Data Representation in Multidimensional
Space *
A number of measured and hinary categorical variables were observed for several days in a group of patients hospitalized for suspected myocardial infarction:
temperature. systolic and diastolic blood pressure, pulse. respiratory rate, P-R interval (electrocardiogram).
white blood count, serum enzyme levels (IBH, SGOT, SGPT). along with the presence or absence of chest pain. abnormal rhythm. ventricular gallop, t-ales. cardiac arrest, external cardiac pacing, assisted respiration, and the administration of digitalis, diuretics. antiarrhythmic agents, and vasopressorh. Volumes of data of this magnitude are often not comprehensible in graphical or numerical form. In order lo aid in the compression a-d interpretation of the data. each patient on a given day was represented a5 a single point in a multidimensional space. Computed distances between points are measures of clinical dissimilarity. Trajectories in the space are indicative of the clinical course of the patient's illness. A computer program was used to connect points to their nearest neighbors so as to yield a "minimum coverage tree," of which the connections, branches, etc., provide information concerning relationships between points. A twodimensional graphical representation of the points was generated, locating the points by minimizing the sum of the squared differences between rz-dimensional and two-dimensional squared distances. The presence of an important nonobserved variable may be signaled by a long series of minimum coverage connections between two apparent neighbors. These mtrltidimensional spatial techniques offer promise of usefulness in a variety of other types of clinical research studie.
Rather frequently in clinical investigation large groups of patients arc observed with respect to multiple variables. If an important objective of the research is to classify the patients into two or more subgroups on the basis of the values for the observed variables, some criticism must be employed by the investigator -::