• The Korean Journal of Applied Statistics
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• v.26 no.5
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• pp.747-758
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• 2013

The covariance matrix is important in multivariate statistical analysis and a sample covariance matrix is used as an estimator of the covariance matrix. High dimensional data has a larger dimension than the sample size; therefore, the sample covariance matrix may not be suitable since it is known to perform poorly and event not invertible. A number of covariance matrix estimators have been recently proposed with three different approaches of shrinkage, thresholding, and modified Cholesky decomposition. We compare the performance of these newly proposed estimators in various situations.

• Journal of Digital Contents Society
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• v.19 no.4
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• pp.731-737
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• 2018

The recommendation system is actively researched for the purpose of suggesting information that users may be interested in in many fields such as contents, online commerce, social network, advertisement system, and the like. However, there are many recommendation systems that propose based on past preference data, and it is difficult to provide users with little or no data in the past. Therefore, interest in higher-order data analysis is increasing and Matrix Factorization is attracting attention. In this paper, we study and propose a comparison and replay of the Factorization Machines Leaning(FM) model which is attracting attention in the recommendation system and High-Order Factorization Machines Learning(HOFM) which is a high - dimensional data analysis.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.10 no.7
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• pp.1307-1311
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• 2006

In this paper, we propose new speech feature parameter using the Matrix Factorization for appearance part-based features of speech spectrum. The proposed parameter represents effective dimensional reduced data from multi-dimensional feature data through matrix factorization procedure under all of the matrix elements are the non-negative constraint. Reduced feature data presents p art-based features of input data. We verify about usefulness of NMF(Non-Negative Matrix Factorization) algorithm for speech feature extraction applying feature parameter that is got using NMF in Mel-scaled filter bank output. According to recognition experiment results, we confirm that proposed feature parameter is superior to MFCC(Mel-Frequency Cepstral Coefficient) in recognition performance that is used generally.

• The KIPS Transactions:PartB
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• v.13B no.6 s.109
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• pp.625-632
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• 2006

Collaborative filtering is a technology that aims at teaming predictive models of user preferences. Collaborative filtering systems have succeeded in Ecommerce market but they have shortcomings of high dimensionality and sparsity. In this paper we propose the nearest neighbor collaborative filtering method using non-negative matrix factorization(NNMF). We replace the missing values in the user-item matrix by using the user variance coefficient method as preprocessing for matrix decomposition and apply non-negative factorization to the matrix. The positive decomposition method using the non-negative decomposition represents users as semantic vectors and classifies the users into groups based on semantic relations. We compute the similarity between users by using vector similarity and selects the nearest neighbors based on the similarity. We predict the missing values of items that didn't rate by a new user based on the values that the nearest neighbors rated items.

• The Korean Journal of Applied Statistics
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• v.37 no.2
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• pp.157-176
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• 2024

Integrative analysis for better understanding of complex biological systems gains more attention. Observing subjects from various perspectives and conducting integrative analysis of those multiple datasets enables a deeper understanding of the subject. In this paper, we compared two methods that simultaneously consider two datasets gathered from the same objects, canonical correlation analysis (CCA) and co-inertia analysis (CIA). Since CCA cannot handle the case when the data exhibit high-dimensionality, two strategies were considered instead: Utilization of a ridge constant (CCA-ridge) and substitution of covariance matrices of each data to identity matrix and then applying penalized singular value decomposition (CCA-PMD). To illustrate CIA and CCA, both extensions of CCA and CIA were applied to NCI60 cell line data. It is shown that both methods yield biologically meaningful and significant results by identifying important genes that enhance our comprehension of the data. Their results shows some dissimilarities arisen from the different criteria used to measure the relationship between two sets of data in each method. Additionally, CIA exhibits variations dependent on the weight matrices employed.

• Journal of the Korea Society for Simulation
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• v.33 no.1
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• pp.19-26
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• 2024

The phase-type, PH, distribution is defined as the time to absorption into a terminal state in a continuous-time Markov chain. As the PH distribution includes family of exponential distributions, it has been widely used in stochastic models. Since the PH distribution is represented and generated by an initial probability vector and a generator matrix which is called the Markovian representation, we need to find a vector and a matrix that are consistent with given set of moments if we want simulate a PH distribution. In this paper, we propose an approach to simulate a PH distribution based on distribution function which can be obtained directly from moments. For the simulation of PH distribution of order 2, closed-form formula and streamlined procedures are given based on the Jordan decomposition and the minimal Laplace transform which is computationally more efficient than the moment matching methods for the Markovian representation. Our approach can be used more effectively than the Markovian representation in generating higher order PH distribution in queueing network simulation.