# TableĀ 1 Comparison of four NMF algorithms

NMF_MU $$fW,H = \frac{1}{2}\parallel V - WH\parallel_{F}^{2}$$ $$H \leftarrow H.*\frac{{V^{T} W}}{{HW^{T} W}}$$
$$W \leftarrow W.*\frac{VH}{{WH^{T} H}}$$
HALS $$h_{i} \leftarrow \frac{1}{{w_{i}^{T} w_{i} }}\left[ {V_{i}^{T} w_{i} } \right]$$
$$w_{i} \leftarrow \frac{1}{{h_{i}^{T} h_{i} }}\left[ {V_{i}^{ } h_{i} } \right]$$
lraNMF_MU $$F\;\left( {\overset{\lower0.5em\hbox{\smash{\scriptscriptstyle\frown}}}{W} ,\;\overset{\lower0.5em\hbox{\smash{\scriptscriptstyle\frown}}}{H} ,\;W,\;H} \right)\; = \;\parallel V\; - \;\overset{\lower0.5em\hbox{\smash{\scriptscriptstyle\frown}}}{W} \overset{\lower0.5em\hbox{\smash{\scriptscriptstyle\frown}}}{H}^{T} \parallel_{F}^{2} \; + \;\parallel \overset{\lower0.5em\hbox{\smash{\scriptscriptstyle\frown}}}{W} \overset{\lower0.5em\hbox{\smash{\scriptscriptstyle\frown}}}{H}^{T} \; - \;WH^{T} \parallel_{F}^{2}$$ $$H \leftarrow H.*\frac{{\left[ {\overset{\lower0.5em\hbox{\smash{\scriptscriptstyle\frown}}}{H} \left( {\overset{\lower0.5em\hbox{\smash{\scriptscriptstyle\frown}}}{W}^{T} W} \right)} \right]}}{{H\left( {W^{T} W} \right)}}$$
$$W \leftarrow W.*\frac{{\left[ {\overset{\lower0.5em\hbox{\smash{\scriptscriptstyle\frown}}}{W} \left( {\overset{\lower0.5em\hbox{\smash{\scriptscriptstyle\frown}}}{H}^{T} H} \right)} \right]}}{{W\left( {H^{T} H} \right)}}$$
lraNMF_HALS $$h_{i} \leftarrow \frac{1}{{w_{i}^{T} w_{i} }}\left[ {\overset{\lower0.5em\hbox{\smash{\scriptscriptstyle\frown}}}{H} \left( {\overset{\lower0.5em\hbox{\smash{\scriptscriptstyle\frown}}}{W}^{T} w_{i} } \right)\; - \;\overline{{H_{i} }} \left( {\overline{{W_{i} }}^{T} w_{i} } \right)} \right]$$
$$w_{i} \leftarrow \frac{1}{{h_{i}^{T} h_{i} }}\left[ {\overset{\lower0.5em\hbox{\smash{\scriptscriptstyle\frown}}}{W} \left( {\overset{\lower0.5em\hbox{\smash{\scriptscriptstyle\frown}}}{H}^{T} h_{i} } \right) - \;\overline{{W_{i} }} \left( {\overline{{H_{i} }}^{T} h_{i} } \right)} \right]$$