From b1ae4472774da5215b6a55f950693334a6b40ff3 Mon Sep 17 00:00:00 2001 From: Ivikhostrup Date: Mon, 27 May 2024 09:55:22 +0200 Subject: [PATCH 1/4] max abs ready for review --- report_thesis/src/references.bib | 9 +++++++++ report_thesis/src/sections/background.tex | 13 ++++++++++++- 2 files changed, 21 insertions(+), 1 deletion(-) diff --git a/report_thesis/src/references.bib b/report_thesis/src/references.bib index fa431bac..a0e5909c 100644 --- a/report_thesis/src/references.bib +++ b/report_thesis/src/references.bib @@ -469,3 +469,12 @@ @article{druckerSVR author = {Drucker, Harris and Burges, Christopher J C and Kaufman, Linda and Smola, Alex J and Vapnik, Vladimir}, file = {Drucker et al. - Support Vector Regression Machines.pdf:C\:\\Users\\Patrick\\Zotero\\storage\\RZEXUIXV\\Drucker et al. - Support Vector Regression Machines.pdf:application/pdf}, } + +@book{Vasques2024, + title = {Machine Learning Theory and Applications: Hands-on Use Cases with Python on Classical and Quantum Machines}, + author = {Xavier Vasques}, + year = {2024}, + publisher = {Wiley}, + address = {Hoboken, New Jersey}, + isbn = {9781394220618} +} \ No newline at end of file diff --git a/report_thesis/src/sections/background.tex b/report_thesis/src/sections/background.tex index 2ede24a9..0d9c7db0 100644 --- a/report_thesis/src/sections/background.tex +++ b/report_thesis/src/sections/background.tex @@ -4,8 +4,19 @@ \subsection{Preprocessing} \subsubsection{Standard Scaler} \subsubsection{Max Absolute Scaler} +Max absolute scaling is a normalization technique similar to min-max scaling described in~\ref{subsec:minmax_scaler}. +The primary distinction between the two techniques lies in their scaling methodology: maximum absolute scaling normalizes the data to a range between 0 and 1 by utilizing the maximum absolute value of each feature, as opposed to employing the minimum and maximum values. +The formula for max absolute scaling is given by: +$$ +\zeta = \frac{x}{\max(|x|)} +$$ +where $x$ is the original feature value and $\zeta$ is the normalized feature value. +This scaling method is useful for data that has been centered at zero or data that is sparse, as max absolute scaling does not center the data. +This maintains the sparsity of the data by not introducing non-zero values in the zero entries of the data~\cite{Vasques2024}. + + -\subsubsection{MinMax Scaler} +\subsubsection{MinMax Scaler}\label{subsec:minmax_scaler} \subsubsection{Robust Scaler} From 121a7f1573691f68d6e167406b58f54d591cadab Mon Sep 17 00:00:00 2001 From: Ivikhostrup Date: Mon, 27 May 2024 10:06:21 +0200 Subject: [PATCH 2/4] Changed variable --- report_thesis/src/sections/background.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/report_thesis/src/sections/background.tex b/report_thesis/src/sections/background.tex index 0d9c7db0..7d8eb68f 100644 --- a/report_thesis/src/sections/background.tex +++ b/report_thesis/src/sections/background.tex @@ -8,9 +8,9 @@ \subsubsection{Max Absolute Scaler} The primary distinction between the two techniques lies in their scaling methodology: maximum absolute scaling normalizes the data to a range between 0 and 1 by utilizing the maximum absolute value of each feature, as opposed to employing the minimum and maximum values. The formula for max absolute scaling is given by: $$ -\zeta = \frac{x}{\max(|x|)} + X_{\text{scaled}} = \frac{x}{\max(|x|)}, $$ -where $x$ is the original feature value and $\zeta$ is the normalized feature value. +where $x$ is the original feature value and $X_{\text{scaled}}$ is the normalized feature value. This scaling method is useful for data that has been centered at zero or data that is sparse, as max absolute scaling does not center the data. This maintains the sparsity of the data by not introducing non-zero values in the zero entries of the data~\cite{Vasques2024}. From c44ecae13786fb13f709ba04e43a42b07a708ddd Mon Sep 17 00:00:00 2001 From: Ivikhostrup <56341364+Ivikhostrup@users.noreply.github.com> Date: Mon, 27 May 2024 11:45:43 +0200 Subject: [PATCH 3/4] Update report_thesis/src/sections/background.tex Co-authored-by: Pattrigue <57709490+Pattrigue@users.noreply.github.com> --- report_thesis/src/sections/background.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/report_thesis/src/sections/background.tex b/report_thesis/src/sections/background.tex index 7d8eb68f..5e2724d5 100644 --- a/report_thesis/src/sections/background.tex +++ b/report_thesis/src/sections/background.tex @@ -5,7 +5,7 @@ \subsubsection{Standard Scaler} \subsubsection{Max Absolute Scaler} Max absolute scaling is a normalization technique similar to min-max scaling described in~\ref{subsec:minmax_scaler}. -The primary distinction between the two techniques lies in their scaling methodology: maximum absolute scaling normalizes the data to a range between 0 and 1 by utilizing the maximum absolute value of each feature, as opposed to employing the minimum and maximum values. +The primary distinction between the two techniques lies in their scaling methodology: maximum absolute scaling normalizes the data to a range between -1 and 1 by utilizing the maximum absolute value of each feature, as opposed to employing the minimum and maximum values. The formula for max absolute scaling is given by: $$ X_{\text{scaled}} = \frac{x}{\max(|x|)}, From c4fcf18cee64037c1134d618ccf77c1871988d11 Mon Sep 17 00:00:00 2001 From: Ivikhostrup <56341364+Ivikhostrup@users.noreply.github.com> Date: Mon, 27 May 2024 11:52:55 +0200 Subject: [PATCH 4/4] Update report_thesis/src/sections/background.tex Co-authored-by: Pattrigue <57709490+Pattrigue@users.noreply.github.com> --- report_thesis/src/sections/background.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/report_thesis/src/sections/background.tex b/report_thesis/src/sections/background.tex index 5e2724d5..73c5869e 100644 --- a/report_thesis/src/sections/background.tex +++ b/report_thesis/src/sections/background.tex @@ -4,8 +4,8 @@ \subsection{Preprocessing} \subsubsection{Standard Scaler} \subsubsection{Max Absolute Scaler} -Max absolute scaling is a normalization technique similar to min-max scaling described in~\ref{subsec:minmax_scaler}. -The primary distinction between the two techniques lies in their scaling methodology: maximum absolute scaling normalizes the data to a range between -1 and 1 by utilizing the maximum absolute value of each feature, as opposed to employing the minimum and maximum values. +Max absolute scaling is a normalization technique that scales each feature individually so that the maximum absolute value of each feature is 1. +This results in the data being normalized to a range between -1 and 1. The formula for max absolute scaling is given by: $$ X_{\text{scaled}} = \frac{x}{\max(|x|)},