rrcov (version 0.4-08)

bus: Automatic vehicle recognition data

Description

The data set bus (Hettich and Bay, 1999) corresponds to a study in automatic vehicle recognition (see Maronna et al. 2006, page 213, Example 6.3)). This data set from the Turing Institute, Glasgow, Scotland, contains measures of shape features extracted from vehicle silhouettes. The images were acquired by a camera looking downward at the model vehicle from a fixed angle of elevation. Each of the 218 rows corresponds to a view of a bus silhouette, and contains 18 attributes of the image.

Usage

data(bus)

source

Hettich, S. and Bay, S.D. (1999), The UCI KDD Archive, Irvine, CA:University of California, Department of Information and Computer Science, http://kdd.ics.uci.edu

References

Maronna, R., Martin, D. and Yohai, V., (2006). Robust Statistics: Theory and Methods. Wiley, New York.

Examples

## Reproduce Table 6.3 from Maronna et al. (2006), page 213
    data(bus)
    bus <- as.matrix(bus)
    
    ## calculate MADN for each variable
    xmad <- apply(bus, 2, mad)      
    cat("Min, Max of MADN: ", min(xmad), max(xmad), "")


    ## MADN vary between 0 (for variable 9) and 34. Therefore exclude 
    ##  variable 9 and divide the remaining variables by their MADNs.
    bus1 <- bus[, -9]
    madbus <- apply(bus1, 2, mad)
    bus2 <- sweep(bus1, 2, madbus, "/", check.margin = FALSE)

    ## Compute classical and robust PCA (Spherical/Locantore, Hubert, MCD and OGK)    
    pca  <- PcaClassic(bus2)
    rpca <- PcaLocantore(bus2)
    pcaHubert <- PcaHubert(bus2, k=17, kmax=17, mcd=FALSE)
    pcamcd <- PcaCov(bus2, cov.control=CovControlMcd())
    pcaogk <- PcaCov(bus2, cov.control=CovControlOgk())

    ev    <- getEigenvalues(pca)
    evrob <- getEigenvalues(rpca)
    evhub <- getEigenvalues(pcaHubert)
    evmcd <- getEigenvalues(pcamcd)
    evogk <- getEigenvalues(pcaogk)

    uvar    <- matrix(nrow=6, ncol=6)
    svar    <- sum(ev)
    svarrob <- sum(evrob)
    svarhub <- sum(evhub)
    svarmcd <- sum(evmcd)
    svarogk <- sum(evogk)
    for(i in 1:6){
        uvar[i,1] <- i
        uvar[i,2] <- round((svar - sum(ev[1:i]))/svar, 3)
        uvar[i,3] <- round((svarrob - sum(evrob[1:i]))/svarrob, 3)
        uvar[i,4] <- round((svarhub - sum(evhub[1:i]))/svarhub, 3)
        uvar[i,5] <- round((svarmcd - sum(evmcd[1:i]))/svarmcd, 3)
        uvar[i,6] <- round((svarogk - sum(evogk[1:i]))/svarogk, 3)
    }
    uvar <- as.data.frame(uvar)
    names(uvar) <- c("q", "Classical","Spherical", "Hubert", "MCD", "OGK")
    cat("Bus data: proportion of unexplained variability for q components
")
    print(uvar)
 
    ## Reproduce Table 6.4 from Maronna et al. (2006), page 214
    ##
    ## Compute classical and robust PCA extracting only the first 3 components
    ## and take the squared orthogonal distances to the 3-dimensional hyperplane
    ##
    pca3 <- PcaClassic(bus2, k=3)               # classical
    rpca3 <- PcaLocantore(bus2, k=3)            # spherical (Locantore, 1999)
    hpca3 <- PcaHubert(bus2, k=3)               # Hubert
    dist <- pca3@od^2
    rdist <- rpca3@od^2
    hdist <- hpca3@od^2

    ## calculate the quantiles of the distances to the 3-dimensional hyperplane
    qclass  <- round(quantile(dist, probs = seq(0, 1, 0.1)[-c(1,11)]), 1)
    qspc <- round(quantile(rdist, probs = seq(0, 1, 0.1)[-c(1,11)]), 1)
    qhubert <- round(quantile(hdist, probs = seq(0, 1, 0.1)[-c(1,11)]), 1)
    qq <- cbind(rbind(qclass, qspc, qhubert), round(c(max(dist), max(rdist), max(hdist)), 0))
    colnames(qq)[10] <- "Max"
    rownames(qq) <- c("Classical", "Spherical", "Hubert")
    cat("Bus data: quantiles of distances to hiperplane
")
    print(qq)

    ## 
    ## Reproduce Fig 6.1 from Maronna et al. (2006), page 214
    ## 
    cat("Bus data: Q-Q plot of logs of distances to hyperplane (k=3) 
from classical and robust estimates. The line is the identity diagonal
")
    plot(sort(log(dist)), sort(log(rdist)), xlab="classical", ylab="robust")
    lines(sort(log(dist)), sort(log(dist)))