JP6849388B2 - 特異値解析法を用いた電子ノイズ除去法 - Google Patents
特異値解析法を用いた電子ノイズ除去法 Download PDFInfo
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実数行列Mを、正規直交ベクトルを表すU行列、同じく正規直交ベクトルを表すV行列、および前記解析データの特異値を対角成分に持つΣ行列、の3つの行列の積の形
M=UΣV
に分解し、
前記Σ行列の特異値のうち測定対象の成分の寄与が小さい特異値を排除した後のΣ行列、および前記U行列、V行列を用いて実数行列Mを再構成するというものである。
実数行列Mを、正規直交ベクトルを表すU行列、同じく正規直交ベクトルを表すV行列、および前記解析データの特異値を対角成分に持つΣ行列、の3つの行列の積の形
M=UΣV
に分解する手順と、
前記Σ行列の中の前記特異値以外の成分を排除する手順と、
該特異値以外の成分を排除した後のΣ行列、および前記U行列、V行列を用いて実数行列Mを再構成する手順と、
を実行させるためのプログラムである。
M=UΣV
Mベクトルを構成する2次元要素をUベクトルとVベクトルに分類し、その際に特異値を対角成分に持つΣベクトルとして表現する。
既存の電子ノイズ除去法においては、ピーク分割の手法を利用している(図1参照)。すなわち、ここでは、PDA(クロマトグラム―波長)行列を行列分解し、その後、Σ行列、U行列、V行列を用いて実数行列Mを再構成する。
再構成に用いる特異値成分の数、別言すれば、再構成に利用する(捨てない)Σ行列の数(以下、符号Wを付して表す)について説明する。
図6に、259nmで切り出した化合物Aのクロマトグラムを示す。図6(B)のSVD処理済のS/Nは18.2であった。一方、図6(A)のSVD未処理のクロマトグラムのS/Nは5.1であった。
Claims (2)
- 液成分の分析における測定対象の解析データ中の特異性を抽出する特異値解析法を実施する際、
実数行列Mを、正規直交ベクトルを表すU行列、同じく正規直交ベクトルを表すV行列、および前記解析データの特異値を対角成分に持つΣ行列、の3つの行列の積の形
M=UΣV
に分解し、
前記Σ行列の特異値のうち測定対象の成分の寄与が小さい特異値を排除した後のΣ行列、および前記U行列、V行列を用い、
複数の前記Σ行列のうちの一部のみを対象として前記特異値以外の成分を排除し、残りの前記Σ行列については前記特異値以外の成分の排除をせず、前記実数行列Mを再構成することを特徴とする特異値解析法を用いた電子ノイズ除去法。 - 前記実数行列Mの縦成分がクロマトグラムであり、横成分がUVスペクトルの波長であり、液成分の分析に用いられることを特徴とする請求項1に記載の特異値解析法を用いた電子ノイズ除去法。
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SG10202002459UA (en) | 2020-03-17 | 2021-10-28 | Shimadzu Corp | Peak analyzing method and waveform processing device |
CN111444963B (zh) * | 2020-03-27 | 2023-08-25 | 中南大学 | 一种基于ssa-svr模型的高炉铁水硅含量预测方法 |
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