Suitable metrics for summarizing or visualizing the spatial activation of components after temporal Independent Component Analysis (ICA) I will first describe the Independent Component Analysis (ICA) steps, so that the question becomes clearer, and more relevant to similar questions. 

Assume we have $N$ sensors distributed in space. From each sensor we obtain a time series of length $T$. We collect these time series as rows in an $N \times T$ matrix $X$. After performing ICA we obtain a decomposition of the form $X = DS$, where $D$ is an $N \times N$ matrix of weights, and $S$ is an $N \times T$ matrix whose rows are the independent sources. To find the contribution of the $i$-th component to the observed signal we then multiply the $i$-th column of the matrix $D$ with the $i$-th row of $S$. The result is an $N \times T$ matrix which we will denote as $X^{i} = D_{*,i}S_{i,*}$. Then we can write: $X = X^{1} + ... + X^{i} + ... + X^{N}$.

In many domains I see single-picture visualizations of the spatial activation of the $i$-th component from ICA. However, it is not clear to me what metric to extract from each row of $X^{i}$ or from matrix $D$ in order to do this. Is it a summary statistic of the rows of $X^{i}$, e.g. the energy of the signals (rows) of $X^{i}$, the weighting coefficients from the $i$-th column of $D$, or something different altogether?

Thank you.
As we know from the instantaneous mixture model of ICA, a signal mixture $X_{N,T}$ is composed of an unknown mixing matrix $D_{N,N}$, and an unknown signal matrix $S_{N,T}$, where:

$$
X = DS
$$

In ICA, we solve for $D_{N,N}$ and $S_{N,T}$ via maximization of absolute kurtosis. (As one method).

If we now look at the $i$th column of $D$, each element therein will now give us weight by which the $i$th signal gets weighted by in all $N$ mixtures. That is, each element $D_{n,i}$, (row $n$, column $i$), gives us signal $i$'s contribution to mixture $n$.  



Those are called 'spatial weights' simply because in many ICA applications, we are de-mixing signals that sample a spatial field at different locations. Thus, each element of a column $D$ corresponds to a weight in space, that weighs signal source $i$. 

In this way, we can show those weights in space as the heatmap above shows, and find the weight each signal gets weighted by, for a particular mixture, at different locations in space.