No Arabic abstract
Recent works have demonstrated the added value of dynamic amino acid positron emission tomography (PET) for glioma grading and genotyping, biopsy targeting, and recurrence diagnosis. However, most of these studies are exclusively based on hand-crafted qualitative or semi-quantitative dynamic features extracted from the mean time activity curve (TAC) within predefined volumes. Voxelwise dynamic PET data analysis could instead provide a better insight into intra-tumour heterogeneity of gliomas. In this work, we investigate the ability of the widely used principal component analysis (PCA) method to extract meaningful quantitative dynamic features from high-dimensional motion-corrected dynamic [S-methyl-11C]methionine PET data in a first cohort of 20 glioma patients. By means of realistic numerical simulations, we demonstrate the robustness of our methodology to noise. In a second cohort of 13 glioma patients, we compare the resulting parametric maps to these provided by standard one- and two-tissue compartment pharmacokinetic (PK) models. We show that our PCA model outperforms PK models in the identification of intra-tumour uptake dynamics heterogeneity while being much less computationally expensive. Such parametric maps could be valuable to assess tumour aggressiveness locally with applications in treatment planning as well as in the evaluation of tumour progression and response to treatment. This work also provides further encouraging results on the added value of dynamic over static analysis of [S-methyl-11C]methionine PET data in gliomas, as previously demonstrated for O-(2-[18F]fluoroethyl)-L-tyrosine.
We show how to efficiently project a vector onto the top principal components of a matrix, without explicitly computing these components. Specifically, we introduce an iterative algorithm that provably computes the projection using few calls to any black-box routine for ridge regression. By avoiding explicit principal component analysis (PCA), our algorithm is the first with no runtime dependence on the number of top principal components. We show that it can be used to give a fast iterative method for the popular principal component regression problem, giving the first major runtime improvement over the naive method of combining PCA with regression. To achieve our results, we first observe that ridge regression can be used to obtain a smooth projection onto the top principal components. We then sharpen this approximation to true projection using a low-degree polynomial approximation to the matrix step function. Step function approximation is a topic of long-term interest in scientific computing. We extend prior theory by constructing polynomials with simple iterative structure and rigorously analyzing their behavior under limited precision.
In recent years, Independent Component Analysis (ICA) has successfully been applied to remove noise and artifacts in images obtained from Three-dimensional Polarized Light Imaging (3D-PLI) at the mesoscale (i.e., 64 $mu$m). Here, we present an automatic denoising procedure for gray matter regions that allows to apply the ICA also to microscopic images, with reasonable computational effort. Apart from an automatic segmentation of gray matter regions, we applied the denoising procedure to several 3D-PLI images from a rat and a vervet monkey brain section.
Head-related transfer function (HRTF) plays an important role in the construction of 3D auditory display. This paper presents an individual HRTF modeling method using deep neural networks based on spatial principal component analysis. The HRTFs are represented by a small set of spatial principal components combined with frequency and individual-dependent weights. By estimating the spatial principal components using deep neural networks and mapping the corresponding weights to a quantity of anthropometric parameters, we predict individual HRTFs in arbitrary spatial directions. The objective and subjective experiments evaluate the HRTFs generated by the proposed method, the principal component analysis (PCA) method, and the generic method. The results show that the HRTFs generated by the proposed method and PCA method perform better than the generic method. For most frequencies the spectral distortion of the proposed method is significantly smaller than the PCA method in the high frequencies but significantly larger in the low frequencies. The evaluation of the localization model shows the PCA method is better than the proposed method. The subjective localization experiments show that the PCA and the proposed methods have similar performances in most conditions. Both the objective and subjective experiments show that the proposed method can predict HRTFs in arbitrary spatial directions.
Principal component analysis has been widely adopted to reduce the dimension of data while preserving the information. The quantum version of PCA (qPCA) can be used to analyze an unknown low-rank density matrix by rapidly revealing the principal components of it, i.e. the eigenvectors of the density matrix with largest eigenvalues. However, due to the substantial resource requirement, its experimental implementation remains challenging. Here, we develop a resonant analysis algorithm with the minimal resource for ancillary qubits, in which only one frequency scanning probe qubit is required to extract the principal components. In the experiment, we demonstrate the distillation of the first principal component of a 4$times$4 density matrix, with the efficiency of 86.0% and fidelity of 0.90. This work shows the speed-up ability of quantum algorithm in dimension reduction of data and thus could be used as part of quantum artificial intelligence algorithms in the future.
Dimension reduction for high-dimensional compositional data plays an important role in many fields, where the principal component analysis of the basis covariance matrix is of scientific interest. In practice, however, the basis variables are latent and rarely observed, and standard techniques of principal component analysis are inadequate for compositional data because of the simplex constraint. To address the challenging problem, we relate the principal subspace of the centered log-ratio compositional covariance to that of the basis covariance, and prove that the latter is approximately identifiable with the diverging dimensionality under some subspace sparsity assumption. The interesting blessing-of-dimensionality phenomenon enables us to propose the principal subspace estimation methods by using the sample centered log-ratio covariance. We also derive nonasymptotic error bounds for the subspace estimators, which exhibits a tradeoff between identification and estimation. Moreover, we develop efficient proximal alternating direction method of multipliers algorithms to solve the nonconvex and nonsmooth optimization problems. Simulation results demonstrate that the proposed methods perform as well as the oracle methods with known basis. Their usefulness is illustrated through an analysis of word usage pattern for statisticians.