Re: Does SSVD supports eigendecomposition of non-symmetric & non-positive-semidefinitive matrix better than Lanczos?
Thanks a lot Sebastian, Ted and Dmitriy, I'll try Giraph for a performance benchmark. You are right, power iteration is just the most simple form of Lanczos, it shouldn't be in the scope. On Tue 18 Feb 2014 03:59:57 AM EST, Sebastian Schelter wrote: You can also use giraph for a superfast PageRank implementation. Giraph even runs on standard hadoop clusters. Pagerank is usually computed by power iteration, which is much simpler than lanczos or ssvd and only gives the eigenvector associated with the largest eigenvalue. Am 18.02.2014 09:33 schrieb "Peng Cheng" : Really? I guess PageRank in mahout was removed due to inherited network bottleneck of mapreduce. But I didn't know MLlib has the implementation. Is mllib implementation based on Lanczos or SSVD? Just curious... On 17/02/2014 11:11 PM, Dmitriy Lyubimov wrote: I bet page rank in mllib in spark finds stationary distribution much faster. On Feb 17, 2014 1:33 PM, "peng" wrote: Agreed, and this is the case where Lanczos algorithm is obsolete. My point is: if SSVD is unable to find the eigenvector of asymmetric matrix (this is a common formulation of PageRank, and some random walks, and many other things), then we still have to rely on large-scale Lanczos algorithm. On Mon 17 Feb 2014 04:25:16 PM EST, Ted Dunning wrote: For the symmetric case, SVD is eigen decomposition. On Mon, Feb 17, 2014 at 1:12 PM, peng wrote: If SSVD is not designed for such eigenvector problem. Then I would vote for retaining the Lanczos algorithm. However, I would like to see the opposite case, I have tested both algorithms on symmetric case and SSVD is much faster and more accurate than its competitor. Yours Peng On Wed 12 Feb 2014 03:25:47 PM EST, peng wrote: In PageRank I'm afraid I have no other option than eigenvector \lambda, but not singular vector u & v:) The PageRank in Mahout was removed with other graph-based algorithm. On Tue 11 Feb 2014 06:34:17 PM EST, Ted Dunning wrote: SSVD is very probably better than Lanczos for any large decomposition. That said, it does SVD, not eigen decomposition which means that the question of symmetrical matrices or positive definiteness doesn't much matter. Do you really need eigen-decomposition? On Tue, Feb 11, 2014 at 2:55 PM, peng wrote: Just asking for possible replacement of our Lanczos-based PageRank implementation. - Peng
Re: Does SSVD supports eigendecomposition of non-symmetric & non-positive-semidefinitive matrix better than Lanczos?
You can also use giraph for a superfast PageRank implementation. Giraph even runs on standard hadoop clusters. Pagerank is usually computed by power iteration, which is much simpler than lanczos or ssvd and only gives the eigenvector associated with the largest eigenvalue. Am 18.02.2014 09:33 schrieb "Peng Cheng" : > Really? I guess PageRank in mahout was removed due to inherited network > bottleneck of mapreduce. But I didn't know MLlib has the implementation. Is > mllib implementation based on Lanczos or SSVD? Just curious... > > On 17/02/2014 11:11 PM, Dmitriy Lyubimov wrote: > >> I bet page rank in mllib in spark finds stationary distribution much >> faster. >> On Feb 17, 2014 1:33 PM, "peng" wrote: >> >> Agreed, and this is the case where Lanczos algorithm is obsolete. >>> My point is: if SSVD is unable to find the eigenvector of asymmetric >>> matrix (this is a common formulation of PageRank, and some random walks, >>> and many other things), then we still have to rely on large-scale Lanczos >>> algorithm. >>> >>> On Mon 17 Feb 2014 04:25:16 PM EST, Ted Dunning wrote: >>> >>> For the symmetric case, SVD is eigen decomposition. On Mon, Feb 17, 2014 at 1:12 PM, peng wrote: If SSVD is not designed for such eigenvector problem. Then I would vote > for retaining the Lanczos algorithm. > However, I would like to see the opposite case, I have tested both > algorithms on symmetric case and SSVD is much faster and more accurate > than > its competitor. > > Yours Peng > > On Wed 12 Feb 2014 03:25:47 PM EST, peng wrote: > > In PageRank I'm afraid I have no other option than eigenvector > >> \lambda, but not singular vector u & v:) The PageRank in Mahout was >> removed with other graph-based algorithm. >> >> On Tue 11 Feb 2014 06:34:17 PM EST, Ted Dunning wrote: >> >> SSVD is very probably better than Lanczos for any large >> decomposition. >> >>> That said, it does SVD, not eigen decomposition which means that >>> the >>> question of symmetrical matrices or positive definiteness doesn't >>> much >>> matter. >>> >>> Do you really need eigen-decomposition? >>> >>> >>> >>> On Tue, Feb 11, 2014 at 2:55 PM, peng wrote: >>> >>>Just asking for possible replacement of our Lanczos-based PageRank >>> >>> implementation. - Peng >
Re: Does SSVD supports eigendecomposition of non-symmetric & non-positive-semidefinitive matrix better than Lanczos?
Really? I guess PageRank in mahout was removed due to inherited network bottleneck of mapreduce. But I didn't know MLlib has the implementation. Is mllib implementation based on Lanczos or SSVD? Just curious... On 17/02/2014 11:11 PM, Dmitriy Lyubimov wrote: I bet page rank in mllib in spark finds stationary distribution much faster. On Feb 17, 2014 1:33 PM, "peng" wrote: Agreed, and this is the case where Lanczos algorithm is obsolete. My point is: if SSVD is unable to find the eigenvector of asymmetric matrix (this is a common formulation of PageRank, and some random walks, and many other things), then we still have to rely on large-scale Lanczos algorithm. On Mon 17 Feb 2014 04:25:16 PM EST, Ted Dunning wrote: For the symmetric case, SVD is eigen decomposition. On Mon, Feb 17, 2014 at 1:12 PM, peng wrote: If SSVD is not designed for such eigenvector problem. Then I would vote for retaining the Lanczos algorithm. However, I would like to see the opposite case, I have tested both algorithms on symmetric case and SSVD is much faster and more accurate than its competitor. Yours Peng On Wed 12 Feb 2014 03:25:47 PM EST, peng wrote: In PageRank I'm afraid I have no other option than eigenvector \lambda, but not singular vector u & v:) The PageRank in Mahout was removed with other graph-based algorithm. On Tue 11 Feb 2014 06:34:17 PM EST, Ted Dunning wrote: SSVD is very probably better than Lanczos for any large decomposition. That said, it does SVD, not eigen decomposition which means that the question of symmetrical matrices or positive definiteness doesn't much matter. Do you really need eigen-decomposition? On Tue, Feb 11, 2014 at 2:55 PM, peng wrote: Just asking for possible replacement of our Lanczos-based PageRank implementation. - Peng
Re: Does SSVD supports eigendecomposition of non-symmetric & non-positive-semidefinitive matrix better than Lanczos?
I bet page rank in mllib in spark finds stationary distribution much faster. On Feb 17, 2014 1:33 PM, "peng" wrote: > Agreed, and this is the case where Lanczos algorithm is obsolete. > My point is: if SSVD is unable to find the eigenvector of asymmetric > matrix (this is a common formulation of PageRank, and some random walks, > and many other things), then we still have to rely on large-scale Lanczos > algorithm. > > On Mon 17 Feb 2014 04:25:16 PM EST, Ted Dunning wrote: > >> For the symmetric case, SVD is eigen decomposition. >> >> >> >> >> On Mon, Feb 17, 2014 at 1:12 PM, peng wrote: >> >> If SSVD is not designed for such eigenvector problem. Then I would vote >>> for retaining the Lanczos algorithm. >>> However, I would like to see the opposite case, I have tested both >>> algorithms on symmetric case and SSVD is much faster and more accurate >>> than >>> its competitor. >>> >>> Yours Peng >>> >>> On Wed 12 Feb 2014 03:25:47 PM EST, peng wrote: >>> >>> In PageRank I'm afraid I have no other option than eigenvector \lambda, but not singular vector u & v:) The PageRank in Mahout was removed with other graph-based algorithm. On Tue 11 Feb 2014 06:34:17 PM EST, Ted Dunning wrote: SSVD is very probably better than Lanczos for any large decomposition. >That said, it does SVD, not eigen decomposition which means that the > question of symmetrical matrices or positive definiteness doesn't much > matter. > > Do you really need eigen-decomposition? > > > > On Tue, Feb 11, 2014 at 2:55 PM, peng wrote: > > Just asking for possible replacement of our Lanczos-based PageRank > >> implementation. - Peng >> >> >> > >>
Re: Does SSVD supports eigendecomposition of non-symmetric & non-positive-semidefinitive matrix better than Lanczos?
Agreed, and this is the case where Lanczos algorithm is obsolete. My point is: if SSVD is unable to find the eigenvector of asymmetric matrix (this is a common formulation of PageRank, and some random walks, and many other things), then we still have to rely on large-scale Lanczos algorithm. On Mon 17 Feb 2014 04:25:16 PM EST, Ted Dunning wrote: For the symmetric case, SVD is eigen decomposition. On Mon, Feb 17, 2014 at 1:12 PM, peng wrote: If SSVD is not designed for such eigenvector problem. Then I would vote for retaining the Lanczos algorithm. However, I would like to see the opposite case, I have tested both algorithms on symmetric case and SSVD is much faster and more accurate than its competitor. Yours Peng On Wed 12 Feb 2014 03:25:47 PM EST, peng wrote: In PageRank I'm afraid I have no other option than eigenvector \lambda, but not singular vector u & v:) The PageRank in Mahout was removed with other graph-based algorithm. On Tue 11 Feb 2014 06:34:17 PM EST, Ted Dunning wrote: SSVD is very probably better than Lanczos for any large decomposition. That said, it does SVD, not eigen decomposition which means that the question of symmetrical matrices or positive definiteness doesn't much matter. Do you really need eigen-decomposition? On Tue, Feb 11, 2014 at 2:55 PM, peng wrote: Just asking for possible replacement of our Lanczos-based PageRank implementation. - Peng
Re: Does SSVD supports eigendecomposition of non-symmetric & non-positive-semidefinitive matrix better than Lanczos?
For the symmetric case, SVD is eigen decomposition. On Mon, Feb 17, 2014 at 1:12 PM, peng wrote: > If SSVD is not designed for such eigenvector problem. Then I would vote > for retaining the Lanczos algorithm. > However, I would like to see the opposite case, I have tested both > algorithms on symmetric case and SSVD is much faster and more accurate than > its competitor. > > Yours Peng > > On Wed 12 Feb 2014 03:25:47 PM EST, peng wrote: > >> In PageRank I'm afraid I have no other option than eigenvector >> \lambda, but not singular vector u & v:) The PageRank in Mahout was >> removed with other graph-based algorithm. >> >> On Tue 11 Feb 2014 06:34:17 PM EST, Ted Dunning wrote: >> >>> SSVD is very probably better than Lanczos for any large decomposition. >>> That said, it does SVD, not eigen decomposition which means that the >>> question of symmetrical matrices or positive definiteness doesn't much >>> matter. >>> >>> Do you really need eigen-decomposition? >>> >>> >>> >>> On Tue, Feb 11, 2014 at 2:55 PM, peng wrote: >>> >>> Just asking for possible replacement of our Lanczos-based PageRank implementation. - Peng >>>
Re: Does SSVD supports eigendecomposition of non-symmetric & non-positive-semidefinitive matrix better than Lanczos?
If SSVD is not designed for such eigenvector problem. Then I would vote for retaining the Lanczos algorithm. However, I would like to see the opposite case, I have tested both algorithms on symmetric case and SSVD is much faster and more accurate than its competitor. Yours Peng On Wed 12 Feb 2014 03:25:47 PM EST, peng wrote: In PageRank I'm afraid I have no other option than eigenvector \lambda, but not singular vector u & v:) The PageRank in Mahout was removed with other graph-based algorithm. On Tue 11 Feb 2014 06:34:17 PM EST, Ted Dunning wrote: SSVD is very probably better than Lanczos for any large decomposition. That said, it does SVD, not eigen decomposition which means that the question of symmetrical matrices or positive definiteness doesn't much matter. Do you really need eigen-decomposition? On Tue, Feb 11, 2014 at 2:55 PM, peng wrote: Just asking for possible replacement of our Lanczos-based PageRank implementation. - Peng
Re: Does SSVD supports eigendecomposition of non-symmetric & non-positive-semidefinitive matrix better than Lanczos?
In PageRank I'm afraid I have no other option than eigenvector \lambda, but not singular vector u & v:) The PageRank in Mahout was removed with other graph-based algorithm. On Tue 11 Feb 2014 06:34:17 PM EST, Ted Dunning wrote: SSVD is very probably better than Lanczos for any large decomposition. That said, it does SVD, not eigen decomposition which means that the question of symmetrical matrices or positive definiteness doesn't much matter. Do you really need eigen-decomposition? On Tue, Feb 11, 2014 at 2:55 PM, peng wrote: Just asking for possible replacement of our Lanczos-based PageRank implementation. - Peng
Re: Does SSVD supports eigendecomposition of non-symmetric & non-positive-semidefinitive matrix better than Lanczos?
SSVD is very probably better than Lanczos for any large decomposition. That said, it does SVD, not eigen decomposition which means that the question of symmetrical matrices or positive definiteness doesn't much matter. Do you really need eigen-decomposition? On Tue, Feb 11, 2014 at 2:55 PM, peng wrote: > Just asking for possible replacement of our Lanczos-based PageRank > implementation. - Peng >
