A Survey of Flow Cytometry Data Analysis Methods <s> Unsupervised Techniques for <s> [Read at a RESEARCH METHODS MEETING of the SOCIETY, April 8th, 1964, Professor D. V. LINDLEY in the Chair] SUMMARY In the analysis of data it is often assumed that observations Yl, Y2, *-, Yn are independently normally distributed with constant variance and with expectations specified by a model linear in a set of parameters 0. In this paper we make the less restrictive assumption that such a normal, homoscedastic, linear model is appropriate after some suitable transformation has been applied to the y's. Inferences about the transformation and about the parameters of the linear model are made by computing the likelihood function and the relevant posterior distribution. The contributions of normality, homoscedasticity and additivity to the transformation are separated. The relation of the present methods to earlier procedures for finding transformations is discussed. The methods are illustrated with examples. <s> BIB001 </s> A Survey of Flow Cytometry Data Analysis Methods <s> Unsupervised Techniques for <s> Abstract The t distribution provides a useful extension of the normal for statistical modeling of data sets involving errors with longer-than-normal tails. An analytical strategy based on maximum likelihood for a general model with multivariate t errors is suggested and applied to a variety of problems, including linear and nonlinear regression, robust estimation of the mean and covariance matrix with missing data, unbalanced multivariate repeated-measures data, multivariate modeling of pedigree data, and multivariate nonlinear regression. The degrees of freedom parameter of the t distribution provides a convenient dimension for achieving robust statistical inference, with moderate increases in computational complexity for many models. Estimation of precision from asymptotic theory and the bootstrap is discussed, and graphical methods for checking the appropriateness of the t distribution are presented. <s> BIB002 </s> A Survey of Flow Cytometry Data Analysis Methods <s> Unsupervised Techniques for <s> Flow cytometry has recently been introduced in aquatic ecology. Its unique feature is to measure several optical characteristics simultaneously on a large number of cells. Until now, these data have generally been analyzed in simple ways, e.g., frequency histograms and bivariate scatter diagrams, so that the multivariate potential of the data has not been fully exploited. This paper presents a way of answering ecologically meaningful questions, using the multivariate characteristics of the data. In order to do so, the multivariate data are reduced to a small number of classes by clustering, which reduces the data to a categorical variable. Multivariate pairwise comparisons can then be performed among samples using these new data vectors. The test case presented in the paper forms a time series of observations from which the new method enables us to study on the temporal evolution of cell types. <s> BIB003 </s> A Survey of Flow Cytometry Data Analysis Methods <s> Unsupervised Techniques for <s> Abstract : The classification maximum likelihood approach is sufficiently general to encompass many current clustering algorithms, including those based on the sum of squares criterion and on the criterion of Friedman and Rubin (1967). However, as currently implemented, it does not allow the specification of which features (orientation, size and shape) are to be common to all clusters and which may differ between clusters. Also, it is restricted to Gaussian distributions and it does not allow for noise. We propose ways of overcoming these limitations. A reparameterization of the covariance matrix allows us to specify that some features, but not all, be the same for all clusters. A practical framework for non-Gaussian clustering is outlined, and a means of incorporating noise in the form of a Poisson process is described. An approximate Bayesian method for choosing the number of clusters is given. The performance of the proposed methods is studied by simulation, with encouraging results. The methods are applied to the analysis of a data set arising in the study of diabetes, and the results seem better than those of previous analyses. (RH) <s> BIB004 </s> A Survey of Flow Cytometry Data Analysis Methods <s> Unsupervised Techniques for <s> Abstract Starting from the well-known fuzzy k-means method, which was mainly intended for spherical clusters, several methods are considered which incorporate cluster-specific scatter matrices. This enables them to describe elliptical clusters with different orientation. The distinction between these methods lies in the way they deal with clusters of different volume, cardinality, and density. Some industrial examples show that different applications may lead to different goals and preferences, which affect the choice of the clustering method. <s> BIB005 </s> A Survey of Flow Cytometry Data Analysis Methods <s> Unsupervised Techniques for <s> Using an eigenvalue decomposition of variance matrices, Celeux and Govaert (1993) obtained numerous and powerful models for Gaussian model-based clustering and discriminant analysis. Through Monte Carlo simulations, we compare the performances of many classical criteria to select these models: information criteria as AIC, the Bayesian criterion BIC, classification criteria as NEC and cross-validation. In the clustering context, information criteria and BIC outperform the classification criteria. In the discriminant analysis context, cross-validation shows good performance but information criteria and BIC give satisfactory results as well with, by far, less time-computing. <s> BIB006 </s> A Survey of Flow Cytometry Data Analysis Methods <s> Unsupervised Techniques for <s> We propose an assessing method of mixture model in a cluster analysis setting with integrated completed likelihood. For this purpose, the observed data are assigned to unknown clusters using a maximum a posteriori operator. Then, the integrated completed likelihood (ICL) is approximated using the Bayesian information criterion (BIC). Numerical experiments on simulated and real data of the resulting ICL criterion show that it performs well both for choosing a mixture model and a relevant number of clusters. In particular, ICL appears to be more robust than BIC to violation of some of the mixture model assumptions and it can select a number of dusters leading to a sensible partitioning of the data. <s> BIB007 </s> A Survey of Flow Cytometry Data Analysis Methods <s> Unsupervised Techniques for <s> Cluster analysis is the automated search for groups of related observations in a dataset. Most clustering done in practice is based largely on heuristic but intuitively reasonable procedures, and most clustering methods available in commercial software are also of this type. However, there is little systematic guidance associated with these methods for solving important practical questions that arise in cluster analysis, such as how many clusters are there, which clustering method should be used, and how should outliers be handled. We review a general methodology for model-based clustering that provides a principled statistical approach to these issues. We also show that this can be useful for other problems in multivariate analysis, such as discriminant analysis and multivariate density estimation. We give examples from medical diagnosis, minefield detection, cluster recovery from noisy data, and spatial density estimation. Finally, we mention limitations of the methodology and discuss recent development... <s> BIB008 </s> A Survey of Flow Cytometry Data Analysis Methods <s> Unsupervised Techniques for <s> Normal mixture models are being increasingly used to model the distributions of a wide variety of random phenomena and to cluster sets of continuous multivariate data. However, for a set of data containing a group or groups of observations with longer than normal tails or atypical observations, the use of normal components may unduly affect the fit of the mixture model. In this paper, we consider a more robust approach by modelling the data by a mixture of t distributions. The use of the ECM algorithm to fit this t mixture model is described and examples of its use are given in the context of clustering multivariate data in the presence of atypical observations in the form of background noise. <s> BIB009 </s> A Survey of Flow Cytometry Data Analysis Methods <s> Unsupervised Techniques for <s> Background ::: ::: Artificial neural networks (ANNs) have been shown to be valuable in the analysis of analytical flow cytometric (AFC) data in aquatic ecology. Automated extraction of clusters is an important first stage in deriving ANN training data from field samples, but AFC data pose a number of challenges for many types of clustering algorithm. The fuzzy k-means algorithm recently has been extended to address nonspherical clusters with the use of scatter matrices. Four variants were proposed, each optimizing a different measure of clustering “goodness.” ::: ::: ::: ::: Methods ::: ::: With AFC data obtained from marine phytoplankton species in culture, the four fuzzy k-means algorithm variants were compared with each other and with another multivariate clustering algorithm based on critical distances currently used in flow cytometry. ::: ::: ::: ::: Results ::: ::: One of the algorithm variants (adaptive distances, also known as the Gustafson–Kessel algorithm) was found to be robust and reliable, whereas the others showed various problems. ::: ::: ::: ::: Conclusions ::: ::: The adaptive distances algorithm was superior in use to the clustering algorithms against which it was tested, but the problem of automatic determination of the number of clusters remains to be addressed. Cytometry 44:210–217, 2001. © 2001 Wiley-Liss, Inc. <s> BIB010 </s> A Survey of Flow Cytometry Data Analysis Methods <s> Unsupervised Techniques for <s> Myelodysplastic syndromes (MDSs) are heterogeneous diseases of bone marrow (BM) cell precursors for which immunophenotypic characterization is still considered irrelevant despite the accuracy and sensitivity of flow cytometry techniques. The aim of this study was to determine whether immunophenotypic abnormalities could be defined In MDSs and could correlate with the French-American-British classification and cytogenetics. Analysis was performed on 275 BM samples (207 MDS patients, 68 controls) and 25 control blood samples. immunophenotyping was based on a primary gating of blast cells, monocytes, and granulocytes according to CD45 antigen expression and side scatter light diffraction. Immunophenotypic hierarchical clustering was performed to analyze the results, The data obtained show that (1) immunophenotypic clustering partly discriminates patients with refractory anemia with excess blasts/refractory anemia with excess blasts in transformation (RAEB/RAEB-T), chronic myelomonocytic leukemia (CMML), and refractory anemia/refractory anemia with ring sideroblasts (RA/RARS) for CD45(lo) blast cells and patients with RA/CMML, RARS, and RAEB/RAEB-T for CD45(hi)/side scafter(hi) (SShi) granulocytes; (2) the most discriminating markers were CD16, CD34, CD36, CD38, CD71, and HLA-DR for blast cells and CD11b, CD13, CD33, CD36, CD38, CD71, and HLA-DR for CD45(hi)/SShi granulocytes; (3) clusters related to CD34 expression were associated with high levels of blast cells on BM smear; (4) clusters related to high levels of CD36 expression on CD45(lo) blast cells and CID45(hi)/SShi granulocytes were associated with a poor International Prognosis Scoring System score; and (5) high levels of CD71 expression on CD45(hi)/SShi granulocytes were associated with the RARS category. These results show a close relationship between Immunophenotypic abnormalities and BM dysplasia and suggest that flow cytometry could be a future tool for the characterization of MDSs. (C) 2002 by The American Society of Hematology. <s> BIB011 </s> A Survey of Flow Cytometry Data Analysis Methods <s> Unsupervised Techniques for <s> Background: Flow cytometry produces large multi-dimensional datasets of the physical and molecular characteristics of individual cells. The objective of this study was to simplify the cytometry datasets by arranging or clustering ''objects'' (cells) into a smaller number of relatively homogeneous groups (clusters) on the basis of interobject similarities and dissimilarities. Results: The algorithm was designed to be driven by histogram features; that is, the relevant single parameter histogram features were used to guide multidimensional k-means clustering without an a priori estimate of cluster number. To test this approach, we simulated cell-derived datasets using protein-coated microspheres (artificial ''cells''). The microspheres were constructed to provide 119 populations in 40 samples. The feature-guided (FG) approach accurately identified 100% of the predetermined cluster combinations. In contrast, an approach based on the partition index (PI) cluster validity measure accurately identified 83.2% of the clusters. Direct comparisons of the two methods indicated that the FG method was significantly more accurate than PI in identifying both the number of clusters and the number of objects within the clusters (p<.0001). Conclusion: We conclude that parameter feature analysis can be used to effectively guide k-means clustering of flow cytometry datasets. <s> BIB012 </s> A Survey of Flow Cytometry Data Analysis Methods <s> Unsupervised Techniques for <s> BACKGROUND ::: Polychromatic flow cytometry (PFC) allows the simultaneous determination of multiple antigens in the same cell, resulting in the generation of a high number of subsets. As a consequence, data analysis is the main difficulty with this technology. Here we show the use of cluster analysis (CA) and principal component analyses (PCA) to simplify multicolor data visualization and to allow subjects' classification. ::: ::: ::: METHODS ::: By eight-colour cytofluorimetric analysis, we investigated the T cell compartment in donors of different age (young, middle-aged, and centenarians). T cell subsets were identified by combining positive and negative expression of antigens. The resulting data set was organized into a matrix and subjected to CA and PCA. ::: ::: ::: RESULTS ::: CA clustered people of different ages on the basis of cytofluorimetric profile. PCA of the cellular subsets identified centenarians within a different cluster from young donors, while middle-aged donors were scattered between these groups. These approaches identified T cell phenotypes that changed with increasing age. In young donors, memory T cell subsets tended to be CD127+ and CD95- whereas CD127-, CD95+ phenotypes were found at higher frequencies in people with advanced age. ::: ::: ::: CONCLUSIONS ::: Our data suggest the use of bioinformatic approaches to analyze large data-sets generated by PFC and to obtain the rapid identification of key populations that best characterize a group of subjects. <s> BIB013 </s> A Survey of Flow Cytometry Data Analysis Methods <s> Unsupervised Techniques for <s> The capability of flow cytometry to offer rapid quantification of multidimensional characteristics for millions of cells has made this technology indispensable for health research, medical diagnosis, and treatment. However, the lack of statistical and bioinformatics tools to parallel recent high-throughput technological advancements has hindered this technology from reaching its full potential. We propose a flexible statistical model-based clustering approach for identifying cell populations in flow cytometry data based on t-mixture models with a Box–Cox transformation. This approach generalizes the popular Gaussian mixture models to account for outliers and allow for nonelliptical clusters. We describe an Expectation-Maximization (EM) algorithm to simultaneously handle parameter estimation and transformation selection. Using two publicly available datasets, we demonstrate that our proposed methodology provides enough flexibility and robustness to mimic manual gating results performed by an expert researcher. In addition, we present results from a simulation study, which show that this new clustering framework gives better results in terms of robustness to model misspecification and estimation of the number of clusters, compared to the popular mixture models. The proposed clustering methodology is well adapted to automated analysis of flow cytometry data. It tends to give more reproducible results, and helps reduce the significant subjectivity and human time cost encountered in manual gating analysis. © 2008 International Society for Analytical Cytology <s> BIB014
The above-mentioned characteristics of FCM data make unsupervised analysis challenging as existing clustering algorithms either do not address or have limitations in addressing these requirements. Clustering algorithms require the number of clusters that they should identify to be specified apriori. There are several approaches for choosing the number of clusters, including resampling, cross-validation, and various information criteria BIB006 . Zeng et al. BIB012 use the peaks of density distribution of each channel of FCM data and estimate the numbers of clusters to be identified by k-Means algorithm. Lo et al. BIB014 propose to use Bayesian information criteria (BIC) in the context of a model-based clustering approach to estimate the optimal number of clusters. BIC is computationally cheap to compute once maximum likelihood estimation for the model parameters has been completed, an advantage over other approaches, especially in the context of FCM where datasets tend to be very large. While computationally cheap, BIC relies heavily on an approximation of marginal likelihoods, which might not be very accurate for some data. Alternative approaches such as the integrated completed likelihood BIB007 may improve the estimation of the number of clusters. Nevertheless, combined with expert knowledge, such approaches can provide guidance on choosing a reasonable starting number of clusters. Sometimes it is possible that even if the actual number of clusters is known, the clustering algorithm may not identify the correct clusters at the level of separation that is desired. This can happen when there is a rare cell population within the FCM data. In this case, the clustering algorithm may consider the rare population as an outlier or as part of a larger cell population and instead divide larger cell populations into smaller populations. One approach to overcome this problem might be clustering the data with higher number of clusters with the hope that the rare populations are represented by separate clusters and use some merging algorithm to combine the clusters that are similar according to a criterion. k-means clustering algorithm is one of the methods that have been used in literature. While this approach performs well when the clusters are spherical in shape, clusters in FCM data usually are not spherical. Demers et al. BIB003 have proposed an extension of k-means allowing for nonspherical clusters, but this algorithm has been shown to lead to inferior performance compared to fuzzy k-means clustering BIB010 . In fuzzy k-means BIB005 , each cell can belong to several clusters with different association degrees, rather than belonging to only one cluster. Even though fuzzy k-means takes into consideration some form of classification uncertainty, it is a heuristic-based algorithm and lacks a formal statistical foundation. Other choices include hierarchical clustering algorithms (e.g., linkage or Pearson coefficients method). However, these algorithms are not appropriate for FCM data, since the size of the pairwise distance matrix increases in the order of n 2 with the number of cells, unless they are applied to some preliminary partition of the data  , or they are used to cluster across samples, each of which is represented by a few statistics aggregating measurements of individual cells BIB013 BIB011 . Since the required processing time for some clustering algorithms increases significantly by the increase in the number of events and parameters of FCM data, subsampling the data might be a suitable approach to reduce the processing time. Care should be taken when performing subsampling to make sure that the properties of the original data are preserved after this process. For example, a random uniform sampling of data may not be a suitable approach as it can discard the small populations present in the data. One alternative might be using a guided sampling approach in which representative events are selected from low-density populations as well. This might be achieved by different strategies such as looking at density distributions of the data or performing a coarse clustering before subsampling procedure. An alternative approach for FCM data gating is to model the FCM data with mixtures of distributions. The most commonly used model-based clustering approach is based on finite Gaussian mixture models BIB008  . However, Gaussian mixture models rely on the assumption that each component follows a Gaussian distribution, which is often not the case when modeling FCM data. A common approach is to look for transformations of the data that make the normality assumption more realistic. Lo et al. BIB014 proposed the use of the Box-Cox BIB001 transformation prior to using a modelbased clustering. In addition to nonnormality, there is also the problem of outlier identification in mixture modeling. As mentioned earlier, replacing the Gaussian distribution with a more robust one (e.g., t BIB009  ) or adding an extra component to model the outliers (e.g., uniform BIB004 ) is suggested to deal with outliers. The t-distribution is similar in shape to the Gaussian distribution with heavier tails and thus provides a robust alternative BIB002 . The Box-Cox transformation is a type of power transformation, which can bring skewed data back to symmetry, a property of both the Gaussian and t-distributions. In particular, the BoxCox transformation is effective for data where the dispersion increases with the magnitude, a scenario not uncommon to FCM data BIB014 . One of the benefits of model-based clustering approach is that it provides mechanism for both "hard" clustering (i.e., the partitioning of the whole data into separate clusters) Advances in Bioinformatics 15 and fuzzy clustering (i.e., a "soft" clustering approach in which each event may be associated with more than one cluster) BIB014 . The latter approach is in line with the rationale that there exists uncertainty about to which cluster an event should be assigned.