Algorithm 1: The online optimization of our method at round t.

Input: the t-th data chunk with features ${\overrightarrow{\mathbf{X}}}^{(t)}$; information stored in our memory ${\overrightarrow{\mathbf{V}}}_m^{(t)}$; auxiliary variables ${\mathbf{C}}_1^{(t-1)}$, ${\mathbf{C}}_2^{(t-1)}$, and ${\mathbf{C}}_3^{(t-1)}$; trade-off parameters; iteration number T.

Output: Projection matrix ${\mathbf{W}}^{(t)}$.

Procedure:

Randomly initialize all variables ${\mathbf{W}}^{(t)}$, ${\mathbf{G}}^{(t)}$, ${\overrightarrow{\mathbf{R}}}^{(t)}$, and ${\overrightarrow{\mathbf{V}}}^{(t)}$;

for iter = $1,\cdots ,T$ do

Updating ${\mathbf{W}}^{(t)}$ with (6);

Updating ${\mathbf{G}}^{(t)}$ with (8);

Updating ${\overrightarrow{\mathbf{R}}}^{(t)}$ with (10);

Updating ${\overrightarrow{\mathbf{V}}}^{(t)}$ with (12);

end for

Return: auxiliary variables ${\mathbf{C}}_1^{(t)}$, ${\mathbf{C}}_2^{(t)}$, and ${\mathbf{C}}_3^{(t)}$; variables ${\mathbf{W}}^{(t)}$, ${\mathbf{G}}^{(t)}$, ${\overrightarrow{\mathbf{R}}}^{(t)}$, and ${\overrightarrow{\mathbf{V}}}^{(t)}$.