BEGIN:VCALENDAR VERSION:2.0 PRODID:-//pretalx//talks.staging.osgeo.org//foss4g-europe-2025//speaker//JR T3S9 BEGIN:VTIMEZONE TZID:CET BEGIN:STANDARD DTSTART:20001029T040000 RRULE:FREQ=YEARLY;BYDAY=-1SU;BYMONTH=10 TZNAME:CET TZOFFSETFROM:+0200 TZOFFSETTO:+0100 END:STANDARD BEGIN:DAYLIGHT DTSTART:20000326T030000 RRULE:FREQ=YEARLY;BYDAY=-1SU;BYMONTH=3 TZNAME:CEST TZOFFSETFROM:+0100 TZOFFSETTO:+0200 END:DAYLIGHT END:VTIMEZONE BEGIN:VEVENT UID:pretalx-foss4g-europe-2025-MTM3ZA@talks.staging.osgeo.org DTSTART;TZID=CET:20250718T113000 DTEND;TZID=CET:20250718T120000 DESCRIPTION:Quantitative thematic mapping is widely used in meteorology (e. g.\, weather maps)\, geology (e.g.\, topographic maps)\, and environmental science (e.g.\, pollution distribution). However\, mapping continuous qua ntitative data is challenging\, especially when data is sparse or unreliab le. Sparse data arises from uneven measurement distribution\, while unreli able data stems from inconsistencies or errors\, such as subjective self-r eports or satellite-derived estimates. These challenges intensify when map ping hidden variables requiring indirect proxies[Ervin\, 2009]\, introduci ng further uncertainty. Advanced techniques for integrating multiple datas ets and statistical methods like interpolation or machine learning are ess ential for improving accuracy.\nMapping walkability and fire risk in wilde rness areas is particularly difficult due to the hidden nature of these va riables and data limitations. Wilderness walkability depends on factors su ch as trail connectivity\, slope\, surface quality\, and accessibility\, w hich are difficult to measure comprehensively. Desktop analyses often miss real-world obstacles like debris or vegetation overgrowth. Similarly\, fi re risk is influenced by vegetation dryness\, wind patterns\, topography\, and human activity—complex interactions that are hard to quantify due t o sparse sensor coverage and environmental variability. Both require indir ect proxies\, such as fire behavior data or trail condition audits\, which introduce inaccuracies. Addressing these challenges demands advanced mapp ing techniques that integrate multiple data sources\, including crowdsourc ed trail reviews\, IoT sensors\, and remote sensing data.\nThis study focu ses on thematic mapping of walkability. Unlike urban walkability[Horak\,20 22]\, which is linked to built infrastructure\, wilderness walkability dep ends on natural terrain features such as slope\, surface stability\, veget ation density\, and trail connectivity. Measuring these factors directly i s difficult due to terrain heterogeneity and dynamics. For instance\, stee p inclines and loose surfaces can impede movement\, while dense undergrowt h or debris can block trails entirely.\nWalkability can be assessed using GPX trail data by calculating walking speed along trails\, providing an ob jective measure of terrain difficulty. GPX files contain time-stamped geog raphic coordinates that allow speed calculations based on distance and tim e. However\, individual differences in fitness\, experience\, and preferen ces introduce subjectivity when expressing walkability as walking speed. O ne hiker may struggle on rocky trails\, while another navigates them with ease. Aggregating data from multiple users helps mitigate these biases\, c apturing broader patterns and providing a more accurate walkability repres entation. Walking speed alone is insufficient for defining inherent walkab ility\, so we propose matrix factorization as a technique for revealing la tent walkability values. Using multiple GPX trails\, we evaluate different matrix factorization methods for thematic mapping.\nData\nWe collected 1\ ,620 GPX trails from users across Croatia\, including mountain rescue team s\, hikers\, runners\, dog walkers\, and casual users. To ensure anonymity \, each GPX file was assigned a unique user ID without personal informatio n. Each trail contained geographic coordinates and timestamps\, though var iations in recording instruments led to differences in segment lengths. Mo vement speed was calculated by comparing time and location of neighboring segments. After filtering out outliers\, we obtained 1\,795\,663 valid seg ments described by location\, time\, user ID\, and speed.\nTo address inco nsistencies\, segments were grouped into 100-meter spatial cells per user. The median movement speed per user-cell combination was computed\, result ing in 127\,478 user-cell speed descriptions. The final dataset was struct ured as a 1\,609 × 24\,349 sparse matrix\, where rows represent users and columns represent terrain cells\, with values indicating median walking s peed.\nMethods\nWhen factorizing user-item rating matrices\, various techn iques uncover latent features and improve predictions (Khalitov\,2021\; Du \,2023). \nSingular Value Decomposition (SVD) factorizes the matrix into three components\, capturing latent relationships through eigenvalue calcu lations. Truncated SVD retains only the top k singular values\, primar ily for dimensionality reduction in preprocessing. Non-Negative Matrix F actorization (NMF) \, similar to SVD\, enforces non-negative components\, making results more interpretable by representing additive user-item inter actions. For large datasets\, Stochastic Gradient Descent (SGD) iterati vely updates latent factors to minimize prediction error\, while Alternat ing Least Squares (ALS) optimizes user and item factors in a least-square s framework. Fast Independent Component Analysis (FastICA) extracts sta tistically independent latent factors\, assuming non-Gaussian distribution s\, and is mainly used for feature extraction and preprocessing.\nEvaluati on\nAll factorization techniques were tested on the dataset using Python\, scikit-learn\, and custom implementations. Factorization extracted a sing le latent factor per user and per cell. Performance was evaluated by calcu lating RMSE between reconstructed values (user-cell latent factor product) and original sensed values.\nA cell's latent factor represents its inferr ed walkability. Walkability maps generated from each technique were compar ed with satellite imagery\, topography\, and land cover data using GRASS G IS statistical tools.\nResults\nRMSE obtained for the constructed dataset evaluation was 0.4148 (NMF and TruncatedSVD) \, 0.4665 (SVD) \, 0.4666 ( FastICA)\, 2.2839 (ALS) and 5.2349 (SGD)\nConclusion\nResults confirm that matrix factorization effectively separates user and terrain latent data i n sparse datasets. NMF\, with its explainability\, proves particularly use ful for mapping hidden values\, as it ensures non-negative components that directly relate to real-world factors influencing walkability. This prope rty makes it especially suited for modeling walkability.\nExtracted latent factors provide insights into spatial walkability patterns\, revealing ar eas where walking conditions are more or less favorable. These factors can serve as a foundation for extrapolating walkability across larger areas u sing geospatial datasets\, including land cover classifications\, slope gr adients\, and aspect orientations. Additionally\, integrating these result s with external environmental datasets could lead to predictive models for walkability in natural landscapes. Future research should explore method transferability across diverse geographical regions and other applications \, such as fire risk mapping\, where fire behavior data could quantify fir e susceptibility. DTSTAMP:20260527T015035Z LOCATION:PA01 (Quarticle) SUMMARY:Evaluating Matrix Factorization Techniques for Thematic Mapping of Wilderness Walkability Using Multiple GPX Datasets - Ljiljana Seric\, Bori s Draško URL:https://talks.staging.osgeo.org/foss4g-europe-2025/talk/MTM3ZA/ END:VEVENT END:VCALENDAR