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In the era of big data, data-driven based classification has become an essential method in smart manufacturing to guide production and optimize inspection. The industrial data obtained in practice is usually time-series data collected by soft sensors, which are highly nonlinear, nonstationary, imbalanced, and noisy. Most existing soft-sensing machine learning models focus on capturing either intra-series temporal dependencies or pre-defined inter-series correlations, while ignoring the correlation between labels as each instance is associated with multiple labels simultaneously. In this paper, we propose a novel graph based soft-sensing neural network (GraSSNet) for multivariate time-series classification of noisy and highly-imbalanced soft-sensing data. The proposed GraSSNet is able to 1) capture the inter-series and intra-series dependencies jointly in the spectral domain; 2) exploit the label correlations by superimposing label graph that built from statistical co-occurrence information; 3) learn features with attention mechanism from both textual and numerical domain; and 4) leverage unlabeled data and mitigate data imbalance by semi-supervised learning. Comparative studies with other commonly used classifiers are carried out on Seagate soft sensing data, and the experimental results validate the competitive performance of our proposed method.