22622233
Using Uncorrelated Discriminant Analysis for Tissue Classification with Gene Expression Data
The classification of tissue samples based on gene expression data is an important problem in medical diagnosis of diseases such as cancer. In gene expression data, the number of genes is usually very high (in the thousands) compared to the number of data samples (in the tens or low hundreds); that is, the data dimension is large compared to the number of data points (such data is said to be undersampled). To cope with performance and accuracy problems associated with high dimensionality, it is commonplace to apply a preprocessing step that transforms the data to a space of significantly lower dimension with limited loss of the information present in the original data. Linear Discriminant Analysis (LDA) is a well-known technique for dimension reduction and feature extraction, but it is not applicable for undersampled data due to singularity problems associated with the matrices in the underlying representation. This paper presents a dimension reduction and feature extraction scheme, called Uncorrelated Linear Discriminant Analysis (ULDA), for undersampled problems and illustrates its utility on gene expression data. ULDA employs the Generalized Singular Value Decomposition method to handle undersampled data and the features that it produces in the transformed space are uncorrelated, which makes it attractive for gene expression data. The properties of ULDA are established rigorously and extensive experimental results on gene expression data are presented to illustrate its effectiveness in classifying tissue samples. These results provide a comparative study of various state-of-the-art classification methods on well-known gene expression data sets.
9813108
CoFD : An Algorithm for Non-distance Based Clustering in High Dimensional Spaces
The clustering problem, which aims at identifying the distribution of patterns and intrinsic correlations in large data sets by partitioning the data points into similarity clusters, has been widely studied. Traditional clustering algorithms use distance functions to measure similarity and are not suitable for high dimensional spaces. In this paper, we propose CoFD algorithm, which is a non-distance based clustering algorithm for high dimensional spaces. Based on the maximum likelihood principle, CoFD is to optimize parameters to maximize the likelihood between data points and the model generated by the parameters. Experimental results on both synthetic data sets and a real data set show the efficiency and effectiveness of CoFD.
206784011
The Relationships Among Various Nonnegative Matrix Factorization Methods for Clustering
The nonnegative matrix factorization (NMF) has been shown recently to be useful for clustering and various extensions and variations of NMF have been proposed recently. Despite significant research progress in this area, few attempts have been made to establish the connections between various factorization methods while highlighting their differences. In this paper we aim to provide a comprehensive study on matrix factorization for clustering. In particular, we present an overview and summary on various matrix factorization algorithms and theoretically analyze the relationships among them. Experiments are also conducted to empirically evaluate and compare various factorization methods. In addition, our study also answers several previously unaddressed yet important questions for matrix factorizations including the interpretation and normalization of cluster posterior and the benefits and evaluation of simultaneous clustering. We expect our study would provide good insights on matrix factorization research for clustering.
654543
A survey on wavelet applications in data mining
Recently there has been significant development in the use of wavelet methods in various data mining processes. However, there has been written no comprehensive survey available on the topic. The goal of this is paper to fill the void. First, the paper presents a high-level data-mining framework that reduces the overall process into smaller components. Then applications of wavelets for each component are reviewd. The paper concludes by discussing the impact of wavelets on data mining research and outlining potential future research directions and applications.
1750917
A general model for clustering binary data
Clustering is the problem of identifying the distribution of patterns and intrinsic correlations in large data sets by partitioning the data points into similarity classes. This paper studies the problem of clustering binary data. This is the case for market basket datasets where the transactions contain items and for document datasets where the documents contain "bag of words". The contribution of the paper is three-fold. First a general binary data clustering model is presented. The model treats the data and features equally, based on their symmetric association relations, and explicitly describes the data assignments as well as feature assignments. We characterize several variations with different optimization procedures for the general model. Second, we also establish the connections between our clustering model with other existing clustering methods. Third, we also discuss the problem for determining the number of clusters for binary clustering. Experimental results show the effectiveness of the proposed clustering model.
3018061
Instruction Balance and Its Relation to Program Energy Consumption
A computer consists of multiple components such as functional units, cache and main memory. At each moment of execution, a program may have a varied amount of work for each component. Recent development has exploited this imbalance to save energy by slowing the components that have a lower load. Example techniques include dynamic scaling and clock gating used in processors from Transmeta and Intel. Symmetrical to reconfiguring hardware is reorganizing software. We can alter program demand for different components by reordering program instructions. This paper explores the theoretical lower bound of energy consumption assuming that both a program and a machine are fully adjustable. It shows that a program with a balanced load always consumes less energy than the same program with uneven loads under the same execution speed. In addition, the paper examines the relation between energy consumption and program performance. It shows that reducing power is a different problem than that of improving performance. Finally, the paper presents empirical evidence showing that a program may be transformed to have a balanced demand in most parts of its execution.
8716577
Blind identification and deconvolution of linear systems driven by binary random sequences
The problem of blind identification and deconvolution of linear systems with independent binary inputs is addressed. To solve the problem, a linear system is applied to the observed data and adjusted so as to produce binary outputs. It is proved that the system coincides with the inverse of the unknown system (with scale and shift ambiguities), whether it is minimum or nonminimum phase. These results are derived for nonstationary independent binary inputs of infinite or finite length. Based on these results, an identification method is proposed for parametric linear systems. It is shown that under some mild conditions, a consistent estimator of the parameter can be obtained by minimizing a binariness criterion for the output data. Unlike many other blind identification and deconvolution methods, this criterion handles nonstationary signals and does not utilize any moment information of the inputs. Three numerical examples are presented to demonstrate the effectiveness of the proposed method. >
25228668
A joint estimation approach for two-tone image deblurring by blind deconvolution
A new statistical method is proposed for deblurring two-tone images, i.e., images with two unknown grey levels, that are blurred by an unknown linear filter. The key idea of the proposed method is to adjust a deblurring filter until its output becomes two tone. Two optimization criteria are proposed for the adjustment of the deblurring filter. A three-step iterative algorithm (TSIA) is also proposed to minimize the criteria. It is proven mathematically that by minimizing either of the criteria, the original (nonblurred) image, along with the blur filter, will be recovered uniquely (only with possible scale/shift ambiguities) at high SNR. The recovery is guaranteed not only for i.i.d. images but also for correlated and nonstationary images. It does not require a priori knowledge of the statistical parameters or the tone values of the original image; neither does it require a priori knowledge of the phase or other special information (e.g., FIR, symmetry, nonnegativity, etc.) about the blur filter. Numerical experiments are carried out to test the method on synthetic and real images.
42024829
Strong consistency of the contraction mapping method for frequency estimation
Some statistical properties in regard to the contraction mapping (CM) method are discussed. One of the requirements in this method is that the filter be parameterized to satisfy a certain fundamental property. The parameterization clearly depends on the normalized noise spectrum which theoretically has to be known or estimated a priori. If this information is available, one can first whiten the noise with a linear filter and then apply the CM method to the filtered data. In this way, the parameterization only needs to be done under the white noise assumption and filters like the AR(2) can be used by the CM method. In applications, however, prewhitening may not always be necessary. >
2911701
Workload characterization of bioinformatics applications
The exponential growth in the amount of genomic information has spurred growing interest in large scale analysis of genetic data. Bioinformatics applications represent the increasingly important workloads. However, very few results on the behavior of these applications running on the state-of-the-art microprocessor and systems have been published. This paper proposes a suite of widely used bioinformatics applications and studies the execution characteristics of these benchmarks on a representative architecture-the Intel Pentium 4. To understand the impacts and implications of bioinformatics workloads on the microprocessor designs, we contrast the characteristics of bioinformatics workloads and the widely used SPEC 2000 integer benchmarks.
206736471
Wavelet spectrum and its characterization property for random processes
The wavelet spectrum of a random process comprises the variances of the wavelet coefficients of the process computed within each scale. This paper investigates the possibility of using the wavelet spectrum, obtained from a continuous wavelet transform (CWT), to uniquely represent the second-order statistical properties of random processes-particularly, stationary processes and long-memory nonstationary processes. As is well known, the Fourier spectrum of a stationary process is mathematically equivalent to the autocovariance function (ACF) and thus uniquely determines the second-order statistics of the process. This characterization property is shown to be possessed also by the wavelet spectrum under very mild regularity conditions that are easily satisfied by many widely used wavelets. It is also shown that under suitable regularity conditions, the characterization property remains valid for processes with stationary increments including 1/f noise.