Measuring distance preservation in dimensionality reduction Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern) 2019 Moderator Election Q&A - Questionnaire 2019 Community Moderator Election ResultsDeciding about dimensionality reduction, classification and clustering?Dimension reduction techniques in R that do not use the full distance matrixDimensionality reduction with PCA limitationsDimensionality reduction with known colinearity between featuresNon Deterministc Dimensionality reductionApplying dimensionality reduction on OneHotEncoded arrayAre dimensionality reduction techniques useful in deep learningmultivariate clustering, dimensionality reduction and data scalling for regressionDimensionality reduction categoriesSimilarity measure before and after dimensionality reduction or clustering
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Measuring distance preservation in dimensionality reduction
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)
2019 Moderator Election Q&A - Questionnaire
2019 Community Moderator Election ResultsDeciding about dimensionality reduction, classification and clustering?Dimension reduction techniques in R that do not use the full distance matrixDimensionality reduction with PCA limitationsDimensionality reduction with known colinearity between featuresNon Deterministc Dimensionality reductionApplying dimensionality reduction on OneHotEncoded arrayAre dimensionality reduction techniques useful in deep learningmultivariate clustering, dimensionality reduction and data scalling for regressionDimensionality reduction categoriesSimilarity measure before and after dimensionality reduction or clustering
$begingroup$
I am looking to compare the distance preserved during dimension reductions for several techniques. I have read some papers on similar topics here and here.
For example, I would like to use the Euclidean Distance to measure the distance preserved during PCA's dimension reduction. However, my point of confusion what are $X$ and $Y$ in
$$d(X, Y) = sqrtsum^n_i=1left(x_i - y_iright)^2$$
I understand how to calculate $dleft(X, Yright)$ given two vectors/matrices, but I don't understand with context to PCA. Let me try to explain.
Let $W_k times n$ be the matrix of $k$ eigenvectors, $X_dtimes n$ be the original data, and $Z_ktimes n$ be the projection of $X$ onto the reduced subspace.
$Z = W^TX$
Back to calculating $dleft(X, Yright)$. My guess is that the PCA's $X$ correspond to $X$ and $Y$ can correspond to $Z$. But how does this work since $X$ and $Y$ have different dimensions? I have to be oblivious to something here.
Also, I am not concerned if a Euclidean Distance measure is not a good choice for measuring PCA's distance preservation (unless they are incompatible). This is simply exploration.
pca dimensionality-reduction distance
asked 10 mins ago
qq3254qq3254
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New contributor
qq3254 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment |
$begingroup$
I am looking to compare the distance preserved during dimension reductions for several techniques. I have read some papers on similar topics here and here.
For example, I would like to use the Euclidean Distance to measure the distance preserved during PCA's dimension reduction. However, my point of confusion what are $X$ and $Y$ in
$$d(X, Y) = sqrtsum^n_i=1left(x_i - y_iright)^2$$
I understand how to calculate $dleft(X, Yright)$ given two vectors/matrices, but I don't understand with context to PCA. Let me try to explain.
Let $W_k times n$ be the matrix of $k$ eigenvectors, $X_dtimes n$ be the original data, and $Z_ktimes n$ be the projection of $X$ onto the reduced subspace.
$Z = W^TX$
Back to calculating $dleft(X, Yright)$. My guess is that the PCA's $X$ correspond to $X$ and $Y$ can correspond to $Z$. But how does this work since $X$ and $Y$ have different dimensions? I have to be oblivious to something here.
Also, I am not concerned if a Euclidean Distance measure is not a good choice for measuring PCA's distance preservation (unless they are incompatible). This is simply exploration.
pca dimensionality-reduction distance
asked 10 mins ago
qq3254qq3254
1
New contributor
qq3254 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I am looking to compare the distance preserved during dimension reductions for several techniques. I have read some papers on similar topics here and here.
For example, I would like to use the Euclidean Distance to measure the distance preserved during PCA's dimension reduction. However, my point of confusion what are $X$ and $Y$ in
$$d(X, Y) = sqrtsum^n_i=1left(x_i - y_iright)^2$$
I understand how to calculate $dleft(X, Yright)$ given two vectors/matrices, but I don't understand with context to PCA. Let me try to explain.
Let $W_k times n$ be the matrix of $k$ eigenvectors, $X_dtimes n$ be the original data, and $Z_ktimes n$ be the projection of $X$ onto the reduced subspace.
$Z = W^TX$
Back to calculating $dleft(X, Yright)$. My guess is that the PCA's $X$ correspond to $X$ and $Y$ can correspond to $Z$. But how does this work since $X$ and $Y$ have different dimensions? I have to be oblivious to something here.
Also, I am not concerned if a Euclidean Distance measure is not a good choice for measuring PCA's distance preservation (unless they are incompatible). This is simply exploration.
pca dimensionality-reduction distance
asked 10 mins ago
qq3254qq3254
1
New contributor
qq3254 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I am looking to compare the distance preserved during dimension reductions for several techniques. I have read some papers on similar topics here and here.
For example, I would like to use the Euclidean Distance to measure the distance preserved during PCA's dimension reduction. However, my point of confusion what are $X$ and $Y$ in
$$d(X, Y) = sqrtsum^n_i=1left(x_i - y_iright)^2$$
I understand how to calculate $dleft(X, Yright)$ given two vectors/matrices, but I don't understand with context to PCA. Let me try to explain.
Let $W_k times n$ be the matrix of $k$ eigenvectors, $X_dtimes n$ be the original data, and $Z_ktimes n$ be the projection of $X$ onto the reduced subspace.
$Z = W^TX$
Back to calculating $dleft(X, Yright)$. My guess is that the PCA's $X$ correspond to $X$ and $Y$ can correspond to $Z$. But how does this work since $X$ and $Y$ have different dimensions? I have to be oblivious to something here.
Also, I am not concerned if a Euclidean Distance measure is not a good choice for measuring PCA's distance preservation (unless they are incompatible). This is simply exploration.
pca dimensionality-reduction distance
pca dimensionality-reduction distance
asked 10 mins ago
qq3254qq3254
1
New contributor
qq3254 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 10 mins ago
qq3254qq3254
1
New contributor
qq3254 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 10 mins ago
qq3254qq3254
1
New contributor
qq3254 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 10 mins ago
qq3254qq3254
1
asked 10 mins ago
qq3254qq3254
1
1
New contributor
qq3254 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
qq3254 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
qq3254 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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