Background: In recent years, intense research efforts have focused on developing methods for automated flow cytometric data analysis. However, while designing such applications, little or no attention has been paid to the human perspective that is absolutely central to the manual gating process of identifying and characterizing cell populations. In particular, the assumption of many common techniques that cell populations could be modeled reliably with pre-specified distributions may not hold true in real-life samples, which can have populations of arbitrary shapes and considerable inter-sample variation.
Results: To address this, we developed a new framework flowScape for emulating certain key aspects of the human perspective in analyzing flow data, which we implemented in multiple steps. First, flowScape begins with creating a mathematically rigorous map of the high-dimensional flow data landscape based on dense and sparse regions defined by relative concentrations of events around modes. In the second step, these modal clusters are connected with a global hierarchical structure. This representation allows flowScape to perform ridgeline analysis for both traversing the landscape and isolating cell populations at different levels of resolution. Finally, we extended manual gating with a new capacity for constructing templates that can identify target populations in terms of their relative parameters, as opposed to the more commonly used absolute or physical parameters. This allows flowScape to apply such templates in batch mode for detecting the corresponding populations in a flexible, sample-specific manner. We also demonstrated different applications of our framework to flow data analysis and show its superiority over other analytical methods.
Conclusions: The human perspective, built on top of intuition and experience, is a very important component of flow cytometric data analysis. By emulating some of its approaches and extending these with automation and rigor, flowScape provides a flexible and robust framework for computational cytomics.

We present a new approach to factor rotation for functional data. This rotation is achieved by rotating the functional principal components towards a pre-defined space of periodic functions designed to decompose the total variation into components that are nearlyperiodic and nearly-aperiodic with a pre-defined period. We show that the factor rotation can be obtained by calculation of canonical correlations between appropriate spaces which makes the methodology computationally efficient. Moreover we demonstrate that our proposed rotations provide stable and interpretable results in the presence of highly complex covariance. This work is motivated by the goal of finding interpretable sources of variability in vegetation index obtained from remote sensing instruments and we demonstrate our methodology through an application of factor rotation of this data.

Bayes Factors play an important role in comparing the fit of models ranging from multiple regression to mixture models. Full Bayesian analysis calculates a Bayes Factor from an explicit prior distribution. However, computational limitations or lack of an appropriate prior sometimes prevent researchers from using an exact Bayes Factor. Instead, it is approximated, often using Schwarz’s (1978) Bayesian Information Criterion (BIC), or a variant of the BIC. In this paper we provide a comparison of several Bayes Factor approximations, including two new approximations, the SPBIC and IBIC. The SPBIC is justified by using a scaled unit information prior distribution that is more general than the BIC’s unit information prior, and the IBIC approximation utilizes more terms of approximation than in the BIC. In a simulation study we show that several measures perform well in large samples, that performance declines in smaller samples, and that SPBIC and IBIC can provide improvement to existing measures under some conditions, including small sample sizes. We then illustrate the use of the fit measures in an empirical example from the crime data of Ehrlich (1973). We conclude with recommendations for researchers.

The main result of this article states that one can get as many as D + 1 modes from a two component normal mixture in D dimensions. Multivariate mixture models are widely used for modeling homogeneous populations and for cluster analysis. Either the components directly or modes arsing from these components are often used to extract individual clusters. Though in lower dimensions these strategies work well, our results show that high dimensional mixtures are often very complex and researchers should take extra precaution while using mixtures for cluster analysis. Even in the simplest case of mixing only two normal components in D dimensions, we can show that it can have a maximum of D + 1 modes. When we mix more components or if the components are non-normal the number of modes might be even higher, which might lead us to wrong inference on the number of clusters. Further analyses show that the number of modes depend on the component means and eigenvalues of the ratio of the two component covariance matrices, which in turn provides a clear guideline as to when one can use mixture analysis for clustering high dimensional data.

Modalclust is an R package which performs Hierarchical Mode Association Clustering (HMAC) along with its parallel implementation (PHMAC) over several processors. Modal clustering tech- niques are especially designed to efficiently extract clusters in high dimensions with arbitrary density shapes. Further, clustering is performed over several resolutions and the results are summarized as a hierarchical tree, thus providing a model based multi resolution cluster analysis. Finally we implement a novel parallel implementation of HMAC which performs the clustering job over several processors thereby dramatically increasing the speed of clustering procedure especially for large data sets. This package also provides a number of functions for visualizing clusters in high dimensions, which can also be used with other clustering softwares.

Background: The widely used k top scoring pair (k-TSP) algorithm is a simple yet powerful parameter-free classifier. It owes its success in many cancer microarray datasets to an effective feature selection algorithm that is based on relative expression ordering of gene pairs. However, its general robustness does not extend to some difficult datasets, such as those involving cancer outcome prediction, which may be due to the relatively simple voting scheme used by the classifier. We believe that the performance can be enhanced by separating its effective feature selection component and combining it with a powerful classifier such as the support vector machine (SVM). More generally the top scoring pairs generated by the k-TSP ranking algorithm can be used as a dimensionally reduced subspace for other machine learning classifiers.

Results: We developed an approach integrating the k-TSP ranking algorithm (TSP) with other machine learning methods, allowing combination of the computationally efficient, multivariate feature ranking of k-TSP with multivariate classifiers such as SVM. We evaluated this hybrid scheme (k-TSP+SVM) in a range of simulated datasets with known data structures. As compared with other feature selection methods, such as a univariate method similar to Fisher’s discriminant criterion (Fisher), or a recursive feature elimination embedded in SVM (RFE), TSP is increasingly more effective than the other two methods as the informative genes become progressively more correlated, which is demonstrated both in terms of the classification performance and the ability to recover true informative genes. We also applied this hybrid scheme to three cancer prognosis datasets, in which k-TSP+SVM outperforms k-TSP classifier in all datasets, and achieves either comparable or superior performance to that using SVM alone. In concurrence with what is observed in simulation, TSP appears to be a better feature selector than Fisher and RFE in two of the three cancer datasets.

Conclusions: The k-TSP ranking algorithm can be used as a computationally efficient, multivariate filter method for feature selection in machine learning. SVM in combination with k-TSP ranking algorithm outperforms k-TSP and SVM alone in simulated datasets and in some cancer prognosis datasets. Simulation studies suggest that as a feature selector, it is better tuned to certain data characteristics, i.e. correlations among informative genes, which is potentially interesting as an alternative feature ranking method in pathway analysis.

Often researchers must choose among two or more structural equation models for a given set of data. Typically, selection is based on having the highest chi-square p-value or the highest fit index such as the CFI or RMSEA. Though a common situation, there is little evidence on the performance of these fit indices in choosing between models. In other statistical applications, Bayes Factor approximations such as the BIC are commonly used to select between models, but these are rarely used in SEMs. This paper examines several new and old Bayes Factor approximations along with some commonly used fit indices to assess their accuracy in choosing the true model among a broad set of false models. The results show that the Bayes Factor Approximations outperform the other fit indices. Among these approximations one of the new ones, SPBIC, is particularly promising. The commonly used chi-square p-value and the CFI, IFI, and RMSEA do much worse.

Protein microarrays are a high-throughput technology capable of generating large quantities of proteomics data. They can be used for general research or for clinical diagnostics. Bioinformatics and statistical analysis techniques are required for interpretation and reaching biologically relevant conclusions from raw data. We describe essential algorithms for processing protein microarray data, including spot-finding on slide images, Z score, and significance analysis of microarrays (SAM) calculations, as well as the concentration dependent analysis (CDA). We also describe available tools for protein microarray analysis, and provide a template for a step-by-step approach to performing an analysis centered on the CDA method. We conclude with a discussion of fundamental and practical issues and considerations.

Background:
Tumor-specific antigens and their specific epitopes are formulation targets for patientspecific cancer vaccines. A selection of prediction servers are available for identification of peptides that bind major histocompatibility complex class I (MHC-I) molecules. However, the lack of standardized methodology and large number of human MHC-I molecules, make the selection of appropriate prediction servers difficult. This study reports a comparative evaluation of thirty prediction servers for seven human MHC-I molecules.
Results
Of 147 individual predictors 39 have shown excellent, 47 good, 33 marginal, and 28 poor ability to classify binders from non-binders. The classifiers for HLA-A*0201, A*0301, A*1101, B*0702, B*0801, and B*1501 have excellent, and for A*2402 moderate classification accuracy. In addition, 16 prediction servers predict peptide binding affinity to MHC-I molecules with high accuracy; correlation coefficients ranging from r=0.55 (B*0801) to r=0.87 (A*0201).
Conclusions
Non-linear predictors outperform matrix-based predictors, and majority of predictors can be improved by non-linear transformations of their raw prediction scores. The best predictors of peptide binding (both classification and binding affinity) show the best performance in prediction of T-cell epitopes. We propose a new standard for prediction of MHC-I binding Ð a common scale for normalization of prediction scores, that is applicable to both experimental and predicted scores.

In this article we propose a general class of risk measures which can be used for data based evaluation of parametric models. The loss function is defined as generalized quadratic distance between the true density and the proposed model. These distances are characterized by a simple quadratic form structure that is adaptable through the choice of a nonnegative definite kernel and a bandwidth parameter. Using asymptotic results for the quadratic distances we build a quick-to-compute approximation for the risk function. Its derivation is analogous to the Akaike Information Criterion (AIC), but unlike AIC, the quadratic risk is a global comparison tool. The method does not require resampling, a great advantage when point estimators are expensive to comput$

Keywords:Global comparison of models, high dimensional data, model selection, mixture models, quadratic distance, quadratic risk, spectral degrees of freedom.

This work builds a unified framework for the study of quadratic form distance measures as they are used in assessing the goodness of fit of models. Many important procedures have this structure, but the theory for these methods is dispersed and incomplete. Central to the statistical analysis of these distances is the spectral decomposition of the kernel that generates the distance. We show how this determines the limiting distribution of natural goodness of fit tests. Additionally, we develop a new notion, the spectral degrees of freedom of the test, based on this decomposition. The degrees of freedom are easy to compute and estimate, and can be used as a guide in the construction of useful procedures in this class.

Background: A key step in the development of an adaptive immune response to pathogens or vaccines is the binding of short peptides to molecules of the Major Histocompatibility Complex (MHC) for presentation to T lymphocytes, which are thereby activated and dierentiate into effector and memory cells. The rational design of vaccines consists in part in the identication of appropriate peptides to effect this process. There are several algorithms currently in use for making such predictions, but these are limited to a small number of MHC molecules and have good but imperfect prediction power.
Results: We have undertaken an exploration of the power gained by taking advantage of a natural representation of the amino acids in terms of their biophysical properties. We used several well-known statistical classiers using either a naive encoding of amino acids by name or an encoding by biophysical properties. In all cases, the encoding by biophysical properties leads to substantially lower misclassication error.
Conclusion Representation of amino acids using a few important bio-physio-chemical property provide a natural basis for representing peptides and greatly improves peptide-MHC class I binding prediction.

In this paper, we develop a mode-based clustering approach applying new optimization techniques to a nonparametric density estimator. A cluster is formed by those sample points that ascend to the same local maximum (mode) of the density function. The path from a point to its associated mode is efficiently solved by an EM-style algorithm, namely, the Modal EM (MEM). This clustering method shares the major advantages of mixture model based clustering. Moreover, it requires no model fitting and ensures that every cluster corresponds to a bump of the density. A hierarchical clustering algorithm is also developed by applying MEM recursively to kernel density estimators with increasing bandwidths. The issue of diagnosing clustering results is investigated. Specifically, a pairwise cluster separability measure is defined using the ridgeline between the density bumps of two clusters. The ridgeline is solved for by the Ridgeline EM (REM) algorithm, an extension of MEM. Based upon this new measure, a cluster merging procedure is developed to guarantee strong separation between clusters. Experiments demonstrate that our clustering approach tends to combine the strengths of mixture-model-based and linkage-based clustering. Tests on both simulated and real data show that the approach is robust in high dimensions and when clusters deviate substantially from Gaussian distributions. Both of these cases pose difficulty for parametric mixture modeling.

Describing the probability densities of multi-object complexes by describing individual objects and their inter-object relationships leads to desirable locality without ignoring the context of an object. We describe a means of decomposing object variations into self effects and neighbor effects. We describe an approach for estimating the self and neighbor effect probability densities for each object in the complex using augmentation and prediction, supported by PGA on m-reps. We apply this method to the inter-day variation of m-reps of male pelvic organs within an individual patient.

The advancing technology for automatic segmentation of medical images should be accompanied by techniques to inform the user of the credibility of results. To the extent that this technology produces clinically acceptable segmentations for a significant fraction of cases there is a risk that the clinician will assume every result is acceptable. In the less frequent case where segmentation fails we are concerned that unless the user is alerted by the computer, she would 5A5Astill put the result to clinical use. We propose an automated method to signal suspected noncredible regions of the segmentation, triggered by outlier values of the local image match function. The user can focus her validation resources on the noncredible regions. When the local image match function is computed via a Mahalanobis dis- tance, as is the case for PCA-based matches, its value follows the chi-squared distribution. Our method signals a noncredible region wherever the probability of a chi-squared random variable being greater than the match observed is above a threshold level. ROC analysis validates our noncredibility test on m-rep segmentations of the bladder in CT images, using an image match computed by PCA on regional intensity quantile functions. We approximate ground truth as truly noncredible regions have surface distance > 5mm to a reference segmentation. We swept out ROC curves by varying the threshold level. The area under the ROC curve was 0.91. Based on this preliminary result, our method shows potential for validation in an automatic segmentation pipeline.

We study the effect of degrees of freedom on the level and power of quadratic distance based tests. The concept of an \textit{eigendepth index} is introduced and discussed in the context of selecting the optimal degrees of freedom, where optimality refers to high power. We introduce the class of diffusion kernels by the properties we seek these kernels to have and give a method for constructing them by exponentiating the rate matrix of a Markov chain. Product kernels and their spectral decomposition are discussed and shown useful for high dimensional data problems.

This research was initiated by the analysis of NCI60 cancer dataset . The dataset contains gene expression values (from cDNA arrays) corresponding to 3509 genes collected from 60 different patients diagnosed with 8 different cancer types (assumed unknown in the following discussion). The goal is to provide a model based approach for simultaneously clustering cancer types (columns) and the genes (rows) involved in differentiating these cancer types. We formulate a novel two-way mixture framework and adapt our distance-based model selection tool to determine the unknown number of row and column clusters. This methodology avoids two major pitfalls of using model-based clustering in high-dimensions. First, the two-way mixture has a considerably smaller parameter set, compared to the full multivariate analysis, making all parameters estimable. Second, unlike the complex distribution of likelihood-ratio-based tools under the composite null hypothesis of fixed row and column clusters, the distribution of our distance-based model selection tool is well defined, even for composite hypotheses. Finally, based on the geometry of pure Gaussian HDLSS data, we provide an effective visual diagnostic tool to uncover any remaining structure in the data. Through our analysis, we uncovered some interesting sets of gene clusters. But some of our cancer-type clusters did not match the initial cancer labels. On later verification we found that such discordance was due to the close similarity in symptoms and pathological test results of the two types of cancer in question.

Multivariate mixtures provide flexible methods for both fitting and partitioning high-dimensional data. Ray and Lindsay(2005) show that the topography of multivariate mixtures, in the sense of their key features as a density, can be analyzed rigorously in lower dimensions by use of a ridgeline manifold that contains all critical points as well as the ridges of the density. In addition, we have developed a new computing procedure similar to the EM algorithm that can quickly find the modes of a mixture density. This tool can be extended to examine the degree of separation between the modes based on the ridgeline separating them. These tools can be used in various ways. For one, we can take a conventional mixture analysis and cluster together those components whose contribution is actually unimodal. This cluster could then represent a single true component with a more complex distribution. We can also turn kernel density estimation into a hierarchical clustering tool in which the data points become identified with each other by their association with a common mode of the density estimator. Separate clusters must then correspond to gaps in the estimated density. The analysis is multi-scale, as different levels of smoothing provide different aggregations.