linear-algebra   1034

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Gauss's Principle of Least Constraint
Gauss’s principle says that the behavior of a constrained system is as close as possible to the unconstrained behavior while satisfying the constraint.
physics  dynamics  mathematics  blog-posts  linear-algebra  optimization  constrained-optimization 
9 days ago by pash
Graphical Linear Algebra
Applications are open for the ACT Applied Category Theory Research School 2018! And because arithmetic science and geometric science are connected, and support one another, the full knowledge of numbers cannot be presented without encountering some geometry, or without seeing that operating in this way on numbers is close to geometry; the method is full…
maths  categorytheory  linear-algebra 
14 days ago by pmigdal
What exercises go best with 3 blue 1 brown's Linear Algebra videos? - LessWrong 2.0
3 blue 1 brown is a youtube channel that teaches math concepts. I've found it a
much better introduction than other resources I've looked at. The Essence of
series was particularly good.

But one issue is that, while the videos come with a few exercises sprinkled
within (typically one per concept), they don't come with enough to really check
whether I understand a thing.

Last year I tried...
learning  resource  linear-algebra 
16 days ago by sjmarshy
Low-Rank and Sparse Tools for Background Modeling and Subtraction in Videos
Low-Rank and Sparse Tools for Background Modeling and Subtraction in Videos - andrewssobral/lrslibrary
linear-algebra  pca 
19 days ago by yizhexu
Karl Rohe, Jun Tao, Xintian Han, Norbert Binkiewicz. "A Note on Quickly Sampling a Sparse Matrix with Low Rank Expectation ". Journal of Machine Learning Research 19(77):1−13, 2018.
Given matrices X,Y∈Rn×K and S∈RK×K with positive elements, this paper proposes an algorithm fastRG to sample a sparse matrix A with low rank expectation E(A)=XSYT and independent Poisson elements. This allows for quickly sampling from a broad class of stochastic blockmodel graphs (degree-corrected, mixed membership, overlapping) all of which are specific parameterizations of the generalized random product graph model defined in Section 2.2. The basic idea of fastRG is to first sample the number of edges m and then sample each edge. The key insight is that because of the the low rank expectation, it is easy to sample individual edges. The naive “element-wise” algorithm requires O(n2) operations to generate the n×n adjacency matrix A. In sparse graphs, where m=O(n), ignoring log terms, fastRG runs in time O(n). An implementation in R is available on github. A computational experiment in Section 2.4 simulates graphs up to n=10,000,000 nodes with m=100,000,000 edges. For example, on a graph with n=500,000 and m=5,000,000, fastRG runs in less than one second on a 3.5 GHz Intel i5.
26 days ago by quant18

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