How to select Count Property as y-axis for Histogram Plots?

[redundancer]

I have the following code:

private HistogramSeries CreateNewHistogramSeries(string title, double[] data, int numberOfBins, BinningOptions binningOptions)
        {
            var series = new HistogramSeries { Title = title };
            var bins = HistogramHelpers.CreateUniformBins(Enumerable.Min(data),
                Enumerable.Max(data), numberOfBins);
            var items = HistogramHelpers.Collect(data, bins, binningOptions);
            series.Items.AddRange(items);
            return series;
        }

When I put multiple of these series into a new PlotModel(), it suddenly uses the Height property instead of the Count property as y-axis. Why is this and how can I change it back to use the Count property as y-axis?

Here some HistogramItems:

And here how the plot looks like:

It takes the Height property as y-axis which is not the behaviour I expect.

[VisualMelon]

HistogramSeries always uses Height, computed from Area. It ignores the Count for plotting. If you re-project the bins so that the Area is Count * Width that should give you what you want, but note that this only makes sense if all histogram items across all histograms use the same bin width.

[redundancer]

Thank you! This seems very counter intuitive to me. Is it not the usual expectation to have the number of occurrences in each bin as y-axis?

[VisualMelon]

For a bar chart, it would be, but for a histogram it is the area that is the meaningful value (bins concern a continuous range, rather than a discrete category).

[philipaxer]

I also ran across this. This really not very intuitive and leads to situations where frequency can be >1.
In my opinion y-axis should show the relative frequency of how many items are in a specific bin (thus should always be within 0 and 1) or show the absolute count.

[philipaxer]

I still think that for complicated scenarios, HistogramItem is overkill. It only needs a single property value and this is directly what is plotted by the Series.
It is then the task of the Helper or the user to populate this value correctly. The Helper can get an enum which selects one of the three options i previously pointed out or you put there what ever you like. At the time when Item is created, all information that is ever needed is available.

It feels akward to replicated information with the intention that perhaps someone might need it later.

But again, that is probably preference where you want to have complexity.

Matplotlib, for example, only takes a "scale" value per bin. That is the value that ends up on the plot. How you come up with scale is your job.

[VisualMelon]

I'd be disinclined to make the binning helpers configurable in this regard (unless we add even more meaningful properties to HistogramSeries and lean on the Value or Height for presentation independent of all other properties, but that feels dodgy). The numbers are readily fudgeable (demands awareness of the user), but with the existing design it doesn't make sense to make this part of the supported flow because it would too easily lead to flow. We could introduce new helpers that enforce uniform bins: that would avoid the main issues with this.

If this was supported then at present I'd suggest it should be on HistogramSeries (aligns well with the OP, which is asking how to configure the choice of Y axis value: I do see this as a presentation concern). The documentation therefore can make it clear that it only makes sense for uniform bin widths within and between series. Main concern would be what to do with the default tracker format string (probably leave it as is). Also need to check that this sort of configuration makes sense generally: it would have to be treated as a change of data.

[VisualMelon]

@Jonarw I think HistogramSeries predates your involvement here (I could be wrong, but was one of my earliest contributions) so interested to hear your opinion.

[VisualMelon]

Example plots showing the three options:

Left is current behaviour (marginal proportion of whole, height = area / width)
Middle is the count (count)
Right is the proportion (area)

Code at https://gist.github.com/VisualMelon/ec1c6cb255344e26a88eb569cf622bf6 (uses example from existing example library)

Question is whether and how to support the middle and right possibilities in a non-hideous way.

[Jonarw]

Personally, I am most familiar with the Middle variant (showing the count), which I also find the most intuitive. This is not to say that the other variants don't have their uses, maybe they are more widely used in other fields. So I guess ideally all scenarios would be supported equally.

I remember that producing the Count variant is slightly awkward with the current API - you have to calculate the area by count * binwidth, only for the HistogramItem to divide by binwidth again during rendering. Not a big deal, and works well enough, but I understand that people could be confused by it.

I kind of like the idea of HistogramItem being 'dumber' - it really only needs start, end and value to be rendered. The rest could be sorted out by the user, who we could support with some helper methods.

But I also don't see this too critical: The current API does allow for all scenarios, some are just a bit more awkward than others.