I am having a hard time understanding what the color gradient represents on the graph from the formulation of soft clustering. From what I understand the pi_k's give different probability for each point to fall in either cluster k=1,2 or 3. The likelihood of the point given parameters if pi_k*likelihood of the point if it belongs to cluster k. So each point has the same cluster probabilities (pi_1,pi_2,pi_3), why are certain points clearly red while some are a mix of colors.
I think each point has its own pi vector, describing the probability of belonging to each cluster k. So a point x_n has a related vector pi_n where all entries sums to 1. This is why you see a color gradient on the points if it makes sense?
thank you for the answer, but from what I understood pi is a vector of k elements and it is defined for the distribution, not for each point. The sum up to 1 is when summing pi_k over k.
soft clustering
Hello,
I am having a hard time understanding what the color gradient represents on the graph from the formulation of soft clustering. From what I understand the pi_k's give different probability for each point to fall in either cluster k=1,2 or 3. The likelihood of the point given parameters if pi_k*likelihood of the point if it belongs to cluster k. So each point has the same cluster probabilities (pi_1,pi_2,pi_3), why are certain points clearly red while some are a mix of colors.
thank you
I think each point has its own pi vector, describing the probability of belonging to each cluster k. So a point x_n has a related vector pi_n where all entries sums to 1. This is why you see a color gradient on the points if it makes sense?
1
thank you for the answer, but from what I understood pi is a vector of k elements and it is defined for the distribution, not for each point. The sum up to 1 is when summing pi_k over k.
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