A new anomaly detection method called kernel outlier detection (KOD) is proposed. It is designed to address challenges of outlier detection in high-dimensional settings. The aim is to overcome limitations of existing methods, such as dependence on distributional assumptions or on hyperparameters that are hard to tune. KOD starts with a kernel transformation, followed by a projection pursuit approach. Its novelties include a new ensemble of directions to search over, and a new way to combine results of different direction types. This provides a flexible and lightweight approach for outlier detection. Our empirical evaluations illustrate the effectiveness of KOD on three small datasets with challenging structures, and on four large benchmark datasets.