Visualizing Temporal Data using Time-dependent Non-decreasing Monotone Functions

Ahstract- The occurrence of seasonal natural phenomena depends on the conditions leading to it and not directly on the progression of time, meaning its context varies across time and space. Examples of this include comparing plant growth, insect development or wildfire risk during the same time period at different locations or in different time periods at the same location. However, visualizing and comparing such phenomena usually implies plotting it across the time axis as it's perceived as temporal data. Since it's not directly dependent of time, identifying patters of recurrence using this technique is inefficient. Because of this, we proposed transforming (when needed) the dependent function to a non-decreasing monotone one, in order to preserve the monotonic property of time progression. Then we used the resulting function as a time axis replacement to achieve an equal ground of comparison between the different contexts in which the phenomenon occurs. We applied this technique to real data from seasonal natural phenomena, such as plant and insect growth, to compare its progression in different temporal and spatial contexts. Since the dependent function of the phenomenon was scientifically known, we were able to directly use the technique to infer its seasonality patterns. Furthermore, we applied the technique to real data from the coronavirus worldwide pandemic by hypothesizing its dependent function and analysing if it was able to reduce the existing temporal misalignment between different contexts, like years and countries. The results achieved were positive, although not as remarkable as when the dependent function was known.