abclass

The package abclass provides implementations of the multi-category angle-based classifiers (Zhang & Liu, 2014) with the large-margin unified machines (Liu, et al., 2011) for high-dimensional data.

Note

This package is still very experimental and under active development. The function interface is subject to change without guarantee of backward compatibility.

Installation

One can install the released version from CRAN.

install.packages("abclass")

Alternatively, the version under development can be installed as follows:

if (! require(remotes)) install.packages("remotes")
remotes::install_github("wenjie2wang/abclass", upgrade = "never")

Getting Started

A toy example is as follows:

library(abclass)
packageVersion("abclass")

## [1] '0.5.0'

## toy examples for demonstration purpose
## reference: example 1 in Zhang and Liu (2014)
ntrain <- 400  # size of training set
ntest <- 10000 # size of testing set
p0 <- 5        # number of actual predictors
p1 <- 45       # number of random predictors
k <- 5         # number of categories

set.seed(1)
n <- ntrain + ntest; p <- p0 + p1
train_idx <- seq_len(ntrain)
y <- sample(k, size = n, replace = TRUE)         # response
mu <- matrix(rnorm(p0 * k), nrow = k, ncol = p0) # mean vector
## normalize the mean vector so that they are distributed on the unit circle
mu <- mu / apply(mu, 1, function(a) sqrt(sum(a ^ 2)))
x0 <- t(sapply(y, function(i) rnorm(p0, mean = mu[i, ], sd = 0.25)))
x1 <- matrix(rnorm(p1 * n, sd = 0.3), nrow = n, ncol = p1)
x <- cbind(x0, x1)
train_x <- x[train_idx, ]
test_x <- x[- train_idx, ]
y <- factor(paste0("label_", y))
train_y <- y[train_idx]
test_y <- y[- train_idx]

### logistic deviance loss with elastic-net penalty
model1 <- cv.abclass(train_x, train_y, nlambda = 100, nfolds = 5,
                     loss = "logistic", penalty = "lasso", alpha = 0.9)
pred1 <- predict(model1, test_x)
table(test_y, pred1)

##          pred1
## test_y    label_1 label_2 label_3 label_4 label_5
##   label_1    1704       0       3     296       0
##   label_2       0    1862       0       0     106
##   label_3       4      11    1739       0     198
##   label_4       3      12       0    1947      70
##   label_5       0      63      30       1    1951

mean(test_y == pred1) # accuracy

## [1] 0.9203

### with groupwise lasso
model2 <- cv.abclass(train_x, train_y, nlambda = 100, nfolds = 5,
                     loss = "logistic", penalty = "glasso")
pred2 <- predict(model2, test_x)
table(test_y, pred2)

##          pred2
## test_y    label_1 label_2 label_3 label_4 label_5
##   label_1    1994       1       2       3       3
##   label_2       0    1784       0       0     184
##   label_3       4       2    1336       0     610
##   label_4      12      27       0    1963      30
##   label_5       0      10       2       0    2033

mean(test_y == pred2) # accuracy

## [1] 0.911

## tuning by ET-Lasso instead of cross-validation
model3 <- et.abclass(train_x, train_y, nlambda = 100,
                     loss = "logistic", penalty = "glasso")
pred3 <- predict(model3, test_x)
table(test_y, pred3)

##          pred3
## test_y    label_1 label_2 label_3 label_4 label_5
##   label_1    1991       1       5       5       1
##   label_2       0    1842       0       0     126
##   label_3       3       7    1643       0     299
##   label_4       7      13       0    1997      15
##   label_5       0      18      11       0    2016

mean(test_y == pred3) # accuracy

## [1] 0.9489

References

• Zhang, C., & Liu, Y. (2014). Multicategory Angle-Based Large-Margin Classification. Biometrika, 101(3), 625–640.
• Liu, Y., Zhang, H. H., & Wu, Y. (2011). Hard or soft classification? large-margin unified machines. Journal of the American Statistical Association, 106(493), 166–177.

License

GNU General Public License (≥ 3)

Copyright holder: Eli Lilly and Company