We developed Long Short-Term Memory (LSTM) models to predict the formation of active regions (ARs) on the solar surface. Using the Doppler shift velocity, the continuum intensity, and the magnetic field observations from the Solar Dynamics Observatory (SDO) Helioseismic and Magnetic Imager (HMI), we have created time-series datasets of acoustic power and magnetic flux, which are used to train LSTM models on predicting continuum intensity, 12 hours in advance. These novel machine learning (ML) models are able to capture variations of the acoustic power density associated with upcoming magnetic flux emergence and continuum intensity decrease. Testing of the models' performance was done on data for 5 ARs, unseen from the models during training. Model 8, the best performing model trained, was able to make a successful prediction of emergence for all testing active regions in an experimental setting and three of them in an operational. The model predicted the emergence of AR11726, AR13165, and AR13179 respectively 10, 29, and 5 hours in advance, and variations of this model achieved average RMSE values of 0.11 for both active and quiet areas on the solar disc. This work sets the foundations for ML-aided prediction of solar ARs.

In this paper, we propose a unified clustering approach that can estimate number of clusters and produce clustering against this number simultaneously. Average silhouette width (ASW) is a widely used standard cluster quality index. We define a distance based objective function that optimizes ASW for clustering. The proposed algorithm named as OSil, only, needs data observations as an input without any prior knowledge of the number of clusters. This work is about thorough investigation of the proposed methodology, its usefulness and limitations. A vast spectrum of clustering structures were generated, and several well-known clustering methods including partitioning, hierarchical, density based, and spatial methods were consider as the competitor of the proposed methodology. Simulation reveals that OSil algorithm has shown superior perform in terms of clustering quality than all clustering methods included in the study. OSil can find well separated, compact clusters and have shown better performance for the estimation of number of clusters than several methods. Apart from the proposal of the new methodology and it's investigation this papers offer a systematic analysis on the estimation of cluster indices, some of which never appeared together in comparative simulation setup before. The study offers many insightful findings useful for the selection of the clustering methods and indices.