The article introduces a new method called kernel reconstruction learning for solving machine learning problems. This method uses kernel interpolators to estimate unknown functions by reconstructing them with function values at selected points. It can be applied to any problem that involves estimating functions. The researchers show that popular kernel methods like kernel ridge regression and support vector machines are special cases of this new approach. Additionally, kernel reconstruction learning offers new algorithms for handling large datasets, such as kernel reconstruction vector machine and kernel reconstruction logistic regression, which can provide more accurate predictions with less computational cost.