further work on background section

thesis/sections/background.tex

@@ -176,18 +176,54 @@ These markers provide further physiological context and may include information
 At the time of writing, the dataset contains approximately 65{,}000 annotated cycles, comprising more than 350 million individual temperature measurements.
 
 \subsubsection{Dataset Summary}
+For the present study, the dataset was reduced to approximately 40{,}000 cycles after filtering out entries that were incomplete,
+contained hardware-related anomalies, or fell outside a reasonable cycle length range.
+
+Very short cycles typically result from incorrect cycle start entries or premature termination of temperature recordings.
+Extremely long cycles are often due to data entry errors or pregnancy-related recordings,
+where the sensor was worn continuously throughout gestation—sometimes producing sequences up to nine months long.
+
+While such cases may still contain useful information, they were excluded from this analysis to avoid complications in preprocessing and labeling.
+In most instances, only a small portion of these extended cycles contributes meaningfully to the study objectives.
+The cutoff values for cycle length are 10 and 150 days, respectively.
+
+The cleaned dataset has 40{,}266 menstrual cycles from 6{,}245 users.
+The median number of cycles per user is 4 (IQR: 2--8) and the median cycle length is 28 days (IQR: 26--32).
+
+The average data density—defined as the fraction of available measurements out of the theoretical maximum of 288 measurements per day—is 0.90.
+This corresponds to an average data availability of 90\% per cycle, with an average loss of 10\%.
+
+It should be noted, that both ovulation day and anovulation estimates are based on retrospective algorithmic inference, not human labels.
+Further details are provided in section~\ref{sec:methodology}.
 
 \subsubsection{Irregularities and Confounding Factors}
+Core body temperature is influenced by various factors unrelated to the menstrual cycle.
+Illnesses—especially those involving fever—can significantly affect temperature patterns.
+This poses a challenge for any analysis relying on temperature data, as one of the key physiological indicators of ovulation is a post-ovulatory temperature rise (see Section~\ref{subsubsec:physiological_signs}).
 
+Figure~\ref{fig:background_fever_cycle} shows an example of a cycle where an illness caused a marked increase in temperature.
+This event is particularly problematic because the fever-induced rise occurs just before the expected ovulatory shift, potentially confounding ovulation detection.
+Distinguishing illness-related changes from cycle-related ones requires models that are sensitive to context and robust to outliers.
 
 \begin{figure}[htbp]
     \centering
     \includegraphics[width=0.9\textwidth]{background_fever_cycle}
-    \caption{An example of a cycle with fever significantly altering the temperature data}
+    \caption{Example of a cycle affected by illness, showing a fever-induced temperature rise shortly before the expected ovulatory shift.}
     \label{fig:background_fever_cycle}
 \end{figure}
-Figure~\ref{fig:background_fever_cycle} shows a cycle, where the user had an illness that concluded in a rise of body core temperature.
-These anomalies can make analysis hard, as the resulting rise in temperature is hard to distinguish from the rise in temperature triggered by an ovulation.
+
+Another common irregularity arises when users temporarily remove the sensor during menstruation, typically for hygiene reasons—even though the device is safe to wear continuously.
+This behavior frequently results in missing data at the start of each cycle.
+Depending on the total cycle length, this gap can represent a significant portion of the cycle's data.
+
+Figure~\ref{fig:background_menstruation_data_gap} shows an example cycle with a data gap during menstruation.
+
+\begin{figure}[htbp]
+    \centering
+    \includegraphics[width=0.9\textwidth]{background_menstruation_data_gap}
+    \caption{Example of a cycle with a data gap at the beginning, caused by sensor removal during menstruation.}
+    \label{fig:background_menstruation_data_gap}
+\end{figure}
 
 \subsubsection{Privacy}
 The dataset used in this study contains sensitive personal health information and is handled with strict privacy safeguards.