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duplicates list edited from Why L1 norm for sparse models to Why L1 norm for sparse models, Why does the Lasso provide Variable Selection?
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Sycorax ♦
Sycorax ♦
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Post Closed as "Duplicate" by whuber♦ regression
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The Great
The Great
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I read a tutorial here. In which, I came across the below plots

enter image description here

I read an explanation quoted Fig 8(a) shows the area of L1 and L2 Norms together. For same amount of Bias term generated, the area occupied by L1 Norm is small. But L1 Norm doesn’t concede any space close to the axes. This is what causes the point of intersection between the L1 Norm and Gradient Descent Contour to converge near the axes leading to feature selection.

From the above graphs and explanation, I can understand the below

a) Area occupied by L1 norm is small when compared to L2 norm

But I didn't understand what the author means as But L1 Norm doesn’t concede any space close to the axes. and how this leads to feature selection?

can help me understand this, please?

I read a tutorial here. In which, I came across the below plots

enter image description here

I read an explanation quoted Fig 8(a) shows the area of L1 and L2 Norms together. For same amount of Bias term generated, the area occupied by L1 Norm is small. But L1 Norm doesn’t concede any space close to the axes. This is what causes the point of intersection between the L1 Norm and Gradient Descent Contour to converge near the axes leading to feature selection.

From the above graphs and explanation, I can understand the below

a) Area occupied by L1 norm is small when compared to L2 norm

But I didn't understand what the author means as But L1 Norm doesn’t concede any space close to the axes.

can help me understand this please?

I read a tutorial here. In which, I came across the below plots

enter image description here

I read an explanation quoted Fig 8(a) shows the area of L1 and L2 Norms together. For same amount of Bias term generated, the area occupied by L1 Norm is small. But L1 Norm doesn’t concede any space close to the axes. This is what causes the point of intersection between the L1 Norm and Gradient Descent Contour to converge near the axes leading to feature selection.

From the above graphs and explanation, I can understand the below

a) Area occupied by L1 norm is small when compared to L2 norm

But I didn't understand what the author means as But L1 Norm doesn’t concede any space close to the axes. and how this leads to feature selection?

can help me understand this, please?

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The Great
The Great
  • 3.3k
  • 1
  • 17
  • 43

Why feature selection using `L1` and not using `L2` norm?

I read a tutorial here. In which, I came across the below plots

enter image description here

I read an explanation quoted Fig 8(a) shows the area of L1 and L2 Norms together. For same amount of Bias term generated, the area occupied by L1 Norm is small. But L1 Norm doesn’t concede any space close to the axes. This is what causes the point of intersection between the L1 Norm and Gradient Descent Contour to converge near the axes leading to feature selection.

From the above graphs and explanation, I can understand the below

a) Area occupied by L1 norm is small when compared to L2 norm

But I didn't understand what the author means as But L1 Norm doesn’t concede any space close to the axes.

can help me understand this please?