## 5 Discussion and Future Research Directions  
The experimental results of Section 4.1 suggest that the proposed scale-space methodology can be successful in detecting small changes in a hyperspectral image. To be useful in practice, such a method must have both high sensitivity and high specificity and our results for the artificial mole data clearly show promise in this respect. We are currently in the process of acquiring a large number of HSI data sets related to skin moles and lesions in collaboration with several hospitals in the Canary Islands, Spain. Our long term goal is to design a successful classifier for such data and the preliminary results obtained so far are promising [14]. However, we believe that a system capable of monitoring dynamical changes in a mole will be even more important as it is likely to be the best way to detect severe skin cancer at an early stage. In the future, we will therefore work on the development of such a system and our ultimate goal is to design a decision support tool based on just a few frequency bands so that an affordable version could be implemented on a smart phone and thereby be available for use on an individual basis. One aspect of hyperspectral image data not utilized in the present study is its spatial structure. Taking spatial information into account is important because it can significantly improve the interpretation of the data when changes have been detected. Spatial information can be used both in the development of the change detection algorithm and in the interpretation of the results. Besides mole monitoring applications, a successful change detection method incorporating spatial information could perhaps also be used in the analysis of brain fMRI data for the detection of early signs of, for example, Alzheimer's disease [16]. Another area where the present methodology can be directly applied is in the design of robust controllers for Type 1 Diabetes patients. Successful results in this area are currently being obtained by using reinforcement learning (RL), see, for example, [17]. In the design of such machine learning algorithms, a good description of the patient's state space is needed for the algorithm to be able to learn better strategies. The state space contains information used to describe the patient's condition at a given time. Typically, the elements of state space in this context are time series of the most recent past blood glucose levels of the patient. At the beginning of the learning phase of an RL algorithm, the state space may be chosen reasonably coarse. During the learning process, the state space then may need to change because the algorithm encounters new states, that is, new glucose level time series, not included in the initial state space. The detection of such changes in the state space time series can be accomplished by the kind of methods discussed in this article. Research in this direction will therefore be pursued in the near future. We also plan to further develop our approach to the analysis of fish freshness discussed in Section 4.2. For the design of a practical system that can be reliably used in fish industry one must first analyze data sets from several different fish at several time points after capturing. Then it is possible estimate both the within variance (of a day) and the between variances (between different time points) exhibited by the hyperspectral signatures. We will acquire such data in the future and the goal will be to perform an analysis that demonstrates how early changes in fish (or other types of food) quality can be detected in a reliable way. Finally, we believe that the proposed methodology can be useful in combating problems in the so-called \"\(p>n\)\" problems now commonly found in statistical data analyses. Here \(p\) and \(n\) refer to the number of model parameters and the number of available observations, respectively, and such problems are very common in applications that involve high dimensional data, see e.g., [18; 19].