-
diff --git a/doc/pub/week35/html/week35-reveal.html b/doc/pub/week35/html/week35-reveal.html index 35ceda385..bd74fb666 100644 --- a/doc/pub/week35/html/week35-reveal.html +++ b/doc/pub/week35/html/week35-reveal.html @@ -148,7 +148,7 @@ MathJax.Hub.Config({
-
@@ -1673,8 +1673,18 @@ algorithm based on say LU, QR or Cholesky decomposition may lead to singularitie There is however a way to partially circumvent this problem and also gain some insights about the ordinary least squares approach, and later shrinkage methods like Ridge and Lasso regressions.
-This is given by the Singular Value Decomposition algorithm, perhaps -the most powerful linear algebra algorithm. Let us look at a +This is given by the Singular Value Decomposition (SVD) algorithm, +perhaps the most powerful linear algebra algorithm. The SVD provides +a numerically stable matrix decomposition that is used in a large +swath oc applications and the decomposition is always stable +numerically. + +
+In machine learning it plays a central role in dealing with for example design matrices that may be near singular or singular. +Furthermore, as we will see here, the singular values can be related to the covariance matrix (and thereby the correlation matrix) and in turn the variance of a given quantity. It plays also an important role in the principal component analysis where high-dimensional data can be reduced to the statistically relevant features. + +
+Let us look at a different example where we may have problems with the standard matrix inversion algorithm. Thereafter we dive into the math of the SVD. diff --git a/doc/pub/week35/html/week35-solarized.html b/doc/pub/week35/html/week35-solarized.html index f0904ed88..d76aa761e 100644 --- a/doc/pub/week35/html/week35-solarized.html +++ b/doc/pub/week35/html/week35-solarized.html @@ -300,7 +300,7 @@ MathJax.Hub.Config({
-
@@ -1752,8 +1752,18 @@ algorithm based on say LU, QR or Cholesky decomposition may lead to singularitie
There is however a way to partially circumvent this problem and also gain some insights about the ordinary least squares approach, and later shrinkage methods like Ridge and Lasso regressions.
-This is given by the Singular Value Decomposition algorithm, perhaps -the most powerful linear algebra algorithm. Let us look at a +This is given by the Singular Value Decomposition (SVD) algorithm, +perhaps the most powerful linear algebra algorithm. The SVD provides +a numerically stable matrix decomposition that is used in a large +swath oc applications and the decomposition is always stable +numerically. + +
+In machine learning it plays a central role in dealing with for example design matrices that may be near singular or singular. +Furthermore, as we will see here, the singular values can be related to the covariance matrix (and thereby the correlation matrix) and in turn the variance of a given quantity. It plays also an important role in the principal component analysis where high-dimensional data can be reduced to the statistically relevant features. + +
+Let us look at a different example where we may have problems with the standard matrix inversion algorithm. Thereafter we dive into the math of the SVD. diff --git a/doc/pub/week35/html/week35.html b/doc/pub/week35/html/week35.html index 99a50f6c0..db79e88fa 100644 --- a/doc/pub/week35/html/week35.html +++ b/doc/pub/week35/html/week35.html @@ -305,7 +305,7 @@ MathJax.Hub.Config({
-
@@ -1757,8 +1757,18 @@ algorithm based on say LU, QR or Cholesky decomposition may lead to singularitie
There is however a way to partially circumvent this problem and also gain some insights about the ordinary least squares approach, and later shrinkage methods like Ridge and Lasso regressions.
-This is given by the Singular Value Decomposition algorithm, perhaps -the most powerful linear algebra algorithm. Let us look at a +This is given by the Singular Value Decomposition (SVD) algorithm, +perhaps the most powerful linear algebra algorithm. The SVD provides +a numerically stable matrix decomposition that is used in a large +swath oc applications and the decomposition is always stable +numerically. + +
+In machine learning it plays a central role in dealing with for example design matrices that may be near singular or singular. +Furthermore, as we will see here, the singular values can be related to the covariance matrix (and thereby the correlation matrix) and in turn the variance of a given quantity. It plays also an important role in the principal component analysis where high-dimensional data can be reduced to the statistically relevant features. + +
+Let us look at a different example where we may have problems with the standard matrix inversion algorithm. Thereafter we dive into the math of the SVD. diff --git a/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz b/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz index 421ebf2b7..9f03671e5 100644 Binary files a/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz and b/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz differ diff --git a/doc/pub/week35/ipynb/week35.ipynb b/doc/pub/week35/ipynb/week35.ipynb index 20a7ef0ed..6d35e29e2 100644 --- a/doc/pub/week35/ipynb/week35.ipynb +++ b/doc/pub/week35/ipynb/week35.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: **Sep 3, 2021**\n", + "Date: **Sep 4, 2021**\n", "\n", "Copyright 1999-2021, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n", "\n", @@ -2046,6 +2046,8 @@ "source": [ "This serves also as a useful test of our codes. \n", "\n", + "\n", + "\n", "## The singular value decomposition\n", "\n", "\n", @@ -2065,8 +2067,18 @@ "\n", "There is however a way to partially circumvent this problem and also gain some insights about the ordinary least squares approach, and later shrinkage methods like Ridge and Lasso regressions. \n", "\n", - "This is given by the **Singular Value Decomposition** algorithm, perhaps\n", - "the most powerful linear algebra algorithm. Let us look at a\n", + "This is given by the **Singular Value Decomposition** (SVD) algorithm,\n", + "perhaps the most powerful linear algebra algorithm. The SVD provides\n", + "a numerically stable matrix decomposition that is used in a large\n", + "swath oc applications and the decomposition is always stable\n", + "numerically.\n", + "\n", + "In machine learning it plays a central role in dealing with for example design matrices that may be near singular or singular.\n", + "Furthermore, as we will see here, the singular values can be related to the covariance matrix (and thereby the correlation matrix) and in turn the variance of a given quantity. It plays also an important role in the principal component analysis where high-dimensional data can be reduced to the statistically relevant features. \n", + "\n", + "\n", + "\n", + "Let us look at a\n", "different example where we may have problems with the standard matrix\n", "inversion algorithm. Thereafter we dive into the math of the SVD.\n", "\n", diff --git a/doc/src/week35/week35.do.txt b/doc/src/week35/week35.do.txt index 771324732..1b2d1f0a8 100644 --- a/doc/src/week35/week35.do.txt +++ b/doc/src/week35/week35.do.txt @@ -1266,6 +1266,8 @@ and we have the obvious case This serves also as a useful test of our codes. + + !split ===== The singular value decomposition ===== @@ -1287,8 +1289,18 @@ algorithm based on say LU, QR or Cholesky decomposition may lead to singularitie There is however a way to partially circumvent this problem and also gain some insights about the ordinary least squares approach, and later shrinkage methods like Ridge and Lasso regressions. -This is given by the _Singular Value Decomposition_ algorithm, perhaps -the most powerful linear algebra algorithm. Let us look at a +This is given by the _Singular Value Decomposition_ (SVD) algorithm, +perhaps the most powerful linear algebra algorithm. The SVD provides +a numerically stable matrix decomposition that is used in a large +swath oc applications and the decomposition is always stable +numerically. + +In machine learning it plays a central role in dealing with for example design matrices that may be near singular or singular. +Furthermore, as we will see here, the singular values can be related to the covariance matrix (and thereby the correlation matrix) and in turn the variance of a given quantity. It plays also an important role in the principal component analysis where high-dimensional data can be reduced to the statistically relevant features. + + + +Let us look at a different example where we may have problems with the standard matrix inversion algorithm. Thereafter we dive into the math of the SVD.