334-343, 2008) founded theories for it and developed an estimation approach. Recent research in SDR shows that a semi-parametric approach can outperform conventional non-parametric SDR methods. Yoo (Statistics: A Journal of Theoretical and Applied Statistics, 52, 409-425, 2018) developed a semi-parametric approach for response reduction in Yoo and Cook (2008) context, and Yoo (Journal of the Korean Statistical Society, 2019) completes the semi-parametric approach by proposing an unstructured method. This paper theoretically discusses and provides insightful remarks on three versions of semi-parametric approaches that can be useful for statistical practitioners. It is also possible to avoid numerical instability by presenting the results for an orthogonal transformation of the response variables.

• Communications for Statistical Applications and Methods
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• v.28 no.2
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• pp.205-215
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• 2021

Sufficient dimension reduction is useful dimension reduction tool in regression, and sliced inverse regression (Li, 1991) is one of the most popular sufficient dimension reduction methodologies. In spite of its popularity, it is known to be sensitive to the number of slices. To overcome this shortcoming, the so-called fused sliced inverse regression is proposed by Cook and Zhang (2014). Unfortunately, the two existing methods do not have the direction application to large p-small n regression, in which the dimension reduction is desperately needed. In this paper, we newly propose seeded sliced inverse regression and seeded fused sliced inverse regression to overcome this deficit by adopting iterative projection approach (Cook et al., 2007). Numerical studies are presented to study their asymptotic estimation behaviors, and real data analysis confirms their practical usefulness in high-dimensional data analysis.