norms and sparsity Could anyone please elaborate on why $L^2$ norm moves toward the outliers compared to $L^1$ norm. I mean, what property/quantity in the mathematical expression of the norms makes it perform such way.
One more thing is, how $L^1$ norm introduces more sparsity in the solution?
Thank you.
Praveen 

The $L^2$ norm on any space focuses more on outliers because squaring a large number makes it much much larger compared to the smaller numbers than before; then these large numbers affect the average more, and taking the square root affects everything equally, so the outliers are still influential.
For instance, if you average $2$ and $100$, the second number is 50 times the first, and it pulls the average over to $51$. But $10000$ is $2500$ times bigger than $4$, so if we square them and average them, the $10000=100^2$ dominates even more, giving an average of $5002$, whose square root is 70.725, much closer to the outlier.
