Browsing by Subject "Clustering"

I consider the problem of clustering multiple related groups of data. My approach entails mixture models in the context of hierarchical Dirichlet processes, focusing on their ability to perform inference on the unknown number of components in the mixture, as well as to facilitate the sharing of information and borrowing of strength across the various data groups. Here, I build upon the hierarchical Dirichlet process model proposed by Muller et al. (2004), revising some relevant aspects of the model, as well as improving the MCMC sampler's convergence by combining local Gibbs sampler moves with global Metropolis-Hastings split-merge moves. I demonstrate the strengths of my model by employing it to cluster both synthetic and real datasets.

The immune system is constantly faced with the daunting task of protecting the host from a large number of ever-evolving pathogens. In vertebrates, the immune response results from the interplay of two cellular systems: the innate immunity and the adaptive immunity. In the past decades, dendritic cells have emerged as major players in the modulation of the immune response, being one of the primary links between these two branches of the immune system.

Dendritic cells are pathogen-sensing cells that alert the rest of the immune system of the presence of infection. The signals sent by dendritic cells result in the recruitment of the appropriate cell types and molecules required for effectively clearing the infection. A question of utmost importance in our understanding of the immune response and our ability to manipulate it in the development of vaccines and therapies is: "How do dendritic cells translate the various cues they perceive from the environment into different signals that specifically activate the appropriate parts of the immune system that result in an immune response streamlined to clear the given pathogen?"

Here we have developed computational and statistical methods aimed to address specific aspects of this question. In particular, understanding how dendritic cells ultimately modulate the immune response requires an understanding of the subtleties of their maturation process in response to different environmental signals. Hence, the first part of this dissertation focuses on elucidating the changes in the transcriptional

program of dendritic cells in response to the detection of two common pathogen- associated molecules, LPS and CpG. We have developed a method based on Langevin and Dirichlet processes to model and cluster gene expression temporal data, and have used it to identify, on a large scale, genes that present unique and common transcriptional behaviors in response to these two stimuli. Additionally, we have also investigated a different, but related, aspect of dendritic cell modulation of the adaptive immune response. In the second part of this dissertation, we present a method to predict peptides that will bind to MHC molecules, a requirement for the activation of pathogen-specific T cells. Together, these studies contribute to the elucidation of important aspects of dendritic cell biology.

Purpose: To develop and evaluate an automatic IMRT planning technique for prostate cancer utilizing prior expert plan's dose distribution as guidance.

Methods and Materials: In this study, the anatomical information of prostate cancer cases was parameterized and quantified into two measures: the percent distance-to-prostate (PDP) and the concaveness angle. Based on these two quantities, a plan atlas composed of 5 expert prostate IMRT plans was built out of a 70-case pool at our institution using k-medoids clustering analysis.

Extra 20 cases were used as query cases to evaluate the dose-guided automatic planning (DAP) scheme. Each query case was matched to an atlas case based on PTV-OAR anatomical features followed by deformable registration to enhance fine local matching. Using the deformation field, the expert dose in the matched atlas case was warped onto the query case, creating the goal dose conformal to the query case's anatomy. Dose volume histograms (DVHs) objectives were sampled from the goal dose to guide automatic IMRT treatment planning. Dosimetric comparison between DAP plans and clinical plans were performed.

Results: Generating goal dose is highly efficient by using MIM^TM workflows. The deformable registration provides high-quality goal dose tailored to query case's anatomy in terms of the dose falloff at the PTV-OAR boundary and the overall conformity. Automatic planning in Eclipse^TM takes ~2.5 min (~70 iterations) without human intervention. Compared to clinical plans, DAP plans improved the conformity index from 0.85±0.04 to 0.88±0.02 (p=0.0045), the bladder-gEUD from 40.7±3.2 Gy to 40.0±3.1 Gy (p=0.0003), and rectum-gEUD from 40.4±2.0 Gy to 39.9±2.1 Gy (p=0.0167). Other dosimetric parameter is similar (p>0.05): homogeneity indices are 7.4±0.9% and 7.1±1.5%, for DAP plans and clinical plans, respectively.

Conclusions: Dose-guided automatic treatment planning is feasible and efficient. Atlas-based patient-specific dose objectives can effectively guide the optimizer to achieve similar or better plan quality compared to clinical plans.

A multilevel analysis of malaria risk factors was conducted using data gathered from community-wide surveillance along the Iquitos-Mazan Road and Napo River in Loreto, Peru. In total, 1650 individuals nested within 338 households nested within 18 communities were included in the study. Personal travel (Odds Ratios [OR] 2.48; 95% Confidence Interval [CI] = 1.46, 4.21) and other house member's malaria statuses (OR = 2.54; 95% CI = 1.49, 4.32) were all associated with increased odds in having a malaria episode. Having a large household (>5 individuals) (OR = 0.33; 95% CI = 0.12, 0.93), presence of a community health post / secondary school (OR =0.26; 95% CI = 0.08, 0.80) and church (OR = 0.33; 95% CI = 0.30, 0.78) were associated with lower odds of having a malaria episode. Malaria clustering was evident as 54% of the malaria burden occurred in only 6% of the households surveyed.

In this thesis, we explore techniques in statistics and persistent homology, which detect features among data sets such as graphs, triangulations and point cloud. We accompany our theorems with algorithms and experiments, to demonstrate their effectiveness in practice.

We start with the derivation of graph scan statistics, a measure useful to assess the statistical significance of a subgraph in terms of edge density. We cluster graphs into densely-connected subgraphs based on this measure. We give algorithms for finding such clusterings and experiment on real-world data.

We next study statistics on persistence, for piecewise-linear functions defined on the triangulations of topological spaces. We derive persistence pairing probabilities among vertices in the triangulation. We also provide upper bounds for total persistence in expectation.

We continue by examining the elevation function defined on the triangulation of a surface. Its local maxima obtained by persistence pairing are useful in describing features of the triangulations of protein surfaces. We describe an algorithm to compute these local maxima, with a run-time ten-thousand times faster in practice than previous method. We connect such improvement with the total Gaussian curvature of the surfaces.

Finally, we study a stratification learning problem: given a point cloud sampled from a stratified space, which points belong to the same strata, at a given scale level? We assess the local structure of a point in relation to its neighbors using kernel and cokernel persistent homology. We prove the effectiveness of such assessment through several inference theorems, under the assumption of dense sample. The topological inference theorem relates the sample density with the homological feature size. The probabilistic inference theorem provides sample estimates to assess the local structure with confidence. We describe an algorithm that computes the kernel and cokernel persistence diagrams and prove its correctness. We further experiment on simple synthetic data.

Inferring brain states from EEG signals allows for the management of sleep disorders and brain diseases by providing an insight into the electrophysiological state of the brain. We explore the use of topic modeling – which are popular text processing algorithms – to infer brain states from EEG signals. Latent Dirichlet allocation (LDA) is our preferred topic model because of its mixture-of-mixtures nature and its ability to be trained in an unsupervised manner. First, we present an architecture of a deep convolutional auto-encoder neural network to automatically learn feature representations from EEG signals. The network uses a combination of convolutional and max-pooling layers to achieve reduction in the dimensionality of raw data, and can be trained in an unsupervised manner. We demonstrate an improvement in clustering EEG signals into sleep stages with the LDA topic model using features derived from the auto-encoder, compared to standard manually extracted EEG features. Next, we address the issue of modeling continuous domain data using topic modeling. In the LDA topic model, topics are modeled as discrete distributions over a finite vocabulary of words. Modeling data spanning a continuous domain with the LDA requires discrete approximations of the continuous data, which can lead to loss of information and may not represent the true structure of the underlying data. We present the GMM-LDA topic model, where topics are represented using Gaussian mixture models (GMMs), which are multi-modal distributions spanning a continuous domain. We present results demonstrating superior clustering performance in clustering EEG data into sleep stages using the GMM-LDA topic model compared to the standard LDA and other clustering algorithms. Finally, we explore a set of features that can be potentially used with topic modeling to infer brain states corresponding to brain injury in mice. Spectral, entropy and moment related features are extracted from EEG signals recorded from mice with artificially induced brain injury. We present an analysis on the relative importance of these features using bagged decision trees, and demonstrate that a combination of these features can potentially be used to track the progression of brain injury and also to predict recovery from brain injury in mice.