Row Dimension Research Articles

Sex-Specific Size Analysis of Carpal Bones: Implications for Orthopedic Biomedical Device Design and Therapy Planning.

Consideration of the individual carpal bone characteristics of the wrist plays a key role in well-functioning biomedical devices and successful surgical procedures. Although geometric differences and individual bone sizes have been analyzed in the literature, detailed morphologic descriptions and correlations covering the entire wrist reported in a clinical context are lacking. This study aimed to perform a comprehensive and automatic analysis of the wrist morphology using the freely available "Open Source Carpal Database" (OSCD). We quantified the size of each of the individual carpal bones and their combination. These sizes were extracted in n = 117 datasets of the wrist of the OSCD in anatomical directions and analyzed using descriptive statics and correlation analysis to investigate the morphological characteristics under sex-specific aspects and to provide regression plots and equations to predict individual carpal bone sizes from the proximal and distal row dimensions. The correlations in the proximal row were higher compared to the distal row. We established comprehensive size correlations and size rations and found that there exist statistical differences between sex, particularly of the scaphoid. The regression plots and equations we provided will assist surgeons in a more accurate preoperative morphological evaluation for therapy planning and may be used for future anatomically inspired orthopedic biomedical device designs.

In vivo magnetic resonance spectroscopy by transverse relaxation encoding with narrowband decoupling

Cell pathology in neuropsychiatric disorders has mainly been accessible by analyzing postmortem tissue samples. Although molecular transverse relaxation informs local cellular microenvironment via molecule-environment interactions, precise determination of the transverse relaxation times of molecules with scalar couplings (J), such as glutamate and glutamine, has been difficult using in vivo magnetic resonance spectroscopy (MRS) technologies, whose approach to measuring transverse relaxation has not changed for decades. We introduce an in vivo MRS technique that utilizes frequency-selective editing pulses to achieve homonuclear decoupled chemical shift encoding in each column of the acquired two-dimensional dataset, freeing up the entire row dimension for transverse relaxation encoding with J-refocusing. This results in increased spectral resolution, minimized background signals, and markedly broadened dynamic range for transverse relaxation encoding. The in vivo within-subject coefficients of variation for the transverse relaxation times of glutamate and glutamine, measured using the proposed method in the human brain at 7 T, were found to be approximately 4%. Since glutamate predominantly resides in glutamatergic neurons and glutamine in glia in the brain, this noninvasive technique provides a way to probe cellular pathophysiology in neuropsychiatric disorders for characterizing disease progression and monitoring treatment response in a cell type-specific manner in vivo.

Reduced volume of diabetic pancreatic islets in rodents detected by synchrotron X-ray phase-contrast microtomography and deep learning network

The pancreatic islet is a highly structured micro-organ that produces insulin in response to rising blood glucose. Here we develop a label-free and automatic imaging approach to visualize the islets in situ in diabetic rodents by the synchrotron radiation X-ray phase-contrast microtomography (SRμCT) at the ID17 station of the European Synchrotron Radiation Facility. The large-size images (3.2mm×15.97mm) were acquired in the pancreas in STZ-treated mice and diabetic GK rats. Each pancreas was dissected by 3000 reconstructed images. The image datasets were further analysed by a self-developed deep learning method, AA-Net. All islets in the pancreas were segmented and visualized by the three-dimension (3D) reconstruction. After quantifying the volumes of the islets, we found that the number of larger islets (=>1500 μm3) was reduced by 2-fold (wt 1004±94 vs GK 419±122, P<0.001) in chronically developed diabetic GK rat, while in STZ-treated diabetic mouse the large islets were decreased by half (189±33 vs 90±29, P<0.001) compared to the untreated mice. Our study provides a label-free tool for detecting and quantifying pancreatic islets in situ. It implies the possibility of monitoring the state of pancreatic islets in vivo diabetes without labelling.

Low-Rank Regression Models for Multiple Binary Responses and their Applications to Cancer Cell-Line Encyclopedia Data

In this article, we study high-dimensional multivariate logistic regression models in which a common set of covariates is used to predict multiple binary outcomes simultaneously. Our work is primarily motivated from many biomedical studies with correlated multiple responses such as the cancer cell-line encyclopedia project. We assume that the underlying regression coefficient matrix is simultaneously low-rank and row-wise sparse. We propose an intuitively appealing selection and estimation framework based on marginal model likelihood, and we develop an efficient computational algorithm for inference. We establish a novel high-dimensional theory for this nonlinear multivariate regression. Our theory is general, allowing for potential correlations between the binary responses. We propose a new type of nuclear norm penalty using the smooth clipped absolute deviation, filling the gap in the related non-convex penalization literature. We theoretically demonstrate that the proposed approach improves estimation accuracy by considering multiple responses jointly through the proposed estimator when the underlying coefficient matrix is low-rank and row-wise sparse. In particular, we establish the non-asymptotic error bounds, and both rank and row support consistency of the proposed method. Moreover, we develop a consistent rule to simultaneously select the rank and row dimension of the coefficient matrix. Furthermore, we extend the proposed methods and theory to a joint Ising model, which accounts for the dependence relationships. In our analysis of both simulated data and the cancer cell line encyclopedia data, the proposed methods outperform the existing methods in better predicting responses. Supplementary materials for this article are available online.

Subspace estimation from unbalanced and incomplete data matrices: ℓ2,∞ statistical guarantees

This paper is concerned with estimating the column space of an unknown low-rank matrix A⋆∈Rd1×d2, given noisy and partial observations of its entries. There is no shortage of scenarios where the observations—while being too noisy to support faithful recovery of the entire matrix—still convey sufficient information to enable reliable estimation of the column space of interest. This is particularly evident and crucial for the highly unbalanced case where the column dimension d2 far exceeds the row dimension d1, which is the focal point of the current paper. We investigate an efficient spectral method, which operates upon the sample Gram matrix with diagonal deletion. While this algorithmic idea has been studied before, we establish new statistical guarantees for this method in terms of both ℓ2 and ℓ2,∞ estimation accuracy, which improve upon prior results if d2 is substantially larger than d1. To illustrate the effectiveness of our findings, we derive matching minimax lower bounds with respect to the noise levels, and develop consequences of our general theory for three applications of practical importance: (1) tensor completion from noisy data, (2) covariance estimation/principal component analysis with missing data and (3) community recovery in bipartite graphs. Our theory leads to improved performance guarantees for all three cases.

Suitability of Airborne and Terrestrial Laser Scanning for Mapping Tree Crop Structural Metrics for Improved Orchard Management

Airborne Laser Scanning (ALS) and Terrestrial Laser Scanning (TLS) systems are useful tools for deriving horticultural tree structure estimates. However, there are limited studies to guide growers and agronomists on different applications of the two technologies for horticultural tree crops, despite the importance of measuring tree structure for pruning practices, yield forecasting, tree condition assessment, irrigation and fertilization optimization. Here, we evaluated ALS data against near coincident TLS data in avocado, macadamia and mango orchards to demonstrate and assess their accuracies and potential application for mapping crown area, fractional cover, maximum crown height, and crown volume. ALS and TLS measurements were similar for crown area, fractional cover and maximum crown height (coefficient of determination (R2) ≥ 0.94, relative root mean square error (rRMSE) ≤ 4.47%). Due to the limited ability of ALS data to measure lower branches and within crown structure, crown volume estimates from ALS and TLS data were less correlated (R2 = 0.81, rRMSE = 42.66%) with the ALS data found to consistently underestimate crown volume. To illustrate the effects of different spatial resolution, capacity and coverage of ALS and TLS data, we also calculated leaf area, leaf area density and vertical leaf area profile from the TLS data, while canopy height, tree row dimensions and tree counts) at the orchard level were calculated from ALS data. Our results showed that ALS data have the ability to accurately measure horticultural crown structural parameters, which mainly rely on top of crown information, and measurements of hedgerow width, length and tree counts at the orchard scale is also achievable. While the use of TLS data to map crown structure can only cover a limited number of trees, the assessment of all crown strata is achievable, allowing measurements of crown volume, leaf area density and vertical leaf area profile to be derived for individual trees. This study provides information for growers and horticultural industries on the capacities and achievable mapping accuracies of standard ALS data for calculating crown structural attributes of horticultural tree crops.

SemiMap: A Semi-Folded Convolution Mapping for Speed-Overhead Balance on Crossbars

Crossbar architecture has been widely used in neural network (NN) accelerators, involving conventional and emerging devices. It performs well on the fully connected layer through efficient vector–matrix multiplication. Whereas, the advantages degrade on the convolutional layer with huge data reuse, since the execution speed and resource overhead are imbalanced when using existing fully unfolded or fully folded mapping strategy. To address this issue, we propose a novel semi-folded mapping (SemiMap) framework for implementing the convolution on crossbars. It simultaneously folds the physical resources along the row dimension of feature maps (FMs) and unfolds them along the column dimension. The former reduces the resource overhead, and the latter maintains the parallelism. An FM slicing scheme is further proposed to enable the processing of large-size image. Via our mapping framework, a row-by-row streaming pipeline for intraimage dataflow and periodical pipeline for interimage dataflow are easy to be obtained. To validate the idea, we build a many-crossbar architecture with several designs to guarantee the overall functionality and performance. Based on the measurement data of a fabricated chip, a mapping compiler and a cycle-accurate simulator are developed for the hardware simulation of large-scale networks. We evaluate the proposed SemiMap on various convolutional NNs across different network scale. ${>} 35 {\times }$ resource saving and several hundred times cycle reduction are demonstrated compared to the existing fully unfolded and fully folded strategies, respectively. This paper jumps out of the current extreme mapping schemes, and provides a balanced solution on how to efficiently deploy the computational graphs with data reuse on many-crossbar architecture.

SparseCT: System concept and design of multislit collimators.

SparseCT, an undersampling scheme for compressed sensing (CS) computed tomography (CT), has been proposed to reduce radiation dose by acquiring undersampled projection data from clinical CT scanners (Koesters etal. in, SparseCT: Interrupted-Beam Acquisition and Sparse Reconstruction for Radiation Dose Reduction; 2017). SparseCT partially blocks the x-ray beam with a multislit collimator (MSC) to perform a multidimensional undersampling along the view and detector row dimensions. SparseCT undersamples the projection data within each view and moves the MSC along the z-direction during gantry rotation to change the undersampling pattern. It enables reconstruction of images from undersampled data using CS algorithms. The purpose of this work is to design the spacing and width of the MSC slits and the MSC motion patterns based on beam separation, undersampling efficiency, and image quality. The development and testing of a SparseCT prototype with the designed MSC will be described in a following paper. We chose a few initial MSC designs based on the guidance from two metrics: beam separation and undersampling efficiency. Both beam separation and undersampling efficiency were measured from numerically simulated photon distribution with MSC taken into consideration. Beam separation measures the separation between x-ray beams from consecutive slits, taking into account penumbra effects on both sides of each slit. Undersampling efficiency measures the dose-weighted similarity between penumbra undersampling and binary undersampling, in other words, the effective contribution of the incident dose to the signal to noise ratio of the projection data. We then compared the initially chosen MSC designs in terms of their reconstruction image quality. SparseCT projections were simulated from fully sampled patient projection data according to the MSC design and motion pattern, reconstructed iteratively using a sparsity-enforcing penalized weighted least squares cost function with ordered subsets/momentum algorithm, and compared visually and quantitatively. Simulated photon distributions indicate that the size of the penumbra is dominated by the size of the focal spot. Therefore, a wider MSC slit and a smaller focal spot lead to increased beam separation and undersampling efficiency. For fourfold undersampling with a 1.2mm focal spot, a minimum MSC slit width of three detector rows (projected to the detector surface) is needed for beam separation; for threefold undersampling, a minimum slit width of four detector rows is needed. Simulations of SparseCT projection and reconstruction indicate that the motion pattern of the MSC does not have a visible impact on image quality. An MSC slit width of three or four detector rows yields similar image quality. The MSC is the key component of the SparseCT method. Simulations of MSC designs incorporating x-ray beam penumbra effects showed that for threefold and fourfold dose reductions, an MSC slit width of four detector rows provided reasonable beam separation, undersampling efficiency, and image quality.

A general expression for the shadow geometry for fixed mode horizontal, step-like structure and inclined solar fields

It is a well-known fact that shadow on solar collectors reduces their output power capability, especially photovoltaic systems due to the mismatch losses. For this reason, the estimation of shadow is an essential part of the design, evaluation and optimization for any study. Different from any other works, the work reported here illustrates an analytical derivation of a general expression for the shading of stationary solar collectors (thermal or photovoltaic) whether arranged aligned or staggered and for the three types of solar fields: horizontal, inclined, and step-like structure solar fields. The shading depends on all design parameters: row spacing, row dimension, collector tilt and azimuth angles, it also depends on the time (day and hour), the location, and the type of the solar field. The effect of all design parameters on the productivity of the field is discussed. Two polynomials representing the minimum spacing ratio to avoid shading as a function of the location latitude and PV panel tilt angle are created for horizontal and step-like structure solar fields. Furthermore, an empirical expression for estimating the solar irradiance incident on the rows of the solar field is presented. A simulation of a study case is reported and discussed. To our knowledge, all equations reported here are new and can be added to the database of programs specialized in PV solar fields to increase their reliability and capability.

Stochastic Subsampling for Factorizing Huge Matrices

We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning, sparse component analysis, and non-negative matrix factorization. Our algorithm streams matrix columns while subsampling them to iteratively learn the matrix factors. At each iteration, the row dimension of a new sample is reduced by subsampling, resulting in lower time complexity compared to a simple streaming algorithm. Our method comes with convergence guarantees to reach a stationary point of the matrix-factorization problem. We demonstrate its efficiency on massive functional Magnetic Resonance Imaging data (2 TB), and on patches extracted from hyperspectral images (103 GB). For both problems, which involve different penalties on rows and columns, we obtain significant speed-ups compared to state-of-the-art algorithms.

Fast Multilevel Computation of Low-Rank Representation of ${\mathcal{ H}}$ -Matrix Blocks

A physics-based algorithm for accelerating the computation of method of moments matrix blocks’ low-rank approximation is presented. The algorithm relies on efficient sampling of phase- and amplitude-compensated interactions using nonuniform grids. Rank-revealing analysis is applied, in a multilevel fashion, to matrices of reduced column and row dimensions that describe subdomains’ interactions with these coarse grids, rather than to the original matrix blocks. As a result, significant savings are achieved, especially for the inherently more compressible dynamic quasi-planar and quasi-static cases. The algorithm’s reduced storage and computation time requirements are estimated analytically and verified numerically for representative examples.

A technique for rapid source apportionment applied to ambient organic aerosol measurements from a thermal desorption aerosol gas chromatograph (TAG)

Abstract. We present a rapid method for apportioning the sources of atmospheric organic aerosol composition measured by gas chromatography–mass spectrometry methods. Here, we specifically apply this new analysis method to data acquired on a thermal desorption aerosol gas chromatograph (TAG) system. Gas chromatograms are divided by retention time into evenly spaced bins, within which the mass spectra are summed. A previous chromatogram binning method was introduced for the purpose of chromatogram structure deconvolution (e.g., major compound classes) (Zhang et al., 2014). Here we extend the method development for the specific purpose of determining aerosol samples' sources. Chromatogram bins are arranged into an input data matrix for positive matrix factorization (PMF), where the sample number is the row dimension and the mass-spectra-resolved eluting time intervals (bins) are the column dimension. Then two-dimensional PMF can effectively do three-dimensional factorization on the three-dimensional TAG mass spectra data. The retention time shift of the chromatogram is corrected by applying the median values of the different peaks' shifts. Bin width affects chemical resolution but does not affect PMF retrieval of the sources' time variations for low-factor solutions. A bin width smaller than the maximum retention shift among all samples requires retention time shift correction. A six-factor PMF comparison among aerosol mass spectrometry (AMS), TAG binning, and conventional TAG compound integration methods shows that the TAG binning method performs similarly to the integration method. However, the new binning method incorporates the entirety of the data set and requires significantly less pre-processing of the data than conventional single compound identification and integration. In addition, while a fraction of the most oxygenated aerosol does not elute through an underivatized TAG analysis, the TAG binning method does have the ability to achieve molecular level resolution on other bulk aerosol components commonly observed by the AMS.

An approach to enhance pnetCDF performance in environmental modeling applications

Abstract. Data intensive simulations are often limited by their I/O (input/output) performance, and "novel" techniques need to be developed in order to overcome this limitation. The software package pnetCDF (parallel network Common Data Form), which works with parallel file systems, was developed to address this issue by providing parallel I/O capability. This study examines the performance of an application-level data aggregation approach which performs data aggregation along either row or column dimension of MPI (Message Passing Interface) processes on a spatially decomposed domain, and then applies the pnetCDF parallel I/O paradigm. The test was done with three different domain sizes which represent small, moderately large, and large data domains, using a small-scale Community Multiscale Air Quality model (CMAQ) mock-up code. The examination includes comparing I/O performance with traditional serial I/O technique, straight application of pnetCDF, and the data aggregation along row and column dimension before applying pnetCDF. After the comparison, "optimal" I/O configurations of this application-level data aggregation approach were quantified. Data aggregation along the row dimension (pnetCDFcr) works better than along the column dimension (pnetCDFcc) although it may perform slightly worse than the straight pnetCDF method with a small number of processors. When the number of processors becomes larger, pnetCDFcr outperforms pnetCDF significantly. If the number of processors keeps increasing, pnetCDF reaches a point where the performance is even worse than the serial I/O technique. This new technique has also been tested for a real application where it performs two times better than the straight pnetCDF paradigm.

A block-tridiagonal solver with two-level parallelization for finite element-spectral codes

Two-level parallelization is introduced to solve a massive block-tridiagonal matrix system. One-level is used for distributing blocks whose size is as large as the number of block rows due to the spectral basis, and the other level is used for parallelizing in the block row dimension. The purpose of the added parallelization dimension is to retard the saturation of the scaling due to communication overhead and inefficiencies in the single-level parallelization only distributing blocks. As a technique for parallelizing the tridiagonal matrix, the combined method of “Partitioned Thomas method” and “Cyclic Odd–Even Reduction” is implemented in an MPI-Fortran90 based finite element-spectral code (TORIC) that calculates the propagation of electromagnetic waves in a tokamak. The two-level parallel solver using thousands of processors shows more than 5 times improved computation speed with the optimized processor grid compared to the single-level parallel solver under the same conditions. Three-dimensional RF field reconstructions in a tokamak are shown as examples of the physics simulations that have been enabled by this algorithmic advance.

Compressed Sensing via Dimension Spread in Dimension-Restricted Systems

Compressed sensing (CS) is applied to capture signals at sub-Nyquist rate when the sensing matrix satisfies the restricted isometry property (RIP). When in a dimension-restricted system which has small row dimension and not so good coherence, the RIP and measurement bound will not be satisfied, and compressed sensing can not be applied directly. In this letter, we propose the dimension spread CS to the dimension-restricted system by directed dimension spread and diversity dimension spread, which make the compressed sensing applicable. The spread dimension bounds for the proposed algorithms are deduced to guarantee exact recovery which are also proved by simulations. Meanwhile, the experimental comparisons for the directed dimension spread CS and diversity dimension spread CS are given and different CS recovery algorithms are carried out to show the effectiveness of the proposed algorithms in the dimension-restricted system. The diversity dimension spread CS outperforms the directed dimension spread CS for its effective dimension spread and diversity. The proposed algorithms can be directly applied in channel estimation and multiuser detection in overload system.

ADAPT-lpv Software for Identification of Nonlinear Parameter-Varying Systems

The ADAPT-lpv software for the identification of linear parameter-varying (LPV) and/or nonlinear systems is a direct and simple extension of the canonical variate analysis (CVA) method as implemented in the ADAPTx software for identification of linear time-invariant systems. The computational structure and problem size is very similar to ADAPTx except that the matrix row dimension (number of lagged variables of the past) is multiplied by the effective number of parameter-varying functions. This is in contrast with the exponential explosion in the number of variables using current subspace methods for LPV systems. Compared with current methods, initial results indicate much less computation, maximum likelihood accuracy, and better numerical stability. The method can automatically remove a number of redundancies in the nonlinear models producing near minimal state orders and polynomial degrees by hypothesis testing. There is detailed discussion of the computational methods and structure of the software modules. The software is demonstrated on a widely studied aircraft flutter problem.

A Higher-Order Generalized Singular Value Decomposition for Comparison of Global mRNA Expression from Multiple Organisms

The number of high-dimensional datasets recording multiple aspects of a single phenomenon is increasing in many areas of science, accompanied by a need for mathematical frameworks that can compare multiple large-scale matrices with different row dimensions. The only such framework to date, the generalized singular value decomposition (GSVD), is limited to two matrices. We mathematically define a higher-order GSVD (HO GSVD) for N≥2 matrices , each with full column rank. Each matrix is exactly factored as Di = UiΣiVT, where V, identical in all factorizations, is obtained from the eigensystem SV = VΛ of the arithmetic mean S of all pairwise quotients of the matrices , i≠j. We prove that this decomposition extends to higher orders almost all of the mathematical properties of the GSVD. The matrix S is nondefective with V and Λ real. Its eigenvalues satisfy λk≥1. Equality holds if and only if the corresponding eigenvector vk is a right basis vector of equal significance in all matrices Di and Dj, that is σi,k/σj,k = 1 for all i and j, and the corresponding left basis vector ui,k is orthogonal to all other vectors in Ui for all i. The eigenvalues λk = 1, therefore, define the “common HO GSVD subspace.” We illustrate the HO GSVD with a comparison of genome-scale cell-cycle mRNA expression from S. pombe, S. cerevisiae and human. Unlike existing algorithms, a mapping among the genes of these disparate organisms is not required. We find that the approximately common HO GSVD subspace represents the cell-cycle mRNA expression oscillations, which are similar among the datasets. Simultaneous reconstruction in the common subspace, therefore, removes the experimental artifacts, which are dissimilar, from the datasets. In the simultaneous sequence-independent classification of the genes of the three organisms in this common subspace, genes of highly conserved sequences but significantly different cell-cycle peak times are correctly classified.

Multi-energy CT based on a prior rank, intensity and sparsity model (PRISM)

We propose a compressive sensing approach for multi-energy computed tomography (CT), namely the prior rank, intensity and sparsity model (PRISM). To further compress the multi-energy image for allowing the reconstruction with fewer CT data and less radiation dose, the PRISM models a multi-energy image as the superposition of a low-rank matrix and a sparse matrix (with row dimension in space and column dimension in energy), where the low-rank matrix corresponds to the stationary background over energy that has a low matrix rank, and the sparse matrix represents the rest of distinct spectral features that are often sparse. Distinct from previous methods, the PRISM utilizes the generalized rank, e.g., the matrix rank of tight-frame transform of a multi-energy image, which offers a way to characterize the multi-level and multi-filtered image coherence across the energy spectrum. Besides, the energy-dependent intensity information can be incorporated into the PRISM in terms of the spectral curves for base materials, with which the restoration of the multi-energy image becomes the reconstruction of the energy-independent material composition matrix. In other words, the PRISM utilizes prior knowledge on the generalized rank and sparsity of a multi-energy image, and intensity/spectral characteristics of base materials. Furthermore, we develop an accurate and fast split Bregman method for the PRISM and demonstrate the superior performance of the PRISM relative to several competing methods in simulations.

Robust principal component analysis-based four-dimensional computed tomography

The purpose of this paper for four-dimensional (4D) computed tomography (CT) is threefold. (1) A new spatiotemporal model is presented from the matrix perspective with the row dimension in space and the column dimension in time, namely the robust PCA (principal component analysis)-based 4D CT model. That is, instead of viewing the 4D object as a temporal collection of three-dimensional (3D) images and looking for local coherence in time or space independently, we perceive it as a mixture of low-rank matrix and sparse matrix to explore the maximum temporal coherence of the spatial structure among phases. Here the low-rank matrix corresponds to the ‘background’ or reference state, which is stationary over time or similar in structure; the sparse matrix stands for the ‘motion’ or time-varying component, e.g., heart motion in cardiac imaging, which is often either approximately sparse itself or can be sparsified in the proper basis. Besides 4D CT, this robust PCA-based 4D CT model should be applicable in other imaging problems for motion reduction or/and change detection with the least amount of data, such as multi-energy CT, cardiac MRI, and hyperspectral imaging. (2) A dynamic strategy for data acquisition, i.e. a temporally spiral scheme, is proposed that can potentially maintain similar reconstruction accuracy with far fewer projections of the data. The key point of this dynamic scheme is to reduce the total number of measurements, and hence the radiation dose, by acquiring complementary data in different phases while reducing redundant measurements of the common background structure. (3) An accurate, efficient, yet simple-to-implement algorithm based on the split Bregman method is developed for solving the model problem with sparse representation in tight frames.

Speaker adaptation using generalised low rank approximations of training matrices

A speaker adaptation method based on the low rank approximation of matrices (GLRAM) of training models is described. In the method, each model is represented as a matrix, and a set of such training matrices is decomposed into a set of speaker weights and two basis matrices for row and column spaces by reducing both row and column ranks of the training models. As a result, the speaker weight becomes a matrix, the row and column dimensions of which can be adjusted. In the isolated-word experiment, the proposed method showed better performance than both eigenvoice and MLLR for the adaptation data of about 20 s or longer.