Problem Solving on Scatter Matrix
What is a scatter matrix used for?
A scatter matrix is used for visualizing pairwise relationships between multiple variables in a dataset, helping in identifying correlations, trends, and outliers.
How does a scatter matrix help in feature selection?
By showing correlations between variables, scatter matrices help in identifying redundant features, which can be removed to simplify models and improve performance.
Can scatter matrices detect non-linear relationships?
Yes, scatter matrices can reveal non-linear relationships between variables, aiding in the selection of appropriate machine learning models and feature transformations.
Why are scatter matrices useful in outlier detection?
They allow for the visual identification of outliers, which can then be addressed to improve the accuracy and robustness of predictive models.
Problem Solving on Scatter Matrix
A scatter matrix, also known as a pair plot, is a powerful visualization tool in data analysis. It provides a grid of scatter plots that display relationships between pairs of variables in a dataset, helping engineers and data scientists to identify patterns, correlations, and potential outliers.
Read More: Scatter Plot Matrix
We calculate Sw ( within the class scatter matrix ) and SB ( between the class scatter matrix ) for the available data points.
SW : To minimize variability within a class, inner class scatter.
SB : To increase between class variability, between class scatter.
scatter plot of the points
X1 = (y1, y2) ={ (2,2), (1,2), (1,2), (1,2), (2,2) } X2 = (y1,y2) ={ (9, 10), (6,8), (9,5), (8,7), (10,8) }
Within class scatter matrix:
[Tex]S_W = \sum_{i=1}^{c}S_i \\ S_i = \sum_{x\in D_i}^{c} (x-m_i)(x-m_i)^{T}[/Tex]
Si is the class specific covariance matrix. mi is the mean of individual class
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