A travel company wants an ML model to recommend the next airport destination for users. They have millions of records with user location, recent searches, and 2,000 possible airports. The data includes categorical features and a target expected to be a high-dimensional sparse matrix. The team must use Amazon SageMaker built-in algorithms and has one-hot encoded categorical features. Which built-in algorithm should be used?

Factorization Machines (FM) are well-suited for recommendation systems with high-dimensional sparse data, especially when dealing with categorical features that have been one-hot encoded. FMs can capture interactions between features even when those interactions are rare, which is crucial for sparse recommendation datasets. The target being a high-dimensional sparse matrix (representing airport recommendations) aligns perfectly with FM's capabilities. CatBoost is a gradient boosting algorithm primarily used for tabular data and can handle categorical features directly, but it's not optimized for the specific challenges of high-dimensional sparse matrices in recommendation systems like FMs are. DeepAR is a forecasting algorithm designed for time series data, which is not the primary problem type here. K-means is a clustering algorithm used for grouping similar data points, not for directly predicting a specific next item in a recommendation scenario, and it wouldn't handle the sparse, high-dimensional target effectively.