I don't know whether my ideas are much better than the cartesian product
solution. As a matter of fact at some point we have to replicate the
data to be able to compute the correlations in parallel. There are
basically 3 ideas I had:
1. Broadcast U and V and simply compute the correlation for different
shifts in a mapper. This only works if the time series data is small
enough to be kept in memory of a task manager.
2. Create for each shift and element a join key, join the elements and
reduce them to obtain the final result. This has a communication
complexity of (n^2+n)/2 which is asymptotically the same as the
cartesian product solution. But this solution will probably run for
arbitrarily large correlation intervals.
So let's say we have (u1, u2, u3) and (v1, v2, v3): Then we would first
create the join keys: (1, 1, u1), (2, 1, u1), (3, 1, u1), (1, 2, u2),
(2, 2, u2), (1, 3, u3), (1, 1, v1), (1, 2, v2), (2, 1, v2), (1, 3, v3),
(2, 2, v3), (3, 1, v3). Then join on the first and second field and
compute u*v with the first field as key. Reducing on this field let's
you then compute the correlation.
3. Group the elements of each subinterval with respect to their shift
value and join both grouped subintervals. Then compute the correlation.
This again only works if the grouped data can be kept on the heap of the
task manager.
On Tue, Apr 7, 2015 at 1:29 PM, Sebastian <s...@apache.org
<mailto:s...@apache.org>> wrote:
How large are the individual time series?
-s
On 07.04.2015 12:42, Kostas Tzoumas wrote:
Hi everyone,
I'm forwarding a private conversation to the list with Mats'
approval.
The problem is how to compute correlation between time series in
Flink.
We have two time series, U and V, and need to compute 1000
correlation
measures between the series, each measure shifts one series by
one more
item: corr(U[0:N], V[n:N+n]) for n=0 to n=1000.
Any ideas on how one can do that without a Cartesian product?
Best,
Kostas
---------- Forwarded message ----------
From: *Mats Zachrison* <mats.zachri...@ericsson.com
<mailto:mats.zachri...@ericsson.com>
<mailto:mats.zachrison@__ericsson.com
<mailto:mats.zachri...@ericsson.com>>>
Date: Tue, Mar 31, 2015 at 9:21 AM
Subject:
To: Kostas Tzoumas <kos...@data-artisans.com
<mailto:kos...@data-artisans.com>
<mailto:kostas@data-artisans.__com
<mailto:kos...@data-artisans.com>>>, Stefan Avesand
<stefan.aves...@ericsson.com
<mailto:stefan.aves...@ericsson.com>
<mailto:stefan.avesand@__ericsson.com
<mailto:stefan.aves...@ericsson.com>>>
Cc: "step...@data-artisans.com
<mailto:step...@data-artisans.com>
<mailto:stephan@data-artisans.__com
<mailto:step...@data-artisans.com>>"
<step...@data-artisans.com <mailto:step...@data-artisans.com>
<mailto:stephan@data-artisans.__com
<mailto:step...@data-artisans.com>>>
As Stefan said, what I’m trying to achieve is basically a nice
way to do
a correlation between two large time series. Since I’m looking
for an
optimal delay between the two series, I’d like to delay one of the
series x observations when doing the correlation, and step x
from 1 to
1000.____
__ __
Some pseudo code:____
__ __
For (x = 1 to 1000)____
Shift Series A ‘x-1’ steps____
Correlation[x] = Correlate(Series A and Series B)____
End For____
__ __
In R, using cor() and apply(), this could look like:____
__ __
shift <- as.array(c(1:1000))____
corrAB <- apply(shift, 1, function(x) cor(data[x:nrow(data),
]$ColumnA, data[1:(nrow(data) - (x - 1)), ]$ColumnB))____
__ __
__ __
Since this basically is 1000 independent correlation
calculations, it is
fairly easy to parallelize. Here is an R example using foreach() and
package doParallel:____
__ __
cl <- makeCluster(3)____
registerDoParallel(cl)____
corrAB <- foreach(step = c(1:1000)) %dopar% {____
corrAB <- cor(data[step:nrow(data), ]$ColumnA,
data[1:(nrow(data) - (step - 1)), ]$ColumnB)____
}____
stopCluster(cl)____
__ __
So I guess the question is – how to do this in a Flink
environment? Do
we have to define how to parallelize the algorithm, or can the
cluster
take care of that for us?____
__ __
And of course this is most interesting on a generic level –
given the
environment of a multi-core or –processor setup running Flink,
how hard
is it to take advantage of all the clock cycles? Do we have to
split the
algorithm, and data, and distribute the processing, or can the
system do
much of that for us?____
__
__ __
__