7:00 – 4:30 ASRC MKT

- Alex Steffen – how economies must adapt to cope with climate effects, such as areas (Miami) and industries (Fossil Fuels) that are overvalued because of costs that are not being factored in.
- Going to start writing up (some) of my slides for SASO as a set of essays on Phlog to clarify my thinking
- Add cross-referencing to poster – done!
- More on Foundations of Temporal Text Networks – done!
- More on Graph Laplacians, since this is coming up a lot
- Spectral Partitioning, Part 1 The Graph Laplacian
- Spectral Partitioning Part 2 Springs Fling <- harmonic intuition
- Spectral Partitioning Part 3 Algebraic Connectivity
- Spectral Partitioning, Part 4 Putting It All Together
- Unit 6 7b Spectral Clustering Algorithm <- nice look at PCA
- Spring Systems (Wikipedia)
- Equations of motion for undamped linear systems with many degrees of freedom

- Need to spend some time looking into
- Ok, here we go…. Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec
- Github repo (belongs to lead author, Jiezhong Qiu,)
*Since the invention of word2vec, the skip-gram model has significantly advanced the research of network embedding, such as the recent emergence of the DeepWalk, LINE, PTE, and node2vec approaches. In this work, we show that all of the aforementioned models with negative sampling can be unified into the matrix factorization framework with closed forms. Our analysis and proofs reveal that: (1) DeepWalk empirically produces a low-rank transformation of a network’s normalized Laplacian matrix; (2) LINE, in theory, is a special case of DeepWalk when the size of vertices’ context is set to one; (3) As an extension of LINE, PTE can be viewed as the joint factorization of multiple networks» Laplacians; (4) node2vec is factorizing a matrix related to the stationary distribution and transition probability tensor of a 2nd-order random walk.***We further provide the theoretical connections between skip-gram based network embedding algorithms and the theory of graph Laplacian. Finally, we present the NetMF method as well as its approximation algorithm for computing network embedding. Our method offers significant improvements over DeepWalk and LINE for conventional network mining tasks. This work lays the theoretical foundation for skip-gram based network embedding methods, leading to a better understanding of latent network representation learning.**- So far, my basic insight is that matrix factorization is a form of (lossy) dimension reduction into an embedding space. Not sure yet how to use the factoring matrices as coordinates though. For example, a 2D matrix would be size L by M. For a 2D embedding, do you create an Lx2 and a 2xM factor matrices? Need to read more.

*…learning latent representations for networks, a.k.a., network embedding, has been extensively studied in order to automatically discover and***map a network’s structural properties into a latent space**.- ZOMG!