The paper considers the challenges involved in measuring the similarities between time series, such as time shifts and the mixture of frequencies. To improve recognition accuracy, we investigate an improved linear dynamical system for discovering prominent features by exploiting the evolving dynamics and correlations in a time series, as the quality of unsupervised pattern recognition relies strongly on the extracted features. The proposed approach yields a set of compact extracted features that boosts the accuracy and reliability of clustering for time series data. Experimental evaluations are carried out on time series applications from the scientific, socio-economic, and business domains. The results show that our method exhibits improved clustering performance compared to conventional methods. In addition, the computation time of the proposed approach increases linearly with the length of the time series.