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@@ -78,7 +78,7 @@ Given, $\hat { \mathbf { o } } _ { n , t }$ , a similar procedure is used to com
 
 # 3.4 ATTENTION MAP VISUALISATION
 
-Given cluster representation vectors, $\mathbf { c } _ { k }$ , we can compute a cluster-wise feature-time attention visualisation map as follows. First, we normalise feature-weights $\widehat { \mathbf { a } } _ { t }$ according to a softmax function, $\mathbf { s } _ { t } = \sigma ( \widehat { \pmb { \alpha } } _ { t } ) \in \mathbb { R } ^ { D _ { f } }$ , where $\sigma$ is the softmax function: $\begin{array} { r } { \sigma ( \mathbf { x } ) = \frac { \exp { | \mathbf { x } | } } { \| \exp { | \mathbf { x } | } \| _ { 1 } } } \end{array}$ . Secondly, we compute tsolved as before. We similarly normalise cluster-wise weights, $\gamma _ { t } ^ { k }$ according to a least-square approximation of $\gamma _ { n , t } ^ { k }$ tto obtain cluster temporal scores, $\begin{array} { r } { \dot { \mathbf { c } } _ { k } \approx \sum _ { t = 1 } ^ { T _ { n } } \widehat { \mathbf { o } } _ { n , t } \gamma _ { n , t } ^ { k } } \end{array}$ $e _ { n , t } ^ { k } = \sigma ( \gamma _ { n , t } ^ { k } )$ , and . Finally, we can compute $K$ scoring matrices, $M _ { n } ^ { 1 } , . . . , M _ { n } ^ { K } \in \mathbb { R } _ { T _ { n } \times D _ { f } }$ :  M kn 
 t,f $\left( M _ { n } ^ { k } \right) _ { t , f } = e _ { n , t } ^ { k } \pmb { s } _ { t } ^ { f }$ . Note that: $\begin{array} { r } { \| M _ { n } ^ { k } \| _ { 1 } = \sum _ { t } e _ { n , t } ^ { k } \sum _ { f } s _ { t } ^ { f } = \sum _ { t } e _ { n , t } ^ { k } = 1 } \end{array}$ . Given that Matrices $M _ { n } ^ { k }$ are normalised, they may be consequently, visualised as a normalised feature-time map for cluster assignment relevance and provide further model interpretability.
+Given cluster representation vectors, $\mathbf { c } _ { k }$ , we can compute a cluster-wise feature-time attention visualisation map as follows. First, we normalise feature-weights $\widehat { \mathbf { a } } _ { t }$ according to a softmax function, $\mathbf { s } _ { t } = \sigma ( \widehat { \pmb { \alpha } } _ { t } ) \in \mathbb { R } ^ { D _ { f } }$ , where $\sigma$ is the softmax function: $\begin{array} { r } { \sigma ( \mathbf { x } ) = \frac { \exp { | \mathbf { x } | } } { \| \exp { | \mathbf { x } | } \| _ { 1 } } } \end{array}$ . Secondly, we compute tsolved as before. We similarly normalise cluster-wise weights, $\gamma _ { t } ^ { k }$ according to a least-square approximation of $\gamma _ { n , t } ^ { k }$ tto obtain cluster temporal scores, $\begin{array} { r } { \dot { \mathbf { c } } _ { k } \approx \sum _ { t = 1 } ^ { T _ { n } } \widehat { \mathbf { o } } _ { n , t } \gamma _ { n , t } ^ { k } } \end{array}$ $e _ { n , t } ^ { k } = \sigma ( \gamma _ { n , t } ^ { k } )$ , and . Finally, we can compute $K$ scoring matrices, $M _ { n } ^ { 1 } , . . . , M _ { n } ^ { K } \in \mathbb { R } _ { T _ { n } \times D _ { f } }$ :  M kn 
 t,f $\left( M _ { n } ^ { k } \right) _ { t , f } = e _ { n , t } ^ { k } \pmb { s } _ { t } ^ { f }$ . Note that: $\begin{array} { r } { \| M _ { n } ^ { k } \| _ { 1 } = \sum _ { t } e _ { n , t } ^ { k } \sum _ { f } s _ { t } ^ { f } = \sum _ { t } e _ { n , t } ^ { k } = 1 } \end{array}$ . Given that Matrices $M _ { n } ^ { k }$ are normalised, they may be consequently, visualised as a normalised feature-time map for cluster assignment relevance and provide further model interpretability.
 
 The model is optimised through consideration of three distinct loss functions. We introduce a weighted cross-entropy loss function: