An interactive multivariate analysis of FCM data

Abstract

The procedure and results of the interactive multivariate analysis of FCM data are described. Using principal-components analysis, cluster analysis, and interactive maneuvers, this procedure facilitates an effective data compression from a four-dimensional space into two-dimensional space, then allows cluster separation. The procedure is especially effective for separating clusters, which are degenerated in the usual scatterDevelopments in flow cytometric technologies facilitated the simultaneous rapid measurements of several parameters with respect to each of many cells. Unfortunately, however, the display technology has not been fully developed to give sufficient information to FCM users; i.e., in most multiparametric instruments, we usually observe a scattergram in a two-dimensional space. When the number of parameters does not exceed two, improvements in the graphic presentation succeeded in showing the two-dimensional histogram (l), whereas, for a set of data measured by N-parameter apparatus (N > 2), we need to observe the projected distribution on at least N C~ planes. For example, if we have four-dimensional data, we need to observe six scattergrams. Even if we observed the six scattergrams on a screen simultaneously, for example, in a multiwindow system, it is not easy to grasp the distribution of the cells in a four-dimensional space.In observing the N-dimensional distribution with simple scattergrams, inevitably we have to be content with insufficient information given by projections of the original distribution. Especially when the projection axes are inadequately chosen, two independent clusters may be degenerated on the projected distribution profile. One method of finding out the adequate projections axes is the well known principal-components analysis (5).Another difficulty we often encounter during measurement is in separating the overlapping clusters. Cluster analysis (3) can be applied to this. In this paper, we describe a method and results of a n interactive multivariate analysis of FCM data, effective for separating clusters in multidimensional space, The method consists mainly of principal-components analysis, cluster analysis, and interactive maneuvers.grams. Programs were mostly written in C language on MS-DOS and were tested on fourdimensional analysis of the blood cells, which resulted in a successful separation of the degenerated clusters.Key terms: Flow cytometry, principal-components analysis, cluster analysis, hexagonal segmentation METHODS As described in the literature (5), the principal-components analysis to be applied for data compression into a two-dimensional domain is essentially a procedure to find the axes for the new domain, which are assigned by the longest two eigenvectors of the covariance matrix or correlation matrix of the original data. Before application of the procedure, of course, unnecessary groups of cells are omitted in the preprocessing interactive procedures, as shown in the flow chart in Figure 1.In the application of principal-components analysis to flow ...

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