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During this discussion a suggestion was to see whether unsupervised clustering could help uncover which variables correlate with each other while also highlighting whether there are different types of days. A search in the Show & Tell archives showed that a similar approach had already been tried in the [[100 Days of Summer]] project.
During this discussion a suggestion was to see whether unsupervised clustering could help uncover which variables correlate with each other while also highlighting whether there are different types of days. A search in the Show & Tell archives showed that a similar approach had already been tried in the [[100 Days of Summer]] project.
== Reducing dimensions with a Principal Component Analysis ==
== Preparing data for clustering with Principal Component Analysis ==
To give it a first try, I decided to go ahead and use some of my data to see if such a clustering could work. In order to limit the scope I decided to use data from a variety of sources. To simplify the approach, I decided to use the '''''day''''' as the unit of observation. For this, I either summed up or averaged measurements throughout the day, depending on the metric (see Table below).
To give it a first try, I decided to go ahead and use some of my data to see if such a clustering could work using a simple [[principle component analysis]] (PCA). In order to limit the scope I decided to use data from a variety of sources. To simplify the approach, I decided to use the '''''day''''' as the unit of observation. For this, I either summed up or averaged measurements throughout the day, depending on the metric (see Table below).
=== Metrics used ===
=== Metrics used ===
I exported data for all these variables for a time period between September 1, 2021 and June 08, 2022 as this was the period for which I felt like most data would be complete. Following the export of the data as one large spreadsheet, some more processing was needed.
I exported data for all these variables for a time period between September 1, 2021 and June 08, 2022 as this was the period for which I felt like most data would be complete. Following the export of the data as one large spreadsheet, some more processing was needed.
Doing a [[principal component analysis]] ideally requires a "complete" data set without any missing values. Depending on the metric, the spreadsheet generated above still had gaps in it. Some gaps were due to lack of measurements (e.g. a gap in the weight record represents me not weighing myself), while in other cases a gap means that the value should be zero (e.g. if I did not cycle at all, then Apple Health would report a data gap, but it actually represents zero kilometers cycled).
Doing a PCA ideally requires a "complete" data set without any missing values. Depending on the metric, the spreadsheet generated above still had gaps in it. Some gaps were due to lack of measurements (e.g. a gap in the weight record represents me not weighing myself), while in other cases a gap means that the value should be zero (e.g. if I did not cycle at all, then Apple Health would report a data gap, but it actually represents zero kilometers cycled). To fill the table, I performed a linear interpolation of my weight for missing days, and set missing values to zero for all RescueTime entries as well as for missing cycle distance values (those categories were the only ones affected).
== Running a PCA ==
[[File:PCA test variable alignment.png|thumb|The variable distribution after the PCA, answering how the 37 different variables correlate with each other. Arrows pointing in the same direction positively correlate with each other. Arrows pointing in opposite directions are negatively correlated. Length of the arrows is a metric for how 'well' the variable is represented in the PCA. Colors are the result of kmeans clustering of variables.]]
With the full data table prepared for this time period, I ended up with 280 observations (aka days) that had full data for these 37 variables that I could use to run the PCA. For this I used the [[R]] package <code>FactoMineR</code> as it not only provides the basic functions for running the analysis, but also a wide set of visualization options. Roughly speaking, PCAs are a way to reduce the dimensionality of data by 'rotating' the data in a way that it can be represented in fewer dimensions, ideally no more than 2-3 as this would allow visualizing it in a human-readable space. In this case, we have 37 different dimensions as given by the 37 variables and would like to boil it down to fewer dimensions without losing any information.
=== How do the different metrics correlate? ===
Running the PCA – including a normalization/re-scaling of the variables – results in the graph on the right. Doing an additional clustering by kmeans shows that there are three main groups in which the variables can be clustered:
# The '''top left quadrant''' mainly includes all metrics associated to productivity as measured by RescueTime (regardless of productivity/unproductivity category), as well as different metrics from Oura that relate to inactivity but also my cycling distance.
# The '''bottom right quadrant''' includes mainly different sleep metrics from Oura but also associated metrics such as resting heart rate and average sleeping heart rate and furthermore my weight.
# The '''top right quadrant''' includes metrics that have a 90º vector to both other clusters and mainly includes different metrics to medium & higher intensity activity. These include my overall step count as well as active calorie burn.
The axis-labels also show how much of the overall variance in my data can be explained among these two dimensions that are being plotted, which comes down to 18.5% of variance on the X-axis (dimension 1) and 13.8% on the Y-axis (dimension 2).
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