How can I explore high-dimensional data?

High-dimensional data hinder sample visualiza-tion and limit exploration of data 1. In these cases, we can make use of multivariate analysis techniques, such as Factor Analysis (FA) and/or Principal Component Analysis (PCA), to reduce a complex data set to one of lower dimensions so as to reveal any hidden features and simplify understanding. In order to render interpretation of FA and PCA easier, an example of the practical applications of these techniques is described herein. An orthodontist wants to make a few changes in his clinic in order to ensure higher-quality treatment. However, such changes have to be tailored according to the needs and desires of his target customers. Thus, he decided to implement a questionnaire at the end of orthodontic treatment. Patients had to respond to several questions which were grouped into the following items: 1-staff helpfulness; 2-staff professionalism; 3-staff manners; 4-attention given by the dentist; 5-dentist's technical quality; 6-waiting time; 7-explanation about treatment; 8-comfortable facilities; 9-waiting time to schedule an appointment; 10-convenience of treatment schedule; 11-parking facilities; 12-telephone service; 13-cleanliness. When rating, patients used a score that ranged between 1 and 7, with 1 meaning weak and 7 excellent. A total of 50 patients responded to the questionnaire. Afterwards, the dentist found it difficult to establish a change plan due to the large number of items analyzed. In an attempt to reduce the amount of data and facilitate interpretation, the dentist used Factor Analysis (FA), a type of multivariate analysis. Factor Analysis is useful when there is a large number of variables that may provide redundant or duplicated information. In this case, redundancy means that some variables are correlated to each other — possibly because they are measuring the same " thing ". Thus, it is possible to reduce the observed variables to a smaller number also known as factors — groups of correlated variables that present some information in common. The orthodontist found out that the 13 items in the questionnaire were not in fact measuring 13 different facts due to the apparent redundancy shared by some variables. Thus, four new variables or factors, which were implicit in the correlations, were established: 1-efficiency; 2-comfort; 3-staff-patient relationship; 4-dentist-patient relationship. Factor analysis for the variables used by the orthodontist are observed in Figure 1. Nevertheless, to establish an improvement plan, the orthodontist needed to know the item which most influences patients' satisfaction. To this end, he used