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Cross-lingual sentiment classification (CLSC) seeks to use resources from a source language in order to detect sentiment and classify text in a target language. Almost all research into CLSC has been carried out at sentence and document level, although this level of granularity is often less useful. This paper explores methods for performing aspect-based cross-lingual sentiment classification (aspect-based CLSC) for under-resourced languages. Given the limited nature of parallel data for many languages, we would like to make the most of this resource for our task. We compare zero-shot learning, bilingual word embeddings, stacked denoising autoencoder representations and machine translation techniques for aspect-based CLSC. Each of these approaches requires differing amounts of parallel data. We show that models based on distributed semantics can achieve comparable results to machine translation on aspect-based CLSC and give an analysis of the errors found for each method.