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How to automatically determine the compression rate in PCA?

Is there a computational methods to determine the amount of compression rate in PCA due to features dimension & count? In the first n cols for reduction then I'm testing a one percentage of the data.If the validation is greater than the specified threshold select n cols else increase n and repeat loop. Is this true? is there a better solution?

How to automatically determine the compression rate in PCA?

Is there a computational methods to determine the amount of compression rate in PCA due to features dimension & count?

In the first n cols for reduction then I'm testing a one percentage of the data.If the validation is greater than the specified threshold select n cols else increase n and repeat loop.

Is this true? is there a better solution?

How to automatically determine the compression rate in PCA?

Is there a computational methods to determine the amount of compression rate in PCA due to features dimension & count?

In the first n cols for reduction then I'm testing a perform reproject on one percentage of the data.If data after it compute the difference with original data .If the validation is greater than the specified threshold select n cols else increase n and repeat loop.

Is this true? is there a better solution?