CytoSpec - an APPLICATION FOR HYPERSPECTRAL IMAGING |
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PULL DOWN MENU "MULTIVARIATE STATISTICS" |
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MULTIVARIATE STATISTICS - HCA |
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 HCA imaging ('Image Manipulation' pull down menu).
HCA imaging ).Reformatting data sets for HCA imaging: The following data manipulations are performed to prepare data sets for HCA:
Important: Spectra with a negative Quality Test result, or unselected Regions of Interest are automatically excluded from HCA imaging.
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MULTIVARIATE STATISTICS - PCA |
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PCA imaging ('Image Manipulation' pull down menu).
PCA imaging ).Reformatting data sets for PCA imaging: The following data manipulations are performed to prepare data sets for PCA:
Important: Spectra with a negative Quality Test result, or unselected Regions of Interest are automatically excluded from PCA imaging.
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k-MEANS CLUSTER (KMC) IMAGING |
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Reformatting data sets for KMC imaging: The following data manipulations are performed to prepare data sets for KMC:
Important: Spectra with a negative Quality Test result, or unselected Regions of Interest are automatically excluded from KMC imaging.Once data preparation has been finished, the following KMC imaging dialog box will appear: Button 'spectra': This option becomes available when the k-means clustering calculations are finished. When this button is pressed, a new window comes up that offers additional options such as the calculation of cluster mean spectra or sorting individual map spectra by its cluster membership.  save all spectra: all spectra used for KMC imaging are stored as double column ASCII data. Use the standard windows dialog box to set the path and create the ASCII data files. File names: corenamex_i: x-th spectrum of the i-th cluster. disp averages: average spectra of the selected data block are calculated and plotted in the same color like in the cluster map. save averages: average and standard deviation spectra of the selected data block are calculated. To store these spectra (double column ASCII) use the standard windows dialog box to set the path and chose a file name. Average spectra and standard deviation spectra of the i-th cluster are stored per default in separate files (corename_i - for average spectra and corename_std_i for the standard deviation spectra). Principles of k-means clustering: The algorithm of k-means clustering has been suggested by J.B. MacQueen in 1967 : J.B. MacQueen. In L.M. LeCam and J. Neymann (eds) Proceedings of Fifth Berkeley Symposium on Mathematical Statistics and Probability. 1967 281-297. Related web links (Wikipedia): In the CytoSpec implementation, MacQueens k-means cluster algorithm is used. k-means clustering is a non hierarchical clustering method, which obtains a "hard" (crisp) class membership for each spectrum, that is the class membership of an individual spectrum can be take only the values of zero or one. It uses an iterative algorithm to update randomly selected initial cluster centers, and to obtain the class membership for each spectrum, assuming well-defined boundaries between the clusters. MacQueens iterative algorithm of KMC can be described as follows: Spectra are illustrated as points in a p-dimensional space (p is the number of features of the spectra. In this space a number of k points is initially chosen, where each point represents a cluster to be made. Then, distance values between the points and all objects (spectra) are calculated. Objects are assigned to a cluster on the basis of a minimal distance value. Next, centroids of the clusters are calculated and distance values between the centroids and each of the objects are re-calculated. Then, if the closest centroid is not associated with the cluster to which the object currently belongs, the object will switch its cluster membership to the cluster with the closest centroid. The centroid's positions are re-calculated every time a component has changed the cluster membership. This continues until none of the objects has been re-assigned. Reference to the literature: |
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FUZZY C-MEANS CLUSTER (FCM) IMAGING |
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Reformatting data sets for FCM imaging: The following data manipulations are performed to prepare data sets for FCM:
Important: Spectra with a negative Quality Test result, or unselected Regions of Interest are automatically excluded from FCM imaging.
Button 'spectra': This option becomes available when the fuzzy C-means clustering calculations are finished. When this button is pressed, a new window comes up that offers additional options such as the calculation of cluster mean spectra or sorting individual map spectra by its cluster membership. By pressing any of the buttons (except button 'done') a new FCM imaging approach is initiated by using the settings of the FCM imaging dialog box. disp averages: average spectra of the selected data block are calculated and plotted. save averages: average and standard deviation spectra of the selected data block are calculated. To store these spectra (double column ASCII) use the standard windows dialog box to set the path and chose a file name. Average spectra and standard deviation spectra of the i-th cluster are stored per default in separate files (corename_i - for average spectra and corename_std_i for the standard deviation spectra). Principles of fuzzy C-means clustering: Principles of FCM clustering are given in the following publication: J.C. Bezdek. Pattern Recognition with Fuzzy Objective Function Algorithms, 1981 New York. Plenum Press. Related web links: fuzzy C-means clustering (Wikipedia) Thus, this method departs from the classical two-valued (0 or 1) logic, and uses "soft" linguistic system variables and a continuous range of true values in the interval [0,1]. FCM imaging uses a fuzzy iterative algorithm to calculate the class membership grade for each spectrum. The iterations in FCM clustering are based on minimizing an objective function, which represents the distance from any given data point (spectrum) to the actual cluster center weighted by that data points membership grade. The advantage of the fuzzy C-means clustering over k-means clustering is that both outliers and data, which display properties of more than one class can be characterized by assigning nonzero class membership values to several clusters. In the similarity maps assembled by FCM clustering the membership values are encoded by the colormap, that is by the color intensities in the case of single color colormaps. Reference to the literature:
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