本篇論文裡，我們提出一個單向耦合隱藏式馬可夫模型來分析在家中的日常生活軌跡，利用軌跡分析來分析日常的行為，藉著譜群聚法先對軌跡做分群的動作，再利用單向耦合隱藏式馬可夫模型，來整合軌跡裡的空間跟時間特徵。單向耦合隱藏式馬可夫模型包含兩種模型，一種是空間，一種是時間的模型，兩種的模型長度並不相同，時間的模型耦合到空間的模型，最後計算軌跡及樣板的相似度，如此一來，我們就可以對軌跡做更精確的分析。
在我們的方法裡，我們會從軌跡中取得空間跟時間的特徵，在相同時間間隔去取得空間的特徵，以相同的移動量去取得時間的特徵，接著再利用普群聚法分別對這兩種特徵做分群，先對空間特徵做分群，再對時間特徵做分群，將有相同路徑及速度的軌跡分在同一群。接著利用這些分好群的軌跡來建立樣版，利用這些樣版來建立單向耦合隱藏式馬可夫模型，來進行對軌跡做分析。當新行為伴隨新軌跡的產生時，與每個現存的樣板比較後發現相似度太低，系統將會藉著自我學習的功能來為新的軌跡做樣版。

In this paper, we propose a Single Direction Coupled Hidden Markov Model (SDC-HMM) to analyze daily trajectories in house. We analyze dairy behaviors according to trajectories analysis. First, we use spectral clustering to cluster trajectories into clusters. Then we use SDC-HMM to integrate spatial and temporal features in trajectories. SDC-HMM has two model, one is spatial and another is temporal. The number of states in tow models is different. Temporal model couples to spatial model. Then we use it to calculate similarity between patterns and trajectories. Finally, we can analyze trajectories more precise.
In our approach, we extract time and spatial information from trajectories. The spatial features are extracted from fixing time dwell. The temporal features are extracted from fixing shift distance. Then we use spectral clustering to cluster those trajectories. Trajectories in the same cluster have the same path and the same moving speed. Then we use those clusters to construct patterns, and use those patterns to construct SDC-HMM to do trajectories analysis. Abnormal trajectories are detected with low probability which computed by SDC-HMM. While new behaviors appear with new trajectories, the Self Learning function of the system constructs patterns for them.

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