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Arbitrary-shaped text detection is an important and challenging task in computer vision. Most existing methods require heavy data labeling efforts to produce polygon-level text region labels for supervised training. In order to reduce the cost in data labeling, we study weakly-supervised arbitrary-shaped text detection for combining various weak supervision forms (e.g., image-level tags, coarse, loose and tight bounding boxes), which are far easier for annotation. We propose an Expectation-Maximization (EM) based weakly-supervised learning framework to train an accurate arbitrary-shaped text detector using only a small amount of polygon-level annotated data combined with a large amount of weakly annotated data. Meanwhile, we propose a contour-based arbitrary-shaped text detector, which is suitable for incorporating weakly-supervised learning. Extensive experiments on three arbitrary-shaped text benchmarks (CTW1500, Total-Text and ICDAR-ArT) show that (1) using only 10% strongly annotated data and 90% weakly annotated data, our method yields comparable performance to state-of-the-art methods, (2) with 100% strongly annotated data, our method outperforms existing methods on all three benchmarks. We will make the weakly annotated datasets publicly available in the future.