Chapter 7 tissue type (hence the input label is set at 1 in the top row) and the next three measurements represent a second tissue type (input label value of 1 in the bottom row). Using these matrices an aggregated matrix A is formed, containing the observations X and the corresponding input labels Y. There is also a weighting factor λ between X and Y which indicates the measure of confidence in the observations X versus the labels. The combination matrix A is now used in an algorithm to determine the most interesting features to be used. In this case, however, the labeling information is additionally taken into account by using the labeling Y ensuring a more useful output for characterization. The identified features can be used to construct a transformation B which transforms the observations X into an estimation of the labeling Ŷ. Actually, what is achieved is a learning matrix B based on the observations and the input labeling which estimates as well as possible the labels through the observations, hence: That means that when a new (unlabeled) measurement is acquired, it has to be multiplied by the matrix B to obtain the label of the measurement (in this particular case the most likely tissue type). In the example the learning matrix could now be applied to observations to evaluate how well the system is trained. The result is: ˆ 1.0231 0.9726 0.0550 0.0925 0.1472 Y For instance the first column of the result matrix indicates that the observation was of the first type because the result value of 1.023 is closer to 1 than to 0. And the observation was not likely to be of the second type because the result value of ‐0.0080 is closer to 0 than to 1. It is clear that the result has to approach the real label matrix Y. In case a new unlabeled measurement x is acquired, for example: 104 A X T YT Yˆ X B 0.0080 0.0087 0.9938 1.0281 0.9797 x 0.89 0.42 0.74 0.81 0.87 0.883 0.334 0.098
proefschrift_Schols_SLV
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