• Communications of the Korean Mathematical Society
• /
• v.35 no.4
• /
• pp.1057-1073
• /
• 2020

In this paper, we study some of the factorization aspects of rational multicyclic monoids, that is, additive submonoids of the nonnegative rational numbers generated by multiple geometric sequences. In particular, we provide a complete description of the rational multicyclic monoids M that are hereditarily atomic (i.e., every submonoid of M is atomic). Additionally, we show that the sets of lengths of certain rational multicyclic monoids are finite unions of multidimensional arithmetic progressions, while their unions satisfy the Structure Theorem for Unions of Sets of Lengths. Finally, we realize arithmetic progressions as the sets of distances of some additive submonoids of the nonnegative rational numbers.

• Proceedings of the Korean Society of Broadcast Engineers Conference
• /
• 2009.01a
• /
• pp.714-718
• /
• 2009

3D reconstruction of a human face from an image sequence remains an important problem in computer vision. We propose a method, based on a factorization algorithm, that reconstructs a 3D face model from short image sequences exhibiting rotational motion. Factorization algorithms can recover structure and motion simultaneously from one image sequence, but they usually require that all feature points be well tracked. Under rotational motion, however, feature tracking often fails due to occlusion and frame out of features. Additionally, the paucity of images may make feature tracking more difficult or decrease reconstruction accuracy. The proposed 3D reconstruction approach can handle short image sequences exhibiting rotational motion wherein feature points are likely to be missing. We implement the proposal as a reconstruction method; it employs image sequence division and a feature tracking method that uses Active Appearance Models to avoid the failure of feature tracking. Experiments conducted on an image sequence of a human face demonstrate the effectiveness of the proposed method.

• Korean Management Science Review
• /
• v.21 no.2
• /
• pp.43-60
• /
• 2004

Every iteration of interior-point methods of large scale optimization requires computing at least one orthogonal projection. In the practice, symmetric variants of the Gaussian elimination such as Cholesky factorization are accepted as the most efficient and sufficiently stable method. In this paper several specific implementation issues of the symmetric factorization that can be applied for solving such equations are discussed. The code called McSML being the result of this work is shown to produce comparably sparse factors as another implementations in the $MATLAB^{***}$ environment. It has been used for computing projections in an efficient implementation of self-regular based interior-point methods, McIPM. Although primary aim of developing McSML was to embed it into an interior-point methods optimizer, the code may equally well be used to solve general large sparse systems arising in different applications.

• Journal of information and communication convergence engineering
• /
• v.11 no.4
• /
• pp.241-246
• /
• 2013

A classic document clustering technique may incorrectly classify documents into different clusters when documents that should belong to the same cluster do not have any shared terms. Recently, to overcome this problem, internal and external knowledge-based approaches have been used for text document clustering. However, the clustering results of these approaches are influenced by the inherent structure and the topical composition of the documents. Further, the organization of knowledge into an ontology is expensive. In this paper, we propose a new enhanced text document clustering method using non-negative matrix factorization (NMF) and WordNet. The semantic terms extracted as cluster labels by NMF can represent the inherent structure of a document cluster well. The proposed method can also improve the quality of document clustering that uses cluster labels and term weights based on term mutual information of WordNet. The experimental results demonstrate that the proposed method achieves better performance than the other text clustering methods.

• Proceedings of the Korea Contents Association Conference
• /
• 2008.05a
• /
• pp.92-95
• /
• 2008

NMF(Non-negative Matrix Factorization) has been proposed as an useful algorithm for feature extraction. Using NMF, we can extract low-dimensional feature vectors. Also, we can find clustering effects in the NMF algorithm. Also, it is reported that the sparse NMF algorithm shows better clustering effects. This paper compares the two approaches in the viewpoint of clustering effects.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.25 no.3
• /
• pp.107-116
• /
• 2021

We introduce optimization algorithms using Bregman Divergence for solving non-negative matrix factorization (NMF) problems. Bregman divergence is known a generalization of some divergences such as Frobenius norm and KL divergence and etc. Some algorithms can be applicable to not only NMF with Frobenius norm but also NMF with more general Bregman divergence. Matrix Factorization is a popular non-convex optimization problem, for which alternating minimization schemes are mostly used. We develop the Bregman proximal gradient method applicable for all NMF formulated in any Bregman divergences. In the derivation of NMF algorithm for Bregman divergence, we need to use majorization/minimization(MM) for a proper auxiliary function. We present algorithmic aspects of NMF for Bregman divergence by using MM of auxiliary function.

• Journal of Korea Multimedia Society
• /
• v.22 no.4
• /
• pp.515-526
• /
• 2019

DOOH(Digital Out Of Home) advertising targets for reaching consumers through outdoor digital display medias. Traditionally, scheduling of advertisement contents over DOOH medias is usually done by operator's strategy, but an efficient ad scheduling strategy is not easy to find under various advertising contexts. In this paper, we present a context-aware factorization machine-based recommendation model for the scheduling under various advertising contexts, and provide analysis for understanding of the contexts' effects on advertising based on the recommendation model. Through simulation results on the dataset adapted from a real dataset of RecSys challenge 2015, it is shown that the proposed model and analysis based on the model will be effective for better scheduling of ad contents under advertising contexts over DOOH networks.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.11 no.2
• /
• pp.107-112
• /
• 2011

It is very difficult to factorize composite number, $n=pq$ to integer factorization, p and q that is almost similar length of digits. Integer factorization algorithms, for the most part, find ($a,b$) that is congruence of squares ($a^2{\equiv}b^2$ (mod $n$)) with using factoring(factor base, B) and get the result, $p=GCD(a-b,n)$, $q=GCD(a+b,n)$ with taking the greatest common divisor of Euclid based on the formula $a^2-b^2=(a-b)(a+b)$. The efficiency of these algorithms hangs on finding ($a,b$) and deciding factor base, B. This paper proposes a efficient algorithm. The proposed algorithm extracts B from integer factorization with 3 digits prime numbers of $n+1$ and decides f, the combination of B. And then it obtains $x$(this is, $a=fxy$, $\sqrt{n}$ < $a$ < $\sqrt{2n}$) from integer factorization of $n-2$ and gets $y=\frac{a}{fx}$, $y_1$={1,3,7,9}. Our algorithm is much more effective in comparison with the conventional Fermat algorithm that sequentially finds $\sqrt{n}$ < $a$.

• Journal of the Institute of Electronics and Information Engineers
• /
• v.52 no.8
• /
• pp.89-96
• /
• 2015

Human visual system has chromatic adaptation to determine the color of an object regardless of illumination, whereas digital camera records illumination and reflectance together, giving the color appearance of the scene varied under different illumination. NMFsc(nonnegative matrix factorization with sparseness constraint) was recently introduced to estimate original object color by using sparseness constraint. In NMFsc, low sparseness constraint is used to estimate illumination and high sparseness constraint is used to estimate reflectance. However, NMFsc has an illumination estimation error for images with large uniform area, which is considered as dominant chromaticity. To overcome the defects of NMFsc, illumination estimation via nonnegative matrix factorization with dominant chromaticity image is proposed. First, image is converted to chromaticity color space and analyzed by chromaticity histogram. Chromaticity histogram segments the original image into similar chromaticity images. A segmented region with the lowest standard deviation is determined as dominant chromaticity region. Next, dominant chromaticity is removed in the original image. Then, illumination estimation using nonnegative matrix factorization is performed on the image without dominant chromaticity. To evaluate the proposed method, experimental results are analyzed by average angular error in the real world dataset and it has shown that the proposed method with 5.5 average angular error achieve better illuminant estimation over the previous method with 5.7 average angular error.

• The Journal of the Acoustical Society of Korea
• /
• v.28 no.8
• /
• pp.697-705
• /
• 2009

An unsupervised (blind) method is proposed aiming at extracting rhythmic sources from commercial polyphonic music whose number of channels is limited to one. Commercial music signals are not usually provided with more than two channels while they often contain multiple instruments including singing voice. Therefore, instead of using conventional modeling of mixing environments or statistical characteristics, we should introduce other source-specific characteristics for separating or extracting sources in the under determined environments. In this paper, we concentrate on extracting rhythmic sources from the mixture with the other harmonic sources. An extension of nonnegative matrix factorization (NMF), which is called nonnegative matrix partial co-factorization (NMPCF), is used to analyze multiple relationships between spectral and temporal properties in the given input matrices. Moreover, temporal repeatability of the rhythmic sound sources is implicated as a common rhythmic property among segments of an input mixture signal. The proposed method shows acceptable, but not superior separation quality to referred prior knowledge-based drum source separation systems, but it has better applicability due to its blind manner in separation, for example, when there is no prior information or the target rhythmic source is irregular.