Note the average
Note the average
There are various types of averages, such as additive, geometric, and harmonic averages.
For example, suppose we want to find the average length of the shortest path between any two points in a graph (hereafter referred to as "average path length"). If the graph is not connected, then there is a pair of points where no path exists. If the length of the path between these two points is infinite, the average path length will also be infinite. If we take the "average of the reciprocal of the path length," we can obtain values in the range of 0 to 1 even for unconnected graphs, but the reciprocal of this value will not match the "average path length. Difference between additive and harmonic averaging.
For example, let's say you blur a photo taken with a digital camera using image retouching software. Blurring is a process of taking the average of surrounding pixel values, but blurred images do not resemble natural out-of-focus images. The reason is simple: the brightness between X and Y is much brighter than X+Y/2. When there is a non-linear transformation (see Gamma Value), the average is not additive average appropriate. The average can be taken anywhere between the minimum and maximum values by inserting the appropriate nonlinear function. The harmonic mean corresponds to a nonlinear function called the inverse, and the geometric mean corresponds to a nonlinear function called the logarithm.
For a given distribution A,B, "the mean of A is greater than the mean of B" does not mean that "the probability that a > b is greater than the probability that a < b for randomly selected samples a and b from A and B". In a simple example, A:{0,0,9},B:{1,1,1}. Efron's dice in an elegant example. As this example shows, the latter relationship is not an ordinal relationship. #Efron's dice. __BELOW_IS_AI_GENERATED__
平均に注意 2023-09-05 01:10 omni.icon
Summary of notes.
Averages include additive, geometric, and harmonic averages, each of which has different application situations. For example, when finding the average of the length of the shortest path between any two points in a graph, if the graph is unconnected, there is a pair of points where no path exists, and if the length of the path is infinite, the average path length will also be infinite. However, by taking the average of the reciprocal of the path length, values in the range of 0 to 1 can be obtained even for unconnected graphs. The image blurring process also takes the average of the values of the surrounding pixels, which is different from natural out-of-focus. This is because the brightness between brightness X and Y is brighter than X+Y/2, and the nonlinear transformation makes the average inappropriate for an additive average. Furthermore, the average can be taken anywhere between the minimum and maximum values by interpolating an appropriate nonlinear function.
Relation to Fragment.
The fragment "Harmonic averages to take sharp personnel" is related to the note. The note describes the types of averages and their application situations, and the fragment states that it is possible to select sharp personnel by using the harmonic mean. This is because the harmonic mean has the property of responding appropriately to nonlinear values.
deep thinking
Understanding the different types of averages and their application situations is important in data analysis and decision making. In particular, the fact that harmonic averages, rather than additive averages, should be used for nonlinear values has important implications for evaluating things from a variety of perspectives.
summary of thoughts and title.
Application of Averages to Nonlinear Values: Understanding the types of averages and their application context is important in data analysis and decision making, especially when harmonic averages should be used for nonlinear values.
extra info
TITLES: ["Still no picture blind spot card"], "Average group is not always majority", "Harmonic mean to get sharp", "Harmonic mean of rank to get sharp", "Resolution stages", "Simpson's paradox"]
generated: 2023-09-05 01:10
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