• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.545-558
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• 2013

In this paper, the formulas for calculating the extremal ranks and inertias of the Hermitian least squares solutions to matrix equation AX = B are established. In particular, the necessary and sufficient conditions for the existences of the positive and nonnegative definite solutions to this matrix equation are given. Meanwhile, the least squares problem of the above matrix equation with Hermitian R-symmetric and R-skew symmetric constraints are also investigated.

• Journal of KIISE:Computing Practices and Letters
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• v.14 no.3
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• pp.296-300
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• 2008

Nonnegative tensor factorization(NTF) is a recent multiway(multilineal) extension of nonnegative matrix factorization(NMF), where nonnegativity constraints are imposed on the CANDECOMP/PARAFAC model. In this paper we consider the Tucker model with nonnegativity constraints and develop a new tensor factorization method, referred to as nonnegative Tucker decomposition (NTD). We derive multiplicative updating algorithms for various discrepancy measures: least square error function, I-divergence, and $\alpha$-divergence.

• Proceedings of the Korean Information Science Society Conference
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• 2011.06c
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• pp.393-396
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• 2011

In this paper, we propose a constrained alternating least squares nonnegative matrix factorization algorithm (cALSNMF) to detect active brain regions from single subject's task-related fMRI data. In cALSNMF, we define a new cost function which considers the uncorrelation and noisy problems of fMRI data by adding decorrelation and smoothing constraints in original Euclidean distance cost function. We also generate a novel training procedure by modifying the update rules and combining with optimal brain surgeon (OBS) algorithm. The experimental results on visuomotor task fMRI data show that our cALSNMF fits fMRI data better than original ALSNMF in detecting task-related brain activation from single subject's fMRI data.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.81-85
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• 1992

We design a multi-element photo-detector to measure the size of particles using the diffracted light energy distribution. The scattered profile measured by the photodetector is sampled by a 32 channel analog-to-digital converter. A nonnegative least squares analysis translates the light energy distribution into the corresponding unique particle size distribution. The responses of the particle sizing system are studied theoretically and experimentally.

• Genomics & Informatics
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• v.4 no.1
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• pp.33-39
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• 2006

Alternative splicing (AS) is an important mechanism of producing transcriptome diversity and microarray techniques are being used increasingly to monitor the splice variants. There exist three types of microarrays interrogating AS events-junction, exon, and tiling arrays. Junction probes have the advantage of monitoring the splice site directly. Johnson et al., performed a genome-wide survey of human alternative pre-mRNA splicing with exon junction microarrays (Science 302:2141-2144, 2003), which monitored splicing at every known exon-exon junctions for more than 10,000 multi-exon human genes in 52 tissues and cell lines. Here, we describe an algorithm to deduce the relative concentration of isoforms from the junction array data. Non-negative Matrix Factorization (NMF) is applied to obtain the transcript structure inferred from the expression data. Then we choose the transcript models consistent with the ECgene model of alternative splicing which is based on mRNA and EST alignment. The probe-transcript matrix is constructed using the NMF-consistent ECgene transcripts, and the isoform abundance is deduced from the non-negative least squares (NNLS) fitting of experimental data. Our method can be easily extended to other types of microarrays with exon or junction probes.

• Proceedings of the KIEE Conference
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• 1992.07a
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• pp.437-440
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• 1992

We design a multi-element photo-detector to measure the size of particles using the diffracted light energy distribution. The light energy that is scattered by particles in the collimated laser beam is collected by the Fourier transform lens and directed to the multi-semicircular concentric annular detecters. The scattered profile measured by the photodetector is sampled by a 32 channel analog-to-digital converter. A nonnegative least squares analysis translates the light energy distribution into the corresponding unique particle size distribution.

• Analytical Science and Technology
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• v.20 no.6
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• pp.502-507
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• 2007

X-ray diffraction method has been widely used for qualitative and quantitative analysis of a mixture of materials since every crystalline material gives a unique X-ray diffraction pattern independently of others, with the intensity of each pattern proportional to that material's concentration in a mixture. For determination of mixing ratios, extracting source spectra correctly is important and crucial. Based on the source spectra extracted, a regression model with non-negativity constraint is applied for determining mixing ratios. In some mixtures, however, X-ray diffraction spectrum has sharp and narrow peaks, which may result in partial negative source spectrum from independent component analysis. We propose several procedures of extracting non-negative source spectra and determining mixing ratios. The proposed method is validated with experimental data on powder mixtures.