A new registration method based on Log-Euclidean tensor metrics and its application to genetic studies

In structural brain MRI, group differences or changes in brain structures can be detected using Tensor-Based Morphometry (TBM). This method consists of two steps: (1) a non-linear registration step, that aligns all of the images to a common template, and (2) a subsequent statistical analysis. The numerous registration methods that have recently been developed differ in their detection sensitivity when used for TBM, and detection power is paramount in epidemological studies or drug trials. We therefore developed a new fluid registration method that computes the mappings and performs statistics on them in a consistent way, providing a bridge between TBM registration and statistics. We used the Log-Euclidean framework to define a new regularizer that is a fluid extension of the Riemannian elasticity, which assures diffeomorphic transformations. This regularizer constrains the symmetrized Jacobian matrix, also called the deformation tensor. We applied our method to an MRI dataset from 40 fraternal and identical twins, to revealed voxelwise measures of average volumetric differences in brain structure for subjects with different degrees of genetic resemblance.

Clustering of web users using the tensor decomposed models

We propose to use the Tensor Space Modeling (TSM) to represent and analyze the user’s web log data that consists of multiple interests and spans across multiple dimensions. Further we propose to use the decomposition factors of the Tensors for clustering the users based on similarity of search behaviour. Preliminary results show that the proposed method outperforms the traditional Vector Space Model (VSM) based clustering.

Comparison of fractional and geodesic anisotropy in diffusion tensor images of 90 monozygotic and dizygotic twins

We used diffusion tensor magnetic resonance imaging (DTI) to reveal the extent of genetic effects on brain fiber microstructure, based on tensor-derived measures, in 22 pairs of monozygotic (MZ) twins and 23 pairs of dizygotic (DZ) twins (90 scans). After Log-Euclidean denoising to remove rank-deficient tensors, DTI volumes were fluidly registered by high-dimensional mapping of co-registered MP-RAGE scans to a geometrically-centered mean neuroanatomical template. After tensor reorientation using the strain of the 3D fluid transformation, we computed two widely used scalar measures of fiber integrity: fractional anisotropy (FA), and geodesic anisotropy (GA), which measures the geodesic distance between tensors in the symmetric positive-definite tensor manifold. Spatial maps of intraclass correlations (r) between MZ and DZ twins were compared to compute maps of Falconer's heritability statistics, i.e. the proportion of population variance explainable by genetic differences among individuals. Cumulative distribution plots (CDF) of effect sizes showed that the manifold measure, GA, comparably the Euclidean measure, FA, in detecting genetic correlations. While maps were relatively noisy, the CDFs showed promise for detecting genetic influences on brain fiber integrity as the current sample expands.

Tensor-based analysis of genetic influences on brain integrity using DTI in 100 twins

Information from the full diffusion tensor (DT) was used to compute voxel-wise genetic contributions to brain fiber microstructure. First, we designed a new multivariate intraclass correlation formula in the log-Euclidean framework. We then analyzed used the full multivariate structure of the tensor in a multivariate version of a voxel-wise maximum-likelihood structural equation model (SEM) that computes the variance contributions in the DTs from genetic (A), common environmental (C) and unique environmental (E) factors. Our algorithm was tested on DT images from 25 identical and 25 fraternal twin pairs. After linear and fluid registration to a mean template, we computed the intraclass correlation and Falconer's heritability statistic for several scalar DT-derived measures and for the full multivariate tensors. Covariance matrices were found from the DTs, and inputted into SEM. Analyzing the full DT enhanced the detection of A and C effects. This approach should empower imaging genetics studies that use DTI.

Best individual template selection from deformation tensor minimization

We study the influence of the choice of template in tensor-based morphometry. Using 3D brain MR images from 10 monozygotic twin pairs, we defined a tensor-based distance in the log-Euclidean framework [1] between each image pair in the study. Relative to this metric, twin pairs were found to be closer to each other on average than random pairings, consistent with evidence that brain structure is under strong genetic control. We also computed the intraclass correlation and associated permutation p-value at each voxel for the determinant of the Jacobian matrix of the transformation. The cumulative distribution function (cdf) of the p-values was found at each voxel for each of the templates and compared to the null distribution. Surprisingly, there was very little difference between CDFs of statistics computed from analyses using different templates. As the brain with least log-Euclidean deformation cost, the mean template defined here avoids the blurring caused by creating a synthetic image from a population, and when selected from a large population, avoids bias by being geometrically centered, in a metric that is sensitive enough to anatomical similarity that it can even detect genetic affinity among anatomies.

Time series analysis of a Web search engine transaction log

In this paper, we use time series analysis to evaluate predictive scenarios using search engine transactional logs. Our goal is to develop models for the analysis of searchers’ behaviors over time and investigate if time series analysis is a valid method for predicting relationships between searcher actions. Time series analysis is a method often used to understand the underlying characteristics of temporal data in order to make forecasts. In this study, we used a Web search engine transactional log and time series analysis to investigate users’ actions. We conducted our analysis in two phases. In the initial phase, we employed a basic analysis and found that 10% of searchers clicked on sponsored links. However, from 22:00 to 24:00, searchers almost exclusively clicked on the organic links, with almost no clicks on sponsored links. In the second and more extensive phase, we used a one-step prediction time series analysis method along with a transfer function method. The period rarely affects navigational and transactional queries, while rates for transactional queries vary during different periods. Our results show that the average length of a searcher session is approximately 2.9 interactions and that this average is consistent across time periods. Most importantly, our findings shows that searchers who submit the shortest queries (i.e., in number of terms) click on highest ranked results. We discuss implications, including predictive value, and future research.