![]() Axis 2 could be regarded as a measure of shape, with samples at any axis 1 position (that is, of a given size) having different length-to-width ratios. ![]() In this example, axis 1 could be interpreted as a size measure, likely reflecting age, with samples on the left having both small lengths and widths and samples on the right having large lengths and widths. Mathematically, the orientations of these axes relative to the original variables are called the eigenvectors, and the variances along these axes are called the eigenvalues.īy performing such a rotation, the new axes might have particular explanations. ![]() Last, the new axes created by this rotation are uncorrelated with each other. Also, because we have just rotated the data, their spatial relationships of the points are unchanged: it is the same data, just plotted in a new set of coordinates. Once we have made these vectors, we could measure the coordinates of every data point relative to these two perpendicular vectors and re-plot the data, as shown here (both of these figures are from Swan and Sandilands, 1995).īy rotating the data to this new reference frame, the variance is now greater along axis 1 than it is on axis 2. Both vectors are constrained to pass through the centroid of the data. We could pass one vector through the long axis of the cloud of points, with a second vector at right angles to the first. The two are highly correlated with one another. Suppose we had measured two variables (length and width) and plotted them as shown below. Principal Components Analysis Introduction ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |