  The classification of random objects within metric spaces without a vector
structure has attracted increasing attention. However, the complexity inherent
in such non-Euclidean data often restricts existing models to handle only a
limited number of features, leaving a gap in real-world applications. To
address this, we propose a data-adaptive filtering procedure to identify
informative features from large-scale random objects, leveraging a novel
Kolmogorov-Smirnov-type statistic defined on the metric space. Our method,
applicable to data in general metric spaces with binary labels, exhibits
remarkable flexibility. It enjoys a model-free property, as its implementation
does not rely on any specified classifier. Theoretically, it controls the false
discovery rate while guaranteeing the sure screening property. Empirically,
equipped with a Wasserstein metric, it demonstrates superior sample performance
compared to Euclidean competitors. When applied to analyze a dataset on autism,
our method identifies significant brain regions associated with the condition.
Moreover, it reveals distinct interaction patterns among these regions between
individuals with and without autism, achieved by filtering hundreds of
thousands of covariance matrices representing various brain connectivities.
