In contrast to PCA, TCA can be used to identify trends in neuron activity within trials as well as *across trials.

TCA is a dimensionality reduction technique as PCA. However, it does not enforce strict decorrelation of its components, allow to force non-negative weights and provide a framework to analyze responses against the inherent trial structure shared by a lot of systems neuroscience experiments.

In the end of the whole paragraph, add the following:

We do not aim to cover all uses of TCA, but rather help build a concrete intuition on how TCA can be used and pro and cons of this approach.

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the biggest responses

Change this to "often evoke very reliable responses"

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Line #1.    # it can be seen, there is a large gap between the 9th and 10th stim times

Move the comment to a markdown cell instead of within the code section.

Generally, I suggest to restrict inline comments to be used to mostly understand the code

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We need to add intuition as to how to select rank here. I propose to add the following after the plot:

TCA will identify correlation across neurons, trials and time to build a number of components that maximize the ability to reconstruct the original data matrix.

It is therefore essential to use scientific judgement when using this tool. There are two main decision to take: The final rank to use and making sure that the extracted model is faithfully representing the neuronal activity.

Choosing a final rank is a complex question with no "one-size fits all" answer. Generally, as the rank increases, the objective will decrease as more degrees of freedom allows for better reconstructions. Higher rank models also are more computational expensive to compute.

In some cases, if the rank is too low, you could end up with unreliable models. The model similarity plot is useful to make this evaluation as each dot represents a given model run. A good practice is to pick a rank high enough that provides reliable, similar models at each run. Beyond that, you should use your scientific judgement and choose a rank that allow you to conduct your analysis in practice. If your goal is to identify broader components shared across many neurons, a lower rank might be more appropriate. Increasing the rank will further sub-divide components, improving the objective, but will not provide additional insights. Eventually you can test the sensibility of your analysis against this choice with cross-validation.

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It can be seen in the components plot below that, for some factors, there is differential activity of the neurons between each brain region. The same can be said for the trial factors between the first block of stimulus trials and the second block.

I suggest removing the interpretation here and add a paragraph "After" the plot. I will write something below.

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Suggested markdown:

This given run already provide interesting insights with regards to the neuronal activity during repeats of the natural movies.

Our movie was shown in 2 blocks : Block 0 and 1, each made of successive repeats of the movie. These blocks are identified on the previous plot with a yellow dashed line. TCA identifies several components that are block specific and sometime transiently activated at the onset of the first or second block.

Certain components are evenly distributed across all trials, are non-homogenously distributed across cells (in VISp, VISl, VISpm) and show very strong transient patterns of activity. Those components could be related to specific aspects of the movie.

Overall, this decomposition can be used to refine further analysis of each components and test hypothesis on their respective roles. TCA will also naturally exclude global modes of activity in its decomposition and allow to isolate local components from global components.

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