Nonlinear dimension reduction in pathway-based genome-wide association analysis

Pathway based genome wide association study evolves from pathway analysis for microarray gene expression and is under rapid development as a complementary for single-SNP based genome wide association study. However, it faces new challenges, such as the summarization of SNP statistics to pathway statistics. The current study applies the ridge regularized Kernel Sliced Inverse Regression (KSIR) to achieve dimension reduction and compared this method to the other two widely used methods, the minimal-p-value (minP) approach of assigning the best test statistics of all SNPs in each pathway as the statistics of the pathway and the principal component analysis (PCA) method of utilizing PCA to calculate the principal components of each pathway. Comparison of the three methods using simulated datasets consisting of 500 cases, 500 controls and100 SNPs demonstrated that KSIR method outperformed the other two methods in terms of causal pathway ranking and the statistical power. PCA method showed similar performance as the minP method. KSIR method also showed a better performance over the other two methods in analyzing a real dataset, the WTCCC Ulcerative Colitis dataset consisting of 1762 cases, 3773 controls as the discovery cohort and 591 cases, 1639 controls as the replication cohort. Several immune and non-immune pathways relevant to ulcerative colitis were identified by these methods. Results from the current study provided a reference for further methodology development and identified novel pathways that may be of importance to the development of ulcerative colitis.^

A methodology to compare dimensionality reduction algorithms in terms of loss of quality

Dimensionality Reduction (DR) is attracting more attention these days as a result of the increasing need to handle huge amounts of data effectively. DR methods allow the number of initial features to be reduced considerably until a set of them is found that allows the original properties of the data to be kept. However, their use entails an inherent loss of quality that is likely to affect the understanding of the data, in terms of data analysis. This loss of quality could be determinant when selecting a DR method, because of the nature of each method. In this paper, we propose a methodology that allows different DR methods to be analyzed and compared as regards the loss of quality produced by them. This methodology makes use of the concept of preservation of geometry (quality assessment criteria) to assess the loss of quality. Experiments have been carried out by using the most well-known DR algorithms and quality assessment criteria, based on the literature. These experiments have been applied on 12 real-world datasets. Results obtained so far show that it is possible to establish a method to select the most appropriate DR method, in terms of minimum loss of quality. Experiments have also highlighted some interesting relationships between the quality assessment criteria. Finally, the methodology allows the appropriate choice of dimensionality for reducing data to be established, whilst giving rise to a minimum loss of quality.

A visual framework to accelerate knowledge discovery based on dimensionality reduction minimizing degradation of quality

Tradicionalmente, el uso de técnicas de análisis de datos ha sido una de las principales vías para el descubrimiento de conocimiento oculto en grandes cantidades de datos, recopilados por expertos en diferentes dominios. Por otra parte, las técnicas de visualización también se han usado para mejorar y facilitar este proceso. Sin embargo, existen limitaciones serias en la obtención de conocimiento, ya que suele ser un proceso lento, tedioso y en muchas ocasiones infructífero, debido a la dificultad de las personas para comprender conjuntos de datos de grandes dimensiones. Otro gran inconveniente, pocas veces tenido en cuenta por los expertos que analizan grandes conjuntos de datos, es la degradación involuntaria a la que someten a los datos durante las tareas de análisis, previas a la obtención final de conclusiones. Por degradación quiere decirse que los datos pueden perder sus propiedades originales, y suele producirse por una reducción inapropiada de los datos, alterando así su naturaleza original y llevando en muchos casos a interpretaciones y conclusiones erróneas que podrían tener serias implicaciones. Además, este hecho adquiere una importancia trascendental cuando los datos pertenecen al dominio médico o biológico, y la vida de diferentes personas depende de esta toma final de decisiones, en algunas ocasiones llevada a cabo de forma inapropiada. Ésta es la motivación de la presente tesis, la cual propone un nuevo framework visual, llamado MedVir, que combina la potencia de técnicas avanzadas de visualización y minería de datos para tratar de dar solución a estos grandes inconvenientes existentes en el proceso de descubrimiento de información válida. El objetivo principal es hacer más fácil, comprensible, intuitivo y rápido el proceso de adquisición de conocimiento al que se enfrentan los expertos cuando trabajan con grandes conjuntos de datos en diferentes dominios. Para ello, en primer lugar, se lleva a cabo una fuerte disminución en el tamaño de los datos con el objetivo de facilitar al experto su manejo, y a la vez preservando intactas, en la medida de lo posible, sus propiedades originales. Después, se hace uso de efectivas técnicas de visualización para representar los datos obtenidos, permitiendo al experto interactuar de forma sencilla e intuitiva con los datos, llevar a cabo diferentes tareas de análisis de datos y así estimular visualmente su capacidad de comprensión. De este modo, el objetivo subyacente se basa en abstraer al experto, en la medida de lo posible, de la complejidad de sus datos originales para presentarle una versión más comprensible, que facilite y acelere la tarea final de descubrimiento de conocimiento. MedVir se ha aplicado satisfactoriamente, entre otros, al campo de la magnetoencefalografía (MEG), que consiste en la predicción en la rehabilitación de lesiones cerebrales traumáticas (Traumatic Brain Injury (TBI) rehabilitation prediction). Los resultados obtenidos demuestran la efectividad del framework a la hora de acelerar y facilitar el proceso de descubrimiento de conocimiento sobre conjuntos de datos reales. ABSTRACT Traditionally, the use of data analysis techniques has been one of the main ways of discovering knowledge hidden in large amounts of data, collected by experts in different domains. Moreover, visualization techniques have also been used to enhance and facilitate this process. However, there are serious limitations in the process of knowledge acquisition, as it is often a slow, tedious and many times fruitless process, due to the difficulty for human beings to understand large datasets. Another major drawback, rarely considered by experts that analyze large datasets, is the involuntary degradation to which they subject the data during analysis tasks, prior to obtaining the final conclusions. Degradation means that data can lose part of their original properties, and it is usually caused by improper data reduction, thereby altering their original nature and often leading to erroneous interpretations and conclusions that could have serious implications. Furthermore, this fact gains a trascendental importance when the data belong to medical or biological domain, and the lives of people depends on the final decision-making, which is sometimes conducted improperly. This is the motivation of this thesis, which proposes a new visual framework, called MedVir, which combines the power of advanced visualization techniques and data mining to try to solve these major problems existing in the process of discovery of valid information. Thus, the main objective is to facilitate and to make more understandable, intuitive and fast the process of knowledge acquisition that experts face when working with large datasets in different domains. To achieve this, first, a strong reduction in the size of the data is carried out in order to make the management of the data easier to the expert, while preserving intact, as far as possible, the original properties of the data. Then, effective visualization techniques are used to represent the obtained data, allowing the expert to interact easily and intuitively with the data, to carry out different data analysis tasks, and so visually stimulating their comprehension capacity. Therefore, the underlying objective is based on abstracting the expert, as far as possible, from the complexity of the original data to present him a more understandable version, thus facilitating and accelerating the task of knowledge discovery. MedVir has been succesfully applied to, among others, the field of magnetoencephalography (MEG), which consists in predicting the rehabilitation of Traumatic Brain Injury (TBI). The results obtained successfully demonstrate the effectiveness of the framework to accelerate and facilitate the process of knowledge discovery on real world datasets.

Analysis of pattern recognition and dimensionality reduction techniques for odor biometrics

In this paper, we analyze the performance of several well-known pattern recognition and dimensionality reduction techniques when applied to mass-spectrometry data for odor biometric identification. Motivated by the successful results of previous works capturing the odor from other parts of the body, this work attempts to evaluate the feasibility of identifying people by the odor emanated from the hands. By formulating this task according to a machine learning scheme, the problem is identified with a small-sample-size supervised classification problem in which the input data is formed by mass spectrograms from the hand odor of 13 subjects captured in different sessions. The high dimensionality of the data makes it necessary to apply feature selection and extraction techniques together with a simple classifier in order to improve the generalization capabilities of the model. Our experimental results achieve recognition rates over 85% which reveals that there exists discriminatory information in the hand odor and points at body odor as a promising biometric identifier.

Dimensionality Reduction Through Sub-Space Mapping for Nearest Neighbour Algorithms

Postprint

An adaptive and dynamic dimensionality reduction method for high-dimensional indexing

The notorious "dimensionality curse" is a well-known phenomenon for any multi-dimensional indexes attempting to scale up to high dimensions. One well-known approach to overcome degradation in performance with respect to increasing dimensions is to reduce the dimensionality of the original dataset before constructing the index. However, identifying the correlation among the dimensions and effectively reducing them are challenging tasks. In this paper, we present an adaptive Multi-level Mahalanobis-based Dimensionality Reduction (MMDR) technique for high-dimensional indexing. Our MMDR technique has four notable features compared to existing methods. First, it discovers elliptical clusters for more effective dimensionality reduction by using only the low-dimensional subspaces. Second, data points in the different axis systems are indexed using a single B+-tree. Third, our technique is highly scalable in terms of data size and dimension. Finally, it is also dynamic and adaptive to insertions. An extensive performance study was conducted using both real and synthetic datasets, and the results show that our technique not only achieves higher precision, but also enables queries to be processed efficiently. Copyright Springer-Verlag 2005

Dimensionality reduction in complex models

As a part of the Managing Uncertainty in Complex Models (MUCM) project, research at Aston University will develop methods for dimensionality reduction of the input and/or output spaces of models, as seen within the emulator framework. Towards this end this report describes a framework for generating toy datasets, whose underlying structure is understood, to facilitate early investigations of dimensionality reduction methods and to gain a deeper understanding of the algorithms employed, both in terms of how effective they are for given types of models / situations, and also their speed in applications and how this scales with various factors. The framework, which allows the evaluation of both screening and projection approaches to dimensionality reduction, is described. We also describe the screening and projection methods currently under consideration and present some preliminary results. The aim of this draft of the report is to solicit feedback from the project team on the dataset generation framework, the methods we propose to use, and suggestions for extensions that should be considered.

Exploratory database visualisation: the application and assessment of data and dimensionality reduction

This thesis describes the development of a complete data visualisation system for large tabular databases, such as those commonly found in a business environment. A state-of-the-art 'cyberspace cell' data visualisation technique was investigated and a powerful visualisation system using it was implemented. Although allowing databases to be explored and conclusions drawn, it had several drawbacks, the majority of which were due to the three-dimensional nature of the visualisation. A novel two-dimensional generic visualisation system, known as MADEN, was then developed and implemented, based upon a 2-D matrix of 'density plots'. MADEN allows an entire high-dimensional database to be visualised in one window, while permitting close analysis in 'enlargement' windows. Selections of records can be made and examined, and dependencies between fields can be investigated in detail. MADEN was used as a tool for investigating and assessing many data processing algorithms, firstly data-reducing (clustering) methods, then dimensionality-reducing techniques. These included a new 'directed' form of principal components analysis, several novel applications of artificial neural networks, and discriminant analysis techniques which illustrated how groups within a database can be separated. To illustrate the power of the system, MADEN was used to explore customer databases from two financial institutions, resulting in a number of discoveries which would be of interest to a marketing manager. Finally, the database of results from the 1992 UK Research Assessment Exercise was analysed. Using MADEN allowed both universities and disciplines to be graphically compared, and supplied some startling revelations, including empirical evidence of the 'Oxbridge factor'.

A Bayesian approach for place recognition

This paper presents a robust place recognition algorithm for mobile robots. The framework proposed combines nonlinear dimensionality reduction, nonlinear regression under noise, and variational Bayesian learning to create consistent probabilistic representations of places from images. These generative models are learnt from a few images and used for multi-class place recognition where classification is computed from a set of feature-vectors. Recognition can be performed in near real-time and accounts for complexity such as changes in illumination, occlusions and blurring. The algorithm was tested with a mobile robot in indoor and outdoor environments with sequences of 1579 and 3820 images respectively. This framework has several potential applications such as map building, autonomous navigation, search-rescue tasks and context recognition.

A bayesian approach for place recognition

This paper presents a robust place recognition algorithm for mobile robots that can be used for planning and navigation tasks. The proposed framework combines nonlinear dimensionality reduction, nonlinear regression under noise, and Bayesian learning to create consistent probabilistic representations of places from images. These generative models are incrementally learnt from very small training sets and used for multi-class place recognition. Recognition can be performed in near real-time and accounts for complexity such as changes in illumination, occlusions, blurring and moving objects. The algorithm was tested with a mobile robot in indoor and outdoor environments with sequences of 1579 and 3820 images, respectively. This framework has several potential applications such as map building, autonomous navigation, search-rescue tasks and context recognition.

On the relation of slow feature analysis and Laplacian eigenmaps

The past decade has seen a rise of interest in Laplacian eigenmaps (LEMs) for nonlinear dimensionality reduction. LEMs have been used in spectral clustering, in semisupervised learning, and for providing efficient state representations for reinforcement learning. Here, we show that LEMs are closely related to slow feature analysis (SFA), a biologically inspired, unsupervised learning algorithm originally designed for learning invariant visual representations. We show that SFA can be interpreted as a function approximation of LEMs, where the topological neighborhoods required for LEMs are implicitly defined by the temporal structure of the data. Based on this relation, we propose a generalization of SFA to arbitrary neighborhood relations and demonstrate its applicability for spectral clustering. Finally, we review previous work with the goal of providing a unifying view on SFA and LEMs. © 2011 Massachusetts Institute of Technology.

Computational information geometry and its applications

Digitization is the main feature of modern Information Science. Conjoining the digits and the coordinates, the relation between Information Science and high-dimensional space is consanguineous, and the information issues are transformed to the geometry problems in some high-dimensional spaces. From this basic idea, we propose Computational Information Geometry (CIG) to make information analysis and processing. Two kinds of applications of CIG are given, which are blurred image restoration and pattern recognition. Experimental results are satisfying. And in this paper, how to combine with groups of simple operators in some 2D planes to implement the geometrical computations in high-dimensional space is also introduced. Lots of the algorithms have been realized using software.

一种基于改进LLE方法的传感器故障诊断方法研究

针对非线性系统传感器故障诊断难以解决的问题,提出了一种新的基于局部嵌入映射(LLE)的方法,解决了非线性数据的特征映射问题。首先,改进了基于分形维估计的内在维数的估计,通过线性拟合解决了线性区域的自动确定。然后,将故障状态与空间分布结合起来,通过确定数据点在空间超球内的分布完成故障的检测,在这个过程中将超球的确定与LLE算法中基于核函数的样本外数据扩展结合起来,大大减少了计算量,提高了算法的实时性,从而为复杂非线性传感器的故障诊断提供了一种新的有效的方法。

Evaluating perceptual maps of asymmetries for gait symmetry quantification and pathology detection

Le mouvement de la marche est un processus essentiel de l'activité humaine et aussi le résultat de nombreuses interactions collaboratives entre les systèmes neurologiques, articulaires et musculo-squelettiques fonctionnant ensemble efficacement. Ceci explique pourquoi une analyse de la marche est aujourd'hui de plus en plus utilisée pour le diagnostic (et aussi la prévention) de différents types de maladies (neurologiques, musculaires, orthopédique, etc.). Ce rapport présente une nouvelle méthode pour visualiser rapidement les différentes parties du corps humain liées à une possible asymétrie (temporellement invariante par translation) existant dans la démarche d'un patient pour une possible utilisation clinique quotidienne. L'objectif est de fournir une méthode à la fois facile et peu dispendieuse permettant la mesure et l'affichage visuel, d'une manière intuitive et perceptive, des différentes parties asymétriques d'une démarche. La méthode proposée repose sur l'utilisation d'un capteur de profondeur peu dispendieux (la Kinect) qui est très bien adaptée pour un diagnostique rapide effectué dans de petites salles médicales car ce capteur est d'une part facile à installer et ne nécessitant aucun marqueur. L'algorithme que nous allons présenter est basé sur le fait que la marche saine possède des propriétés de symétrie (relativement à une invariance temporelle) dans le plan coronal.