The immense amount of time series data produced by astronomical surveys has called for the use of machine learning algorithms to discover and classify several million celestial sources. In the case of variable stars, supervised learning approaches have become commonplace. However, this needs a considerable collection of expert-labeled light curves to achieve adequate performance, which is costly to construct. To solve this problem, we introduce two approaches. First, a semi-supervised hierarchical method, which requires substantially less trained data than supervised methods. Second, a clustering analysis procedure that finds groups that may correspond to classes or sub-classes of variable stars. Both methods are primarily supported by dimensionality reduction of the data for visualization and to avoid the curse of dimensionality. We tested our methods with catalogs collected from OGLE, CSS, and Gaia surveys. The semi-supervised method reaches a performance of around 90% for all of our three selected catalogs of variable stars using only 5% of the data in the training. This method is suitable for classifying the main classes of variable stars when there is only a small amount of training data. Our clustering analysis confirms that most of the clusters found have a purity over 90% with respect to classes and 80% with respect to sub-classes, suggesting that this type of analysis can be used in large-scale variability surveys as an initial step to identify which classes or sub-classes of variable stars are present in the data and/or to build training sets, among many other possible applications.