  Big data mining is well known to be an important task for data science,
because it can provide useful observations and new knowledge hidden in given
large datasets. Proximity-based data analysis is particularly utilized in many
real-life applications. In such analysis, the distances to k nearest neighbors
are usually employed, thus its main bottleneck is derived from data retrieval.
Much efforts have been made to improve the efficiency of these analyses.
However, they still incur large costs, because they essentially need many data
accesses. To avoid this issue, we propose a machine-learning technique that
quickly and accurately estimates the k-NN distances (i.e., distances to the k
nearest neighbors) of a given query. We train a fully connected neural network
model and utilize pivots to achieve accurate estimation. Our model is designed
to have useful advantages: it infers distances to the k-NNs at a time, its
inference time is O(1) (no data accesses are incurred), but it keeps high
accuracy. Our experimental results and case studies on real datasets
demonstrate the efficiency and effectiveness of our solution.
