Detection of perturbation phases and developmental stages in organisms from DNA microarray time series data

Available DNA microarray time series that record gene expression along the developmental stages of multicellular eukaryotes, or in unicellular organisms subject to external perturbations such as stress and diauxie, are analyzed. By pairwise comparison of the gene expression profiles on the basis of a translation-invariant and scale-invariant distance measure corresponding to least-rectangle regression, it is shown that peaks in the average distance values are noticeable and are localized around specific time points. These points systematically coincide with the transition points between developmental phases or just follow the external perturbations. This approach can thus be used to identify automatically, from microarray time series alone, the presence of external perturbations or the succession of developmental stages in arbitrary cell systems. Moreover, our results show that there is a striking similarity between the gene expression responses to these a priori very different phenomena. In contrast, the cell cycle does not involve a perturbation-like phase, but rather continuous gene expression remodeling. Similar analyses were conducted using three other standard distance measures, showing that the one we introduced was superior. Based on these findings, we set up an adapted clustering method that uses this distance measure and classifies the genes on the basis of their expression profiles within each developmental stage or between perturbation phases.     

Nonlinear dimensionality reduction: Alternative ordination approaches for extracting and visualizing biodiversity patterns in tropical montane forest vegetation data

Ecological patterns are difficult to extract directly from vegetation data. The respective surveys provide a high number of interrelated species occurrence variables. Since often only a limited number of ecological gradients determine species distributions, the data might be represented by much fewer but effectively independent variables. This can be achieved by reducing the dimensionality of the data. Conventional methods are either limited to linear feature extraction (e.g., principal component analysis, and Classical Multidimensional Scaling, CMDS) or require a priori assumptions on the intrinsic data dimensionality (e.g., Nonmetric Multidimensional Scaling, NMDS, and self organized maps, SOM).In this study we explored the potential of Isometric Feature Mapping (Isomap). This new method of dimensionality reduction is a nonlinear generalization of CMDS. Isomap is based on a nonlinear geodesic inter-point distance matrix. Estimating geodesic distances requires one free threshold parameter, which defines linear geometry to be preserved in the global nonlinear distance structure. We compared Isomap to its linear (CMDS) and nonmetric (NMDS) equivalents. Furthermore, the use of geodesic distances allowed also extending NMDS to a version that we called NMDS-G. In addition we investigated a supervised Isomap variant (S-Isomap) and showed that all these techniques are interpretable within a single methodical framework.As an example we investigated seven plots (subdivided in 456 subplots) in different secondary tropical montane forests with 773 species of vascular plants. A key problem for the study of tropical vegetation data is the heterogeneous small scale variability implying large ranges of β-diversity. The CMDS and NMDS methods did not reduce the data dimensionality reasonably. On the contrary, Isomap explained 95% of the data variance in the first five dimensions and provided ecologically interpretable visualizations; NMDS-G yielded similar results. The main shortcoming of the latter was the high computational cost and the requirement to predefine the dimension of the embedding space. The S-Isomap learning scheme did not improve the Isomap variant for an optimal threshold parameter but substantially improved the nonoptimal solutions.We conclude that Isomap as a new ordination method allows effective representations of high dimensional vegetation data sets. The method is promising since it does not require a priori assumptions, and is computationally highly effective.     

Gene clustering based on clusterwide mutual information.

Cluster analysis of gene-wide expression data from DNA microarray hybridization studies has proved to be a useful tool for identifying biologically relevant groupings of genes and constructing gene regulatory networks. The motivation for considering mutual information is its capacity to measure a general dependence among gene random variables. We propose a novel clustering strategy based on minimizing mutual information among gene clusters. Simulated annealing is employed to solve the optimization problem. Bootstrap techniques are employed to get more accurate estimates of mutual information when the data sample size is small. Moreover, we propose to combine the mutual information criterion and traditional distance criteria such as the Euclidean distance and the fuzzy membership metric in designing the clustering algorithm. The performances of the new clustering methods are compared with those of some existing methods, using both synthesized data and experimental data. It is seen that the clustering algorithm based on a combined metric of mutual information and fuzzy membership achieves the best performance. The supplemental material is available at www.gspsnap.tamu.edu/gspweb/zxb/glioma_zxb.     

Annotation-based distance measures for patient subgroup discovery in clinical microarray studies

MOTIVATION: Clustering algorithms are widely used in the analysis of microarray data. In clinical studies, they are often applied to find groups of co-regulated genes. Clustering, however, can also stratify patients by similarity of their gene expression profiles, thereby defining novel disease entities based on molecular characteristics. Several distance-based cluster algorithms have been suggested, but little attention has been given to the distance measure between patients. Even with the Euclidean metric, including and excluding genes from the analysis leads to different distances between the same objects, and consequently different clustering results. RESULTS: We describe a new clustering algorithm, in which gene selection is used to derive biologically meaningful clusterings of samples by combining expression profiles and functional annotation data. According to gene annotations, candidate gene sets with specific functional characterizations are generated. Each set defines a different distance measure between patients, leading to different clusterings. These clusterings are filtered using a resampling-based significance measure. Significant clusterings are reported together with the underlying gene sets and their functional definition. CONCLUSIONS: Our method reports clusterings defined by biologically focused sets of genes. In annotation-driven clusterings, we have recovered clinically relevant patient subgroups through biologically plausible sets of genes as well as new subgroupings. We conjecture that our method has the potential to reveal so far unknown, clinically relevant classes of patients in an unsupervised manner. AVAILABILITY: We provide the R package adSplit as part of Bioconductor release 1.9 and on http://compdiag.molgen.mpg.de/software.     

Euclidean sections of protein conformation space and their implications in dimensionality reduction

Dimensionality reduction is widely used in searching for the intrinsic reaction coordinates for protein conformational changes. We find the dimensionality?reduction methods using the pairwise root?mean?square deviation (RMSD) as the local distance metric face a challenge. We use Isomap as an example to illustrate the problem. We believe that there is an implied assumption for the dimensionality‐reduction approaches that aim to preserve the geometric relations between the objects: both the original space and the reduced space have the same kind of geometry, such as Euclidean geometry vs. Euclidean geometry or spherical geometry vs. spherical geometry. When the protein free energy landscape is mapped onto a 2D plane or 3D space, the reduced space is Euclidean, thus the original space should also be Euclidean. For a protein with N atoms, its conformation space is a subset of the 3N‐dimensional Euclidean space R^3N. We formally define the protein conformation space as the quotient space of R^3N by the equivalence relation of rigid motions. Whether the quotient space is Euclidean or not depends on how it is parameterized. When the pairwise RMSD is employed as the local distance metric, implicit representations are used for the protein conformation space, leading to no direct correspondence to a Euclidean set. We have demonstrated that an explicit Euclidean‐based representation of protein conformation space and the local distance metric associated to it improve the quality of dimensionality reduction in the tetra‐peptide and β‐hairpin systems. Proteins 2014; 82:2585–2596. © 2014 Wiley Periodicals, Inc.     

Interactive semisupervised learning for microarray analysis

Microarray technology has generated vast amounts of gene expression data with distinct patterns. Based on the premise that genes of correlated functions tend to exhibit similar expression patterns, various machine learning methods have been applied to capture these specific patterns in microarray data. However, the discrepancy between the rich expression profiles and the limited knowledge of gene functions has been a major hurdle to the understanding of cellular networks. To bridge this gap so as to properly comprehend and interpret expression data, we introduce relevance feedback to microarray analysis and propose an interactive learning framework to incorporate the expert knowledge into the decision module. In order to find a good learning method and solve two intrinsic problems in microarray data, high dimensionality and small sample size, we also propose a semisupervised learning algorithm: kernel discriminant-EM (KDEM). This algorithm efficiently utilizes a large set of unlabeled data to compensate for the insufficiency of a small set of labeled data and it extends the linear algorithm in discriminant-EM (DEM) to a kernel algorithm to handle nonlinearly separable data in a lower dimensional space. The relevance feedback technique and KDEM together construct an efficient and effective interactive semisupervised learning framework for microarray analysis. Extensive experiments on the yeast cell cycle regulation data set and Plasmodium falciparum red blood cell cycle data set show the promise of this approach     

基于流形学习的基因表达谱数据可视化

基因表达谱的可视化本质上是高维数据的降维问题。采用流形学习算法来解决基因表达谱的降维数据可视化,讨论了典型的流形学习算法（Isomap和LLE）在表达谱降维中的适用性。通过类内／类间距离定量评价数据降维的效果,对两个典型基因芯片数据集（结肠癌基因表达谱数据集和急性白血病基因表达谱数据集）进行降维分析,发现两个数据集的本征维数都低于3,因而可以用流形学习方法在低维投影空间中进行可视化。与传统的降维方法（如PCA和MDS）的投影结果作比较,显示Isomap流形学习方法有更好的可视化效果。     

Inferential Clustering Approach for Microarray Experiments with Replicated Measurements

Cluster analysis has proven to be a useful tool for investigating the association structure among genes in a microarray data set. There is a rich literature on cluster analysis and various techniques have been developed. Such analyses heavily depend on an appropriate (dis)similarity measure. In this paper, we introduce a general clustering approach based on the confidence interval inferential methodology, which is applied to gene expression data of microarray experiments. Emphasis is placed on data with low replication (three or five replicates). The proposed method makes more efficient use of the measured data and avoids the subjective choice of a dissimilarity measure. This new methodology, when applied to real data, provides an easy-to-use bioinformatics solution for the cluster analysis of microarray experiments with replicates (see the Appendix). Even though the method is presented under the framework of microarray experiments, it is a general algorithm that can be used to identify clusters in any situation. The method's performance is evaluated using simulated and publicly available data set. Our results also clearly show that our method is not an extension of the conventional clustering method based on correlation or euclidean distance.     

Clustering gene expression data with a penalized graph-based metric

Background  

The search for cluster structure in microarray datasets is a base problem for the so-called "-omic sciences". A difficult problem in clustering is how to handle data with a manifold structure, i.e. data that is not shaped in the form of compact clouds of points, forming arbitrary shapes or paths embedded in a high-dimensional space, as could be the case of some gene expression datasets.     

Application of the S-score algorithm for analysis of oligonucleotide microarrays

In the past several years, oligonucleotide microarrays have emerged as a widely used tool for the simultaneous, non-biased measurement of expression levels for thousands of genes. Several challenges exist in successfully utilizing this biotechnology; principal among these is analysis of microarray data. An experiment to measure differential gene expression can consist of a dozen microarrays, each consisting of over a hundred thousand data points. Previously, we have described the use of a novel algorithm for analyzing oligonucleotide microarrays and assessing changes in gene expression. This algorithm describes changes in expression in terms of the statistical significance (S-score) of change, which combines signals detected by multiple probe pairs according to an error model characteristic of oligonucleotide arrays. Software is available that simplifies the use of the application of this algorithm so that it may be applied to improving the analysis of oligonucleotide microarray data. The application of this method to problems of the central nervous system is discussed.     

Isomap transform for segmenting human body shapes

Segmentation of the 3D human body is a very challenging problem in applications exploiting volume capture data. Direct clustering in the Euclidean space is usually complex or even unsolvable. This paper presents an original method based on the Isomap (isometric feature mapping) transform of the volume data-set. The 3D articulated posture is mapped by Isomap in the pose of Da Vinci's Vitruvian man. The limbs are unrolled from each other and separated from the trunk and pelvis, and the topology of the human body shape is recovered. In such a configuration, Hoshen-Kopelman clustering applied to concentric spherical shells is used to automatically group points into the labelled principal curves. Shepard interpolation is utilised to back-map points of the principal curves into the original volume space. The experimental results performed on many different postures have proved the validity of the proposed method. Reliability of less than 2?cm and 3° in the location of the joint centres and direction axes of rotations has been obtained, respectively, which qualifies this procedure as a potential tool for markerless motion analysis.     

Finding edging genes from microarray data

MOTIVATION: A set of genes and their gene expression levels are used to classify disease and normal tissues. Due to the massive number of genes in microarray, there are a large number of edges to divide different classes of genes in microarray space. The edging genes (EGs) can be co-regulated genes, they can also be on the same pathway or deregulated by the same non-coding genes, such as siRNA or miRNA. Every gene in EGs is vital for identifying a tissue's class. The changing in one EG's gene expression may cause a tissue alteration from normal to disease and vice versa. Finding EGs is of biological importance. In this work, we propose an algorithm to effectively find these EGs. RESULT: We tested our algorithm with five microarray datasets. The results are compared with the border-based algorithm which was used to find gene groups and subsequently divide different classes of tissues. Our algorithm finds a significantly larger amount of EGs than does the border-based algorithm. As our algorithm prunes irrelevant patterns at earlier stages, time and space complexities are much less prevalent than in the border-based algorithm. AVAILABILITY: The algorithm proposed is implemented in C++ on Linux platform. The EGs in five microarray datasets are calculated. The preprocessed datasets and the discovered EGs are available at http://www3.it.deakin.edu.au/~phoebe/microarray.html.     

Application of the S-score algorithm for analysis of oligonucleotide microarrays

In the past several years, oligonucleotide microarrays have emerged as a widely used tool for the simultaneous, non-biased measurement of expression levels for thousands of genes. Several challenges exist in successfully utilizing this biotechnology; principal among these is analysis of microarray data. An experiment to measure differential gene expression can consist of a dozen microarrays, each consisting of over a hundred thousand data points. Previously, we have described the use of a novel algorithm for analyzing oligonucleotide microarrays and assessing changes in gene expression [J. Mol. Biol. 317 (2002) 225]. This algorithm describes changes in expression in terms of the statistical significance (S-score) of change, which combines signals detected by multiple probe pairs according to an error model characteristic of oligonucleotide arrays. Software is available that simplifies the use of the application of this algorithm so that it may be applied to improving the analysis of oligonucleotide microarray data. The application of this method to problems of the central nervous system is discussed.     

Isomap transform for segmenting human body shapes

Segmentation of the 3D human body is a very challenging problem in applications exploiting volume capture data. Direct clustering in the Euclidean space is usually complex or even unsolvable. This paper presents an original method based on the Isomap (isometric feature mapping) transform of the volume data-set. The 3D articulated posture is mapped by Isomap in the pose of Da Vinci's Vitruvian man. The limbs are unrolled from each other and separated from the trunk and pelvis, and the topology of the human body shape is recovered. In such a configuration, Hoshen–Kopelman clustering applied to concentric spherical shells is used to automatically group points into the labelled principal curves. Shepard interpolation is utilised to back-map points of the principal curves into the original volume space. The experimental results performed on many different postures have proved the validity of the proposed method. Reliability of less than 2 cm and 3° in the location of the joint centres and direction axes of rotations has been obtained, respectively, which qualifies this procedure as a potential tool for markerless motion analysis.     

Application of latent semantic indexing to evaluate the similarity of sets of sequences without multiple alignments character-by-character

Most molecular analyses, including phylogenetic inference, are based on sequence alignments. We present an algorithm that estimates relatedness between biomolecules without the requirement of sequence alignment by using a protein frequency matrix that is reduced by singular value decomposition (SVD), in a latent semantic index information retrieval system. Two databases were used: one with 832 proteins from 13 mitochondrial gene families and another composed of 1000 sequences from nine types of proteins retrieved from GenBank. Firstly, 208 sequences from the first database and 200 from the second were randomly selected and compared using edit distance between each pair of sequences and respective cosines and Euclidean distances from SVD. Correlation between cosine and edit distance was -0.32 (P < 0.01) and between Euclidean distance and edit distance was +0.70 (P < 0.01). In order to check the ability of SVD in classifying sequences according to their categories, we used a sample of 202 sequences from the 13 gene families as queries (test set), and the other proteins (630) were used to generate the frequency matrix (training set). The classification algorithm applies a voting scheme based on the five most similar sequences with each query. With a 3-peptide frequency matrix, all 202 queries were correctly classified (accuracy = 100%). This algorithm is very attractive, because sequence alignments are neither generated nor required. In order to achieve results similar to those obtained with edit distance analysis, we recommend that Euclidean distance be used as a similarity measure for protein sequences in latent semantic indexing methods.     

A fast algorithm for computing geodesic distances in tree space

Comparing and computing distances between phylogenetic trees are important biological problems, especially for models where edge lengths play an important role. The geodesic distance measure between two phylogenetic trees with edge lengths is the length of the shortest path between them in the continuous tree space introduced by Billera, Holmes, and Vogtmann. This tree space provides a powerful tool for studying and comparing phylogenetic trees, both in exhibiting a natural distance measure and in providing a euclidean-like structure for solving optimization problems on trees. An important open problem is to find a polynomial time algorithm for finding geodesics in tree space. This paper gives such an algorithm, which starts with a simple initial path and moves through a series of successively shorter paths until the geodesic is attained.     

Two-pass imputation algorithm for missing value estimation in gene expression time series

Gene expression microarray experiments frequently generate datasets with multiple values missing. However, most of the analysis, mining, and classification methods for gene expression data require a complete matrix of gene array values. Therefore, the accurate estimation of missing values in such datasets has been recognized as an important issue, and several imputation algorithms have already been proposed to the biological community. Most of these approaches, however, are not particularly suitable for time series expression profiles. In view of this, we propose a novel imputation algorithm, which is specially suited for the estimation of missing values in gene expression time series data. The algorithm utilizes Dynamic Time Warping (DTW) distance in order to measure the similarity between time expression profiles, and subsequently selects for each gene expression profile with missing values a dedicated set of candidate profiles for estimation. Three different DTW-based imputation (DTWimpute) algorithms have been considered: position-wise, neighborhood-wise, and two-pass imputation. These have initially been prototyped in Perl, and their accuracy has been evaluated on yeast expression time series data using several different parameter settings. The experiments have shown that the two-pass algorithm consistently outperforms, in particular for datasets with a higher level of missing entries, the neighborhood-wise and the position-wise algorithms. The performance of the two-pass DTWimpute algorithm has further been benchmarked against the weighted K-Nearest Neighbors algorithm, which is widely used in the biological community; the former algorithm has appeared superior to the latter one. Motivated by these findings, indicating clearly the added value of the DTW techniques for missing value estimation in time series data, we have built an optimized C++ implementation of the two-pass DTWimpute algorithm. The software also provides for a choice between three different initial rough imputation methods.     

Sequence ordinations: a multivariate analysis approach to analysing large sequence data sets

Ordination is a powerful method for analysing complex data setsbut has been largely ignored in sequence analysis. This papershows how to use principal coordinates analysis to find low–dimensionalrepresentations of distance matrices derived from aligned setsof sequences. The method takes a matrix of Euclidean distancesbetween all pairs of sequence and finds a coordinate space wherethe distances are exactly preserved The main problem is to finda measure of distance between aligned sequences that is Euclidean.The simplest distance function is the square root of the percentagedifference (as measured by identities) between two sequences,where one ignores any positions in the alignment where thereis a gap in any sequence. If one does not ignore positions witha gap, the distances cannot be guaranteed to be Euclidean butthe deleterious effects are trivial. Two examples of using themethod are shown. A set of 226 aligned globins were analysedand the resulting ordination very successfully represents theknown patterns of relationship between the sequences. In theother example, a set of 610 aligned 5S rRNA sequences were analysed.Sequence ordinations complement phylogenetic analyses. Theyshould not be viewed as a complete alternative.     

Reducing the Time Requirement of k-Means Algorithm

Traditional k-means and most k-means variants are still computationally expensive for large datasets, such as microarray data, which have large datasets with large dimension size d. In k-means clustering, we are given a set of n data points in d-dimensional space R^d and an integer k. The problem is to determine a set of k points in R^d, called centers, so as to minimize the mean squared distance from each data point to its nearest center. In this work, we develop a novel k-means algorithm, which is simple but more efficient than the traditional k-means and the recent enhanced k-means. Our new algorithm is based on the recently established relationship between principal component analysis and the k-means clustering. We provided the correctness proof for this algorithm. Results obtained from testing the algorithm on three biological data and six non-biological data (three of these data are real, while the other three are simulated) also indicate that our algorithm is empirically faster than other known k-means algorithms. We assessed the quality of our algorithm clusters against the clusters of a known structure using the Hubert-Arabie Adjusted Rand index (ARI_HA). We found that when k is close to d, the quality is good (ARI_HA>0.8) and when k is not close to d, the quality of our new k-means algorithm is excellent (ARI_HA>0.9). In this paper, emphases are on the reduction of the time requirement of the k-means algorithm and its application to microarray data due to the desire to create a tool for clustering and malaria research. However, the new clustering algorithm can be used for other clustering needs as long as an appropriate measure of distance between the centroids and the members is used. This has been demonstrated in this work on six non-biological data.