I've performed PCA on face images dataset and I'm not sure how can I use the most informative principal components to show the "reduced" image.
The original image is 96*96 pixels (96*96 = 9216) and I use a sample of 70 images here (70 rows and 9216 column). We get 70 principal components (min{num of samples, num of features}=70).
How can I re-construct a 96x96 image in order to show the eigenfaces? I want to show my students how the eigenvectors "predict" the real data.
The dataset I'm using can be downloaded here.
The code:
install.packages("foreach") file ='C:\\I\\Love\\Data Science\\face.training.csv' data_all = read.csv(file , stringsAsFactors=F) dim(data_all) #7049 31 # use only 70 first images data = data_all[1:70,] names(data) str(data) # extract the images data im.train <- data$Image data$Image = NULL # each image is a vector of 96*96 pixels (96*96 = 9216). library(foreach) im.train <- foreach(im = im.train, .combine=rbind) %dopar% { as.integer(unlist(strsplit(im, " "))) } # im.train is a matrix of pixels 70x9216 # show picture number 2 im <- matrix(data=rev(im.train[2,]), nrow=96, ncol=96) image(1:96, 1:96, im, col=gray((0:255)/255)) # Apply PCA pca <- prcomp(im.train, center = TRUE, scale. = TRUE) ## using correlation matrix # There are in general min(n − 1, p) informative principal components in a data set with n observations and p variables. Hence, pca$x is 70x70 # Standard deviation of each component pca$sdev # A numeric matrix which provides the data for the principal components analysis pca$x dim(pca$x) # The print method returns the standard deviation of each of the PCs, # and their rotation (or loadings), which are the coefficients of the linear combinations of the continuous variables. print(pca) #The summary method describe the importance of the PCs. summary(pca) #The first row describe again the standard deviation associated with each PC. #The second row shows the proportion of the variance in the data explained by each component #while the third row describe the cumulative proportion of explained variance. # plot method returns a plot of the variances (y-axis) associated with the PCs (x-axis). # useful to decide how many PCs to retain for further analysis. plot(pca, type = "l") 
