PCA is a transform: it creates new (transformed) features from the original data. In general if you choose fewer dimensions (e.g. you chose to reduce m=12 -> n=2 dimensions), it's lossy and will throw away some of in the information content of the original data. The higher n is, the less you lose, and for m=n, you preserve all the original information (although you still do a vector transform on the data, so the extracted features are != the original data).

It was your (arbitrary) decision to choose the parameter n=2 (number of Principal Components), you could try other values or explore a range. You could have chosen n=5, n=9, or even the maximum possible: n=12.

For standard rules-of-thumb on how to choose n, see e.g. Choosing number of principal components to retain

(Scree plot, Proportion of total variance explained, Average eigenvalue rule, Log-eigenvalue diagram, etc.)

where a Scree Plot is a simple line-segment plot that shows the fraction of total variance in the data as explained or represented by each PC. Usually the scree plot will have a knee where the number of PCs explains most of the variance, and if so that might suggest you an upper bound on n.

There are other rules-of-thumb discussed there too. You can find tons of articles on this subject.

See also e.g. How many principal components to take?

PCA is a transform: it creates new (transformed) features from the original data. In general if you choose fewer dimensions (e.g. you chose to reduce m=12 -> n=2 dimensions), it's lossy and will throw away some of in the information content of the original data. The higher n is, the less you lose, and for m=n, you preserve all the original information (although you still do a vector transform on the data, so the extracted features are != the original data).

It was your (arbitrary) decision to choose the parameter n=2 (number of Principal Components), you could try other values or explore a range. You could have chosen n=5, n=9, or even the maximum possible: n=12.

For standard rules-of-thumb on how to choose n, see e.g. Choosing number of principal components to retain

(Scree plot, Proportion of total variance explained, Average eigenvalue rule, Log-eigenvalue diagram, etc.)

where a Scree Plot is a simple line-segment plot that shows the fraction of total variance in the data as explained or represented by each PC. Usually the scree plot will have a knee where the number of PCs explains most of the variance, and if so that might suggest you an upper bound on n.

There are other rules-of-thumb discussed there too. You can find tons of articles on this subject.

See also e.g. How many principal components to take?

PCA is a transform: it creates new (transformed) features from the original data. In general if you choose fewer dimensions (e.g. you chose to reduce m=12 -> n=2 dimensions), it's lossy and will throw away some of in the information content of the original data. The higher n is, the less you lose, and for m=n, you preserve all the original information (although you still do a vector transform on the data, so the extracted features are != the original data).

It was your (arbitrary) decision to choose the parameter n=2 (number of Principal Components), you could try other values or explore a range. You could have chosen n=5, n=9, or even the maximum possible: n=12.

For standard rules-of-thumb on how to choose n, see e.g. Choosing number of principal components to retain

(Scree plot, Proportion of total variance explained, Average eigenvalue rule, Log-eigenvalue diagram, etc.)

where a Scree Plot is a simple line-segment plot that shows the fraction of total variance in the data as explained or represented by each PC. Usually the scree plot will have a knee where the number of PCs explains most of the variance, and if so that might suggest you an upper bound on n.

There are other rules-of-thumb discussed there too. You can find tons of articles on this subject.

See also e.g. How many principal components to take?

PCA is a transform: it creates new (transformed) features from the original data. In general if you choose fewer dimensions (e.g. you chose to reduce m=12 -> n=2 dimensions), it's lossy and will throw away some of in the information content of the original data. The higher n is, the less you lose, and for m=n, you preserve all the original information (although you still do a vector transform on the data, so the extracted features are != the original data).

It was your (arbitrary) decision to choose the parameter n=2 (number of Principal Components), you could try other values or explore a range. You could have chosen n=5, n=9, or even the maximum possible: n=12.

For standard rules-of-thumb on how to choose n, see e.g. Choosing number of principal components to retain

(Scree plot, Proportion of total variance explained, Average eigenvalue rule, Log-eigenvalue diagram, etc.)

where a Scree Plot is a simple line-segment plot that shows the fraction of total variance in the data as explained or represented by each PC. Usually the scree plot will have a knee where the number of PCs explains most of the variance, and if so that might suggest you an upper bound on n.

There are other rules-of-thumb discussed there too. You can find tons of articles on this subject.

See also e.g. How many principal components to take?