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Incomplete time series classification (ITSC) is an important issue in time series analysis since temporal data often has missing values in practical applications. However, integrating imputation (replacing missing data) and classification within a model often rapidly amplifies the error from imputed values. Reducing this error propagation from imputation to classification remains a challenge. To this end, we propose an adversarial joint-learning recurrent neural network (AJ-RNN) for ITSC, an end-to-end model trained in an adversarial and joint learning manner. We train the system to categorize the time series as well as impute missing values. To alleviate the error introduced by each imputation value, we use an adversarial network to encourage the network to impute realistic missing values by distinguishing real and imputed values. Hence, AJ-RNN can directly perform classification with missing values and greatly reduce the error propagation from imputation to classification, boosting the accuracy. Extensive experiments on 68 synthetic datasets and 4 real-world datasets from the expanded UCR time series archive demonstrate that AJ-RNN achieves state-of-the-art performance. Furthermore, we show that our model can effectively alleviate the accumulating error problem through qualitative and quantitative analysis based on the trajectory of the dynamical system learned by the RNN. We also provide an analysis of the model behavior to verify the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

Time series with missing values (incomplete time series) are ubiquitous in real life on account of noise or malfunctioning sensors. Time-series imputation (replacing missing data) remains a challenge due to the potential for nonlinear dependence on concurrent and previous values of the time series. In this paper, we propose a novel framework for modeling incomplete time series, called a linear memory vector recurrent neural network (LIME-RNN), a recurrent neural network (RNN) with a learned linear combination of previous history states. The technique bears some similarity to residual networks and graph-based temporal dependency imputation. In particular, we introduce a linear memory vector [called the residual sum vector (RSV)] that integrates over previous hidden states of the RNN, and is used to fill in missing values. A new loss function is developed to train our model with time series in the presence of missing values in an end-to-end way. Our framework can handle imputation of both missing-at-random and consecutive missing inputs. Moreover, when conducting time-series prediction with missing values, LIME-RNN allows imputation and prediction simultaneously. We demonstrate the efficacy of the model via extensive experimental evaluation on univariate and multivariate time series, achieving state-of-the-art performance on synthetic and real-world data. The statistical results show that our model is significantly better than most existing time-series univariate or multivariate imputation methods. [ABSTRACT FROM AUTHOR]