Cell Type Deconvolution and Transformation of Microenvironment Microarray Data

Transformations are an important aspect of data analysis. In this work we explore the impact of data transformation on the analysis of high-throughput -omics data. Specifically, we explore two applications where data transformation plays an important role. The first application is estimating cell types using gene expression data. Here we develop dtangle, a method that carefully considers scale transformations when estimating cell type proportion estimates. This method broadly out-performs existing deconvolution methods in a comprehensive meta-analysis. Secondly, we explore the role of simple data transformations for the analysis of microenvironment microarray data. In this section we look at simple data transformations and how they interact with visualization, discovery of latent effects, and data integration. We find that simple transformations applied alone or in sequence can make salient important aspects of the data.PHDStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147575/1/gjhunt_1.pd

グループ分離と線形化による非線形BSSにおける収束性解析

金沢大学理工研究域　電子情報学系2次の非線形混合において，信号群分離と線形化を縦 続構成するブラインドソースセパレーション(BSS) が提 案されている．信号群分離では，信号源とその高次項を含んだ同一グループの信号群に分離される．残った高次項は，線形化を通すことにより抑制される．本稿では，まず，この非線形BSSの分離特性を解析する．センサの数は信号源以外の干渉成分を消去するために，信号源の数より増やす必要がある．また，干渉成分は非線形成分の大きさによって決まる．非線形成分の割合とセンサ数の関係について解析し，非線形成分の割合が低い場合にセンサ数を低減できることを確認した．次に，学習において，分離行列の初期値依存性について解析した．ランダムに発生する初期に対して，約30%の確率で良い分離特性が得られた．これにより，比較的少ない探索回数で有効な初期値が求まることが分かった．また，非線形として3 次までを考慮した場合の影響を解析した．3次項が１次項に比べて約10%程度では良い分離特性が得られることを確認した． A blind source separation (BSS), cascading a signal group separation block and a linearization block has been proposed for low-order nonlinear mixtures. In the separation block, the signal sources are separated into each group, including its high-order components. The high-order components are further suppressed through the linearization block. In this paper, separation performance of the nonlinear BSS is analyzed from several view points. The number of the sensors is increased from that of the signal sources in order to cancel the interference. Moreover, the interference components is decided by a ratio of the nonlinear and the linear components. A relation between the ratio of the components and the number of the sensors is analyzed. The number of the sensors can be reduced when the ratio of the onlinearity is small. Next, e ects of the initial guess of the separation matrix is analyzed. The training was carried out using 50 independent random initial guess, and good separation is obtained by a 30% probability. Moreover, effect of including 3rd-order terms is analyzed. When the 3rd-order term is under 10%, good separation performance can be obtained

Extensions of independent component analysis for natural image data

An understanding of the statistical properties of natural images is useful for any kind of processing to be performed on them. Natural image statistics are, however, in many ways as complex as the world which they depict. Fortunately, the dominant low-level statistics of images are sufficient for many different image processing goals. A lot of research has been devoted to second order statistics of natural images over the years. Independent component analysis is a statistical tool for analyzing higher than second order statistics of data sets. It attempts to describe the observed data as a linear combination of independent, latent sources. Despite its simplicity, it has provided valuable insights of many types of natural data. With natural image data, it gives a sparse basis useful for efficient description of the data. Connections between this description and early mammalian visual processing have been noticed. The main focus of this work is to extend the known results of applying independent component analysis on natural images. We explore different imaging techniques, develop algorithms for overcomplete cases, and study the dependencies between the components by using a model that finds a topographic ordering for the components as well as by conditioning the statistics of a component on the activity of another. An overview is provided of the associated problem field, and it is discussed how these relatively small results may eventually be a part of a more complete solution to the problem of vision.reviewe