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Linear regression How to measure the accuracy of linear regression - - PowerPoint PPT Presentation
Linear regression How to measure the accuracy of linear regression - - PowerPoint PPT Presentation
Linear regression How to measure the accuracy of linear regression models Linear Regression disease disease disease disease disease disease disease disease normal normal normal normal normal normal normal normal normal normal
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Linear Regression
yi = xT
i + ✏i =
X
j
jXi,j + ✏i
disease disease disease disease disease disease disease disease normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal
Fitting error: ✏i
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Linear Regression
disease disease disease disease disease disease disease disease normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal normal
y = X + ✏ β∗ = arg min
β
X
i
(yi − X
j
βjXi,j)2 Assumption: errors are Gaussian noises
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Linear Regression
β∗ = arg min
β
X
i
(yi − X
j
βjXi,j)2 = arg min
β (y − Xβ)T (y − Xβ)
= (XT X)−1XT y Question: How to derive the closed-form solution?
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Clustering
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Finding hidden structure in data
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Brain Liver Blood
Expression analysis
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Single-cell expression analysis
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Clustering: examples
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Network clustering
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Clustering
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Clustering
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Clustering algorithms
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K-means
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K-means for segmentation
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When will K-means fail?
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Hierarchical clustering
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Agglomerative clustering
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Complete Single
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