  Support Vector Machines (SVMs) can solve structured multi-output learning
problems such as multi-label classification, multiclass classification and
vector regression. SVM training is expensive especially for large and high
dimensional datasets. The bottleneck of the SVM training often lies in the
kernel value computation. In many real-world problems, the same kernel values
are used in many iterations during the training, which makes the caching of
kernel values potentially useful. The majority of the existing studies simply
adopt the LRU (least recently used) replacement strategy for caching kernel
values. However, as we analyze in this paper, the LRU strategy generally
achieves high hit ratio near the final stage of the training, but does not work
well in the whole training process. Therefore, we propose a new caching
strategy called EFU (less frequently used) which replaces the less frequently
used kernel values that enhances LFU (least frequently used). Our experimental
results show that EFU often has 20\% higher hit ratio than LRU in the training
with the Gaussian kernel. To further optimize the strategy, we propose a
caching strategy called HCST (hybrid caching for the SVM training), which has a
novel mechanism to automatically adapt the better caching strategy in the
different stages of the training. We have integrated the caching strategy into
ThunderSVM, a recent SVM library on many-core processors. Our experiments show
that HCST adaptively achieves high hit ratios with little runtime overhead
among different problems including multi-label classification, multiclass
classification and regression problems. Compared with other existing caching
strategies, HCST achieves 20\% more reduction in training time on average.
