-
diff --git a/doc/pub/DimRed/html/._DimRed-bs018.html b/doc/pub/DimRed/html/._DimRed-bs018.html index 9796a01be..2df856349 100644 --- a/doc/pub/DimRed/html/._DimRed-bs018.html +++ b/doc/pub/DimRed/html/._DimRed-bs018.html @@ -226,13 +226,18 @@ The following Python code aids in setting up the data
-
n = 1000
+import numpy as np
+import pandas as pd
+from IPython.display import display
+n = 100
mean = (-1, 2)
cov = [[4, 2], [2, 2]]
X = np.random.multivariate_normal(mean, cov, n)
+# Print the X-matrix
+print(X)
-Make thereafter a small Python code which plots the data. Note that the function multivariate returns also the covariance discussed above and that it is defined by dividing by \( n-1 \) instead of \( n \).
+Make thereafter a small Python code which writes out the data. Note that the function multivariate returns also the covariance discussed above and that it is defined by dividing by \( n-1 \) instead of \( n \).
Now we are going to implement the PCA algorithm. We will break it down into various substeps.
@@ -254,6 +259,20 @@ When you are done with these steps, print out \( \mu_n \) to verify it is
close to \( \mu \) and plot your mean centered data to verify it is
centered at the origin! Compare your code with the functionality from Scikit-Learn discussed above.
+
+
+
+
df = pd.DataFrame(X)
+# Pandas does the centering for us
+df = df -df.mean()
+display(df)
+
+# we center it ourselves
+X_centered = X - X.mean(axis=0)
+# test that we get the same as Pandas
+print(X_centered-df)
+
+
Compute the sample covariance
@@ -296,6 +315,25 @@ Finally, collect all these steps and write your own PCA function and
compare this with the functionality included in Scikit-Learn.
Have the input be the data and have the output be the principal components and their associated eigenvalues, sorted in descending order. Can you think of a way to make it more efficient than the algorithm outlined above?
+
+
+
+
#Now we do an SVD
+U, s, V = np.linalg.svd(X_centered)
+c1 = V.T[:, 0]
+c2 = V.T[:, 1]
+W2 = V.T[:, :2]
+X2D = X_centered.dot(W2)
+print(X2D)
+#thereafter we do a PCA with Scikit-learn
+from sklearn.decomposition import PCA
+pca = PCA(n_components = 2)
+X2Dsl = pca.fit_transform(X)
+print("Check that we get the same")
+print(X2D-X2Dsl)
+
+print(pca.components_.T[:, 0])
+
Finally, try out your own PCA function with other data sets.
diff --git a/doc/pub/DimRed/html/DimRed-bs.html b/doc/pub/DimRed/html/DimRed-bs.html
index fcef4f476..db2c29bdc 100644
--- a/doc/pub/DimRed/html/DimRed-bs.html
+++ b/doc/pub/DimRed/html/DimRed-bs.html
@@ -224,7 +224,7 @@ MathJax.Hub.Config({
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
-
Dec 29, 2019
Dec 30, 2019
diff --git a/doc/pub/DimRed/html/DimRed-reveal.html b/doc/pub/DimRed/html/DimRed-reveal.html
index d27980dab..7024e385a 100644
--- a/doc/pub/DimRed/html/DimRed-reveal.html
+++ b/doc/pub/DimRed/html/DimRed-reveal.html
@@ -148,7 +148,7 @@ MathJax.Hub.Config({
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
-
Dec 29, 2019
Dec 30, 2019
@@ -1032,13 +1032,18 @@ The following Python code aids in setting up the data
-
n = 1000
+import numpy as np
+import pandas as pd
+from IPython.display import display
+n = 100
mean = (-1, 2)
cov = [[4, 2], [2, 2]]
X = np.random.multivariate_normal(mean, cov, n)
+# Print the X-matrix
+print(X)
-Make thereafter a small Python code which plots the data. Note that the function multivariate returns also the covariance discussed above and that it is defined by dividing by \( n-1 \) instead of \( n \).
+Make thereafter a small Python code which writes out the data. Note that the function multivariate returns also the covariance discussed above and that it is defined by dividing by \( n-1 \) instead of \( n \).
Now we are going to implement the PCA algorithm. We will break it down into various substeps.
@@ -1064,6 +1069,20 @@ When you are done with these steps, print out \( \mu_n \) to verify it is
close to \( \mu \) and plot your mean centered data to verify it is
centered at the origin! Compare your code with the functionality from Scikit-Learn discussed above.
+
+
+
+
df = pd.DataFrame(X)
+# Pandas does the centering for us
+df = df -df.mean()
+display(df)
+
+# we center it ourselves
+X_centered = X - X.mean(axis=0)
+# test that we get the same as Pandas
+print(X_centered-df)
+
+
Compute the sample covariance
@@ -1109,6 +1128,25 @@ Finally, collect all these steps and write your own PCA function and
compare this with the functionality included in Scikit-Learn.
Have the input be the data and have the output be the principal components and their associated eigenvalues, sorted in descending order. Can you think of a way to make it more efficient than the algorithm outlined above?
+
+
+
+
#Now we do an SVD
+U, s, V = np.linalg.svd(X_centered)
+c1 = V.T[:, 0]
+c2 = V.T[:, 1]
+W2 = V.T[:, :2]
+X2D = X_centered.dot(W2)
+print(X2D)
+#thereafter we do a PCA with Scikit-learn
+from sklearn.decomposition import PCA
+pca = PCA(n_components = 2)
+X2Dsl = pca.fit_transform(X)
+print("Check that we get the same")
+print(X2D-X2Dsl)
+
+print(pca.components_.T[:, 0])
+
Finally, try out your own PCA function with other data sets.
diff --git a/doc/pub/DimRed/html/DimRed-solarized.html b/doc/pub/DimRed/html/DimRed-solarized.html
index f34ee2991..0edd74866 100644
--- a/doc/pub/DimRed/html/DimRed-solarized.html
+++ b/doc/pub/DimRed/html/DimRed-solarized.html
@@ -179,7 +179,7 @@ MathJax.Hub.Config({
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
-
Dec 29, 2019
Dec 30, 2019
@@ -1012,13 +1012,18 @@ The following Python code aids in setting up the data
-
n = 1000
+import numpy as np
+import pandas as pd
+from IPython.display import display
+n = 100
mean = (-1, 2)
cov = [[4, 2], [2, 2]]
X = np.random.multivariate_normal(mean, cov, n)
+# Print the X-matrix
+print(X)
-Make thereafter a small Python code which plots the data. Note that the function multivariate returns also the covariance discussed above and that it is defined by dividing by \( n-1 \) instead of \( n \).
+Make thereafter a small Python code which writes out the data. Note that the function multivariate returns also the covariance discussed above and that it is defined by dividing by \( n-1 \) instead of \( n \).
Now we are going to implement the PCA algorithm. We will break it down into various substeps.
@@ -1040,6 +1045,20 @@ When you are done with these steps, print out \( \mu_n \) to verify it is
close to \( \mu \) and plot your mean centered data to verify it is
centered at the origin! Compare your code with the functionality from Scikit-Learn discussed above.
+
+
+
+
df = pd.DataFrame(X)
+# Pandas does the centering for us
+df = df -df.mean()
+display(df)
+
+# we center it ourselves
+X_centered = X - X.mean(axis=0)
+# test that we get the same as Pandas
+print(X_centered-df)
+
+
Compute the sample covariance
@@ -1082,6 +1101,25 @@ Finally, collect all these steps and write your own PCA function and
compare this with the functionality included in Scikit-Learn.
Have the input be the data and have the output be the principal components and their associated eigenvalues, sorted in descending order. Can you think of a way to make it more efficient than the algorithm outlined above?
+
+
+
+
#Now we do an SVD
+U, s, V = np.linalg.svd(X_centered)
+c1 = V.T[:, 0]
+c2 = V.T[:, 1]
+W2 = V.T[:, :2]
+X2D = X_centered.dot(W2)
+print(X2D)
+#thereafter we do a PCA with Scikit-learn
+from sklearn.decomposition import PCA
+pca = PCA(n_components = 2)
+X2Dsl = pca.fit_transform(X)
+print("Check that we get the same")
+print(X2D-X2Dsl)
+
+print(pca.components_.T[:, 0])
+
Finally, try out your own PCA function with other data sets.
diff --git a/doc/pub/DimRed/html/DimRed.html b/doc/pub/DimRed/html/DimRed.html
index e5348ddef..c0500aa5f 100644
--- a/doc/pub/DimRed/html/DimRed.html
+++ b/doc/pub/DimRed/html/DimRed.html
@@ -184,7 +184,7 @@ MathJax.Hub.Config({
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
-
Dec 29, 2019
Dec 30, 2019
@@ -1017,13 +1017,18 @@ The following Python code aids in setting up the data
-
n = 1000
+import numpy as np
+import pandas as pd
+from IPython.display import display
+n = 100
mean = (-1, 2)
cov = [[4, 2], [2, 2]]
X = np.random.multivariate_normal(mean, cov, n)
+# Print the X-matrix
+print(X)
-Make thereafter a small Python code which plots the data. Note that the function multivariate returns also the covariance discussed above and that it is defined by dividing by \( n-1 \) instead of \( n \).
+Make thereafter a small Python code which writes out the data. Note that the function multivariate returns also the covariance discussed above and that it is defined by dividing by \( n-1 \) instead of \( n \).
Now we are going to implement the PCA algorithm. We will break it down into various substeps.
@@ -1045,6 +1050,20 @@ When you are done with these steps, print out \( \mu_n \) to verify it is
close to \( \mu \) and plot your mean centered data to verify it is
centered at the origin! Compare your code with the functionality from Scikit-Learn discussed above.
+
+
+
+
df = pd.DataFrame(X)
+# Pandas does the centering for us
+df = df -df.mean()
+display(df)
+
+# we center it ourselves
+X_centered = X - X.mean(axis=0)
+# test that we get the same as Pandas
+print(X_centered-df)
+
+
Compute the sample covariance
@@ -1087,6 +1106,25 @@ Finally, collect all these steps and write your own PCA function and
compare this with the functionality included in Scikit-Learn.
Have the input be the data and have the output be the principal components and their associated eigenvalues, sorted in descending order. Can you think of a way to make it more efficient than the algorithm outlined above?
+
+
+
+
#Now we do an SVD
+U, s, V = np.linalg.svd(X_centered)
+c1 = V.T[:, 0]
+c2 = V.T[:, 1]
+W2 = V.T[:, :2]
+X2D = X_centered.dot(W2)
+print(X2D)
+#thereafter we do a PCA with Scikit-learn
+from sklearn.decomposition import PCA
+pca = PCA(n_components = 2)
+X2Dsl = pca.fit_transform(X)
+print("Check that we get the same")
+print(X2D-X2Dsl)
+
+print(pca.components_.T[:, 0])
+
Finally, try out your own PCA function with other data sets.
diff --git a/doc/pub/DimRed/ipynb/DimRed.ipynb b/doc/pub/DimRed/ipynb/DimRed.ipynb
index da58c850c..97b75d4b2 100644
--- a/doc/pub/DimRed/ipynb/DimRed.ipynb
+++ b/doc/pub/DimRed/ipynb/DimRed.ipynb
@@ -10,7 +10,7 @@
" \n",
"**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
"\n",
- "Date: **Dec 29, 2019**\n",
+ "Date: **Dec 30, 2019**\n",
"\n",
"Copyright 1999-2019, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
"\n",
@@ -1104,17 +1104,22 @@
},
"outputs": [],
"source": [
- "n = 1000\n",
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "from IPython.display import display\n",
+ "n = 100\n",
"mean = (-1, 2)\n",
"cov = [[4, 2], [2, 2]]\n",
- "X = np.random.multivariate_normal(mean, cov, n)"
+ "X = np.random.multivariate_normal(mean, cov, n)\n",
+ "# Print the X-matrix\n",
+ "print(X)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "Make thereafter a small Python code which plots the data. Note that the function **multivariate** returns also the covariance discussed above and that it is defined by dividing by $n-1$ instead of $n$.\n",
+ "Make thereafter a small Python code which writes out the data. Note that the function **multivariate** returns also the covariance discussed above and that it is defined by dividing by $n-1$ instead of $n$.\n",
"\n",
"Now we are going to implement the PCA algorithm. We will break it down into various substeps.\n",
"\n",
@@ -1154,9 +1159,32 @@
"source": [
"When you are done with these steps, print out $\\mu_n$ to verify it is\n",
"close to $\\mu$ and plot your mean centered data to verify it is\n",
- "centered at the origin! Compare your code with the functionality from **Scikit-Learn** discussed above.\n",
- "\n",
+ "centered at the origin! Compare your code with the functionality from **Scikit-Learn** discussed above."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "df = pd.DataFrame(X)\n",
+ "# Pandas does the centering for us\n",
+ "df = df -df.mean()\n",
+ "display(df)\n",
"\n",
+ "# we center it ourselves\n",
+ "X_centered = X - X.mean(axis=0)\n",
+ "# test that we get the same as Pandas\n",
+ "print(X_centered-df)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
"### Compute the sample covariance\n",
"\n",
"Now we are going to use the mean centered data to compute the sample covariance of the data. Recall it is given by:"
@@ -1213,11 +1241,43 @@
"\n",
"Finally, collect all these steps and write your own PCA function and\n",
"compare this with the functionality included in **Scikit-Learn**.\n",
- "Have the input be the data and have the output be the principal components and their associated eigenvalues, sorted in descending order. Can you think of a way to make it more efficient than the algorithm outlined above?\n",
+ "Have the input be the data and have the output be the principal components and their associated eigenvalues, sorted in descending order. Can you think of a way to make it more efficient than the algorithm outlined above?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "#Now we do an SVD\n",
+ "U, s, V = np.linalg.svd(X_centered)\n",
+ "c1 = V.T[:, 0]\n",
+ "c2 = V.T[:, 1]\n",
+ "W2 = V.T[:, :2]\n",
+ "X2D = X_centered.dot(W2)\n",
+ "print(X2D)\n",
+ "#thereafter we do a PCA with Scikit-learn\n",
+ "from sklearn.decomposition import PCA\n",
+ "pca = PCA(n_components = 2)\n",
+ "X2Dsl = pca.fit_transform(X)\n",
+ "print(\"Check that we get the same\")\n",
+ "print(X2D-X2Dsl)\n",
"\n",
+ "print(pca.components_.T[:, 0])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
"Finally, try out your own PCA function with other data sets.\n",
"\n",
"\n",
+ "\n",
+ "\n",
"## Classical PCA Theorem\n",
"\n",
"We assume now that we have a design matrix $\\boldsymbol{X}$ which has been\n",
@@ -1502,7 +1562,7 @@
},
{
"cell_type": "code",
- "execution_count": 12,
+ "execution_count": 14,
"metadata": {
"collapsed": false
},
@@ -1549,7 +1609,7 @@
},
{
"cell_type": "code",
- "execution_count": 13,
+ "execution_count": 15,
"metadata": {
"collapsed": false
},
@@ -1573,7 +1633,7 @@
},
{
"cell_type": "code",
- "execution_count": 14,
+ "execution_count": 16,
"metadata": {
"collapsed": false
},
@@ -1597,7 +1657,7 @@
},
{
"cell_type": "code",
- "execution_count": 15,
+ "execution_count": 17,
"metadata": {
"collapsed": false
},
@@ -1621,7 +1681,7 @@
},
{
"cell_type": "code",
- "execution_count": 16,
+ "execution_count": 18,
"metadata": {
"collapsed": false
},
@@ -1675,7 +1735,7 @@
},
{
"cell_type": "code",
- "execution_count": 17,
+ "execution_count": 19,
"metadata": {
"collapsed": false
},
@@ -1698,7 +1758,7 @@
},
{
"cell_type": "code",
- "execution_count": 18,
+ "execution_count": 20,
"metadata": {
"collapsed": false
},
@@ -1745,7 +1805,7 @@
},
{
"cell_type": "code",
- "execution_count": 19,
+ "execution_count": 21,
"metadata": {
"collapsed": false
},
diff --git a/doc/pub/DimRed/ipynb/ipynb-DimRed-src.tar.gz b/doc/pub/DimRed/ipynb/ipynb-DimRed-src.tar.gz
index 81a89e92b..965253985 100644
Binary files a/doc/pub/DimRed/ipynb/ipynb-DimRed-src.tar.gz and b/doc/pub/DimRed/ipynb/ipynb-DimRed-src.tar.gz differ
diff --git a/doc/pub/DimRed/pdf/DimRed-minted.pdf b/doc/pub/DimRed/pdf/DimRed-minted.pdf
index 5ea117840..0cea4334d 100644
Binary files a/doc/pub/DimRed/pdf/DimRed-minted.pdf and b/doc/pub/DimRed/pdf/DimRed-minted.pdf differ
diff --git a/doc/src/DimRed/DimRed.do.txt b/doc/src/DimRed/DimRed.do.txt
index d347bf325..54b80f7b5 100644
--- a/doc/src/DimRed/DimRed.do.txt
+++ b/doc/src/DimRed/DimRed.do.txt
@@ -779,13 +779,19 @@ this distribution, and store them in the $1000 \times 2$ matrix $\bm{X}$.
The following Python code aids in setting up the data
!bc pycod
-n = 1000
+import numpy as np
+import pandas as pd
+from IPython.display import display
+n = 100
mean = (-1, 2)
cov = [[4, 2], [2, 2]]
X = np.random.multivariate_normal(mean, cov, n)
+# Print the X-matrix
+print(X)
!ec
-Make thereafter a small Python code which plots the data. Note that the function _multivariate_ returns also the covariance discussed above and that it is defined by dividing by $n-1$ instead of $n$.
+
+Make thereafter a small Python code which writes out the data. Note that the function _multivariate_ returns also the covariance discussed above and that it is defined by dividing by $n-1$ instead of $n$.
Now we are going to implement the PCA algorithm. We will break it down into various substeps.
@@ -807,6 +813,18 @@ When you are done with these steps, print out $\mu_n$ to verify it is
close to $\mu$ and plot your mean centered data to verify it is
centered at the origin! Compare your code with the functionality from _Scikit-Learn_ discussed above.
+!bc pycod
+df = pd.DataFrame(X)
+# Pandas does the centering for us
+df = df -df.mean()
+display(df)
+
+# we center it ourselves
+X_centered = X - X.mean(axis=0)
+# test that we get the same as Pandas
+print(X_centered-df)
+!ec
+
=== Compute the sample covariance ===
@@ -843,9 +861,33 @@ Finally, collect all these steps and write your own PCA function and
compare this with the functionality included in _Scikit-Learn_.
Have the input be the data and have the output be the principal components and their associated eigenvalues, sorted in descending order. Can you think of a way to make it more efficient than the algorithm outlined above?
+!bc pycod
+#Now we do an SVD
+U, s, V = np.linalg.svd(X_centered)
+c1 = V.T[:, 0]
+c2 = V.T[:, 1]
+W2 = V.T[:, :2]
+X2D = X_centered.dot(W2)
+print(X2D)
+#thereafter we do a PCA with Scikit-learn
+from sklearn.decomposition import PCA
+pca = PCA(n_components = 2)
+X2Dsl = pca.fit_transform(X)
+print("Check that we get the same")
+print(X2D-X2Dsl)
+
+print(pca.components_.T[:, 0])
+
+
+!ec
+
+
+
Finally, try out your own PCA function with other data sets.
+
+
!split
===== Classical PCA Theorem =====