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The degradation starting time is an important variable affecting the accuracy of degradation path prediction, but little work has been considered in existing studies. This article investigates the problem of predicting the performance of rolling element bearings based on early degradation analysis. Based on an improved dual linear structural support vector machine with envelope spectrum algorithm and $\mu +4\sigma$ criteria, a new health indicator is proposed to detect the degradation starting time. As well the detected time is sensitive to early anomalies. In addition, according to the degradation starting time, a convolutional neural network prediction model is established to predict the degradation path. Experiments show the effectiveness and superiority of the proposed method.