Seasonal influenza surveillance is usually carried out by sentinel general practitioners (GPs) who compile weekly reports based on the number of influenza-like illness (ILI) clinical cases observed among visited patients. This traditional practice for surveillance generally presents several issues, such as a delay of one week or more in releasing reports, population biases in the health-seeking behaviour, and the lack of a common definition of ILI case. On the other hand, the availability of novel data streams has recently led to the emergence of non-traditional approaches for disease surveillance that can alleviate these issues. In Europe, a participatory web-based surveillance system called Influenzanet represents a powerful tool for monitoring seasonal influenza epidemics thanks to aid of self-selected volunteers from the general population who monitor and report their health status through Internet-based surveys, thus allowing a real-time estimate of the level of influenza circulating in the population. In this work, we propose an unsupervised probabilistic framework that combines time series analysis of self-reported symptoms collected by the Influenzanet platforms and performs an algorithmic detection of groups of symptoms, called syndromes. The aim of this study is to show that participatory web-based surveillance systems are capable of detecting the temporal trends of influenza-like illness even without relying on a specific case definition. The methodology was applied to data collected by Influenzanet platforms over the course of six influenza seasons, from 2011-2012 to 2016-2017, with an average of 34,000 participants per season. Results show that our framework is capable of selecting temporal trends of syndromes that closely follow the ILI incidence rates reported by the traditional surveillance systems in the various countries (Pearson correlations ranging from 0.69 for Italy to 0.88 for the Netherlands, with the sole exception of Ireland with a correlation of 0.38). The proposed framework was able to forecast quite accurately the ILI trend of the forthcoming influenza season (2016-2017) based only on the available information of the previous years (2011-2016). Furthermore, to broaden the scope of our approach, we applied it both in a forecasting fashion to predict the ILI trend of the 2016-2017 influenza season (Pearson correlations ranging from 0.60 for Ireland and UK, and 0.85 for the Netherlands) and also to detect gastrointestinal syndrome in France (Pearson correlation of 0.66). The final result is a near-real-time flexible surveillance framework not constrained by any specific case definition and capable of capturing the heterogeneity in symptoms circulation during influenza epidemics in the various European countries.