I realised that torch_geometric library offers both global pooling layers and pooling layers, but I don't really understand what is the difference between these 2 when applied to Graph Neural Networks?
The difference is how the pooling is performed.
Global pooling gives you one supernode that contains the aggregated features from the whole graph.
Local pooling operation on the other hand create clusters and aggregates nodes in them.
Among local pooling you can find for instance Top-K pooling algorithm, SAGPool etc. They both have parameter called "ratio" that lets you specify how many nodes should be removed. Local pooling can give you a bit of hierarchical approach.
Related
I'm new to MPI and I'm trying to understand how MPI (and specifically OpenMPI) work in order to reason about the performance of my system.
I've tried to find resources online to help me understand things a little better, but haven't had much luck. I thought I'd come here.
Right now my question is simple: if I have 3 nodes (1 master, 2 clients) and I issue an MPI_Gather, does the root process handle incoming data sequentially or concurrently? In other words, if processes 1 is the first to make a connection with processes 0, will process 2 have to wait until processes 1 is done sending its data before it can start to send its data?
Thanks!
There are multiple components in Open MPI that implement collective operations and some of them provide multiple algorithms for the implementation of each operation.
What you are most likely interested in is the tuned component of the coll framework as that is what Open MPI uses by default. tuned implements all collectives using point-to-point operations and provides several algorithms for gather:
linear with synchronisation - used when messages are large to mid-size
binomial - used when the number of processes is large or the message size is small
basic linear - used in all other cases
The performance of each algorithm depends strongly on the particular combination of message size and number of ranks, therefore the library comes with a set of heuristics that tries to determine the best algorithm based on the data size and the size of the communicator (as indicated above). There are several mechanisms to override the heuristics and either force a certain algorithm or provide a list of custom algorithm selection rules.
The basic linear algorithm simply has the root loop over all other ranks receiving their messages in sequence. In that case, rank 2 won't be able to send its chunk before rank 1 since the root will first receive the message from rank 1 and only then move on to rank 2.
The linear with synchronisation algorithm splits the chunks into two pieces each. The first pieces are collected in sequence just like in the basic linear algorithm. The second pieces are collected asynchronously using non-blocking receives.
The binomial algorithm arranges the ranks as a binomial tree. The processes at the nodes of the tree receive the chunks from the lower levels and aggregate them into larger chunks that then get passed to the upper levels until they reach the root rank.
You can find the source code of the tuned module in the ompi/mca/coll/tuned folder of the Open MPI source tree. In the development branch, part of the tuned component got promoted to the base implementation of the collective framework and the code for the gather is to be found in ompi/mca/coll/base instead.
Hristo's answer is of course excellent, but I would like to offer a different point of view.
Contrary to your expectation, the question is not simple. It isn't even possible to specifically answer it without knowing more system specifics, as Hristo pointed out. That doesn't mean the question is invalid, but you should start to reason about performance on a different level.
First, consider the complexity of a the gather operation: The total network transfer to the root as well as the memory requirements are linearly growing with the number of processes in the communicator. This naturally limits scalability.
Second, you may assume that your MPI implementation does implement MPI_Gather in the most efficient way possible - better than you could do it by hand. This assumption may very well be wrong, but it is the best starting point to write your program.
Now when you have your program, you should measure and see where time is spent - or wasted. For that you should an MPI performance analysis tools. Now if you have identified that your Gather has a significant impact on performance, you can go ahead and try to optimize that: But to do so, first consider if you can structure your communication conceptually better, e.g. by somehow removing the computation all together or using a clever reduction instead. If you still need to stick to the gather: go ahead and tune your MPI implementation. Afterwards verify that your optimization did indeed improve performance on your specific system.
From what I've read, Riak treats all nodes in a cluster equal. However we'd like to have a heterogeneous cluster, where cpu/mem/hd is not always equal - in fact they can be very different. Each node would of course meet minimal requirements that's required for a node.
Questions:
1) What is the consequence of creating a cluster composed of machines with wildly varying specifications (cpu, diskspace, disk speed, amount and speed of memory, network speed) and
2) Can the cluster detect and compensate for such differences automatically? (assuming no here)
3) Are there ways to take care of this problem in other ways? Think of: prioritizing nodes in load balancer, based on the hardware. Something else?
I'll answer your questions, however, operating Riak in this manner is strongly discouraged as Riak assumes identical capabilities among nodes.
You could possibly have wildly varying performance characteristics
for operations against your node. In general, the "weakest node" in
the system could affect operations throughout the cluster. For
instance, during the PUT phase of an operation, a replica of the
data could be routed to the weakest node and the duration of that
operation could affect the entire PUT operation based on the PUT
operation's quorum value.
No, the cluster assumes identical hardware.
There really is no way to compensate for this.
I know there has some famous graph partition algo tools like METIS which is implemented by karypis Lab (http://glaros.dtc.umn.edu/gkhome/metis/metis/overview)
but I wanna know is there any method to partition graph stored in Neo4j?
or I have to dump the Neo4j's data and transform the node and edge format manually to fit the METIS input format?
Regarding new-ish and interesting algorithms, this is by no means exhaustive or state of the art, but these are the first places I would look:
Specific Algorithm: DiDiC (Distributed Diffusive Clustering) - I used it once in my thesis (Partitioning Graph Databases)
You iterate over all nodes, then for each node retrieve all neighbors, in order to spread some of "some unit" to all your neighbors
Easy to implement.
Can be made deterministic
Iterative - as it's based on iterations (like Super Steps in Pregel) you can stop it at any time. The longer you leave it the better the result, in theory (though in some cases, on certain graph shapes it can be unstable)
When we implemented this we ran it for 100 iterations on a machine with ~30GB RAM, for up to ~4 million nodes - it took no more than two days to complete.
Specific Algorithm: EvoCut "Finding sparse cuts locally using evolving sets" - local probabilistic algorithm from Microsoft - related to these papers
Difficult to implement
Local algorithm - BFS-like access patterns (random walks)
It's been a while since i read that paper, but i remember it was built on clean abstractions:
EvoNibble (pluggable - decides how much of neighborhood to add to the current cluster
EvoCut (calls EvoNibble multiple times to find the local cluster)
EvoPartition (calls EvoCut repeatedly to partition entire graph)
Not deterministic
General Algorithm Family: Hierarchical Graph Clustering
From a high level:
Coarsen the graph by collapsing nodes into aggregate nodes
coarsening strategy is selectable
Find clusters in the coarsened/smaller graph
clustering strategy is selectable
Incrementally decoarsen the graph, refining at the clustering at each step
refining strategy is selectable
Notes:
If the graph changes slowly (or results don't need to be right up to date) it may be possible to coarsen once (or infrequently) then work with the coarsened graph - to save computation
I don't know of a specific algorithm to recommend
General limitations - the things few clustering algorithms do:
Node types not acknowledged - i.e., all nodes treated equally
Relationship types not acknowledged - i.e., all relationships treated equally
Relationship direction not acknowledged - i.e., relationships treated as undirected
Having worked independently with METIS and Neo4j in the past, I am not aware of any tool for generating a METIS file from Neo4j. That being said, writing such a tool should be an easy task and would be a great community contribution.
Another approach for integrating METIS with Neo4j might be in connecting METIS to Neo4j from C++ via JNI. However this is going to be much more involved as it would have to take care of things like transactions, concurrency etc.
On the more general question of partitioning graphs, it is quite possible to implement some of the more known and simple algorithms with reasonable effort.
we have a single threaded application that simulates the interaction of a hundred of thousands of objects over time with the shared memory model.
obviously, it suffers from its inability to scale over multi CPU hardware.
after reading a little about agent based modeling and functional programming/actor model I was considering a rewrite with the message-passing paradigm.
the idea is very simple - each object will be an actor and their interactions will be messages so that the simulation could happen in parallel. given a configuration of objects at a certain time - its future consequences can be easily computed.
the question is how to model the time:
for example let's assume the the behavior of object X depends on A and B, as the actors and the messages calculations order is not guaranteed it could be that when X is to be computed A has already sent its message to X but B didn't.
how to make sure the computation happens correctly?
I hope the question is clear
thanks in advance.
Your approach of using message passing to parallelize a (discrete-event?) simulation is well-known and does not require a functional style per se (although, of course, this does not prevent you to implement it like that).
The basic problem you describe w.r.t. to the timing of events is also known as the local causality constraint (see, for example, this textbook). Basically, you need to use a synchronization protocol to ensure that each object (or agent) processes its messages in the right order. In the domain of parallel discrete-event simulation, such objects are called logical processes, and they communicate via events (i.e. time-stamped messages).
Correctly implementing a synchronization protocol for these events is challenging and the right choice of protocol is highly application-specific. For example, one important factor is the average amount of computation required per event: if there is little computation required, the communication costs dominate the overall execution time and it will be hard to scale the simulation.
I would therefore recommend to look for existing solutions/libraries on top of the actors framework you intend to use before starting from scratch.
I have a filtering algorithm that needs to be applied recursively and I am not sure if MapReduce is suitable for this job. W/o giving too much away, I can say that each object that is being filtered is characterized by a collection if ordered list or queue.
The data is not huge, just about 250MB when I export from SQL to
CSV.
The mapping step is simple: the head of the list contains an object that can classify the list as belonging to one of N mapping nodes. the filtration algorithm at each node works on the collection of lists assigned to the node and at the end of the filtration, either a list remains the same as before the filtration or the head of the list is removed.
The reduce function is simple too: all the map jobs' lists are brought together and may have to be written back to disk.
When all the N nodes have returned their output, the mapping step is repeated with this new set of data.
Note: N can be as much as 2000 nodes.
Simple, but it requires perhaps up to a 1000 recursions before the algorithm's termination conditions are met.
My question is would this job be suitable for Hadoop? If not, what are my options?
The main strength of Hadoop is its ability to transparently distribute work on a large number of machines. In order to fully benefit from Hadoop your application has to be characterized, at least by the following three things:
work with large amounts of data (data which is distributed in the cluster of machines) - which would be impossible to store on one machine
be data-parallelizable (i.e. chunks of the original data can be manipulated independently from other chunks)
the problem which the application is trying to solve lends itself nicely to the MapReduce (scatter - gather) model.
It seems that out of these 3, your application has only the last 2 characteristics (with the observation that you are trying to recursively use a scatter - gather procedure - which means a large number of jobs - equal to the recursion depth; see last paragraph why this might not be appropriate for hadoop).
Given the amount of data you're trying to process, I don't see any reason why you wouldn't do it on a single machine, completely in memory. If you think you can benefit from processing that small amount of data in parallel, I would recommend focusing on multicore processing than on distributed data intensive processing. Of course, using the processing power of a networked cluster is tempting but this comes at a cost: mainly the time inefficiency given by the network communication (network being the most contended resource in a hadoop cluster) and by the I/O. In scenarios which are well-fitted to the Hadoop framework these inefficiency can be ignored because of the efficiency gained by distributing the data and the associated work on that data.
As I can see, you need 1000 jobs. The setup and the cleanup of all those jobs would be an unnecessary overhead for your scenario. Also, the overhead of network transfer is not necessary, in my opinion.
Recursive algos are hard in the distributed systems since they can lead to a quick starvation. Any middleware that would work for that needs to support distributed continuations, i.e. the ability to make a "recursive" call without holding the resources (like threads) of the calling side.
GridGain is one product that natively supports distributed continuations.
THe litmus test on distributed continuations: try to develop a naive fibonacci implementation in distributed context using recursive calls. Here's the GridGain's example that implements this using continuations.
Hope it helps.
Q&D, but I suggest you read a comparison of MongoDB and Hadoop:
http://www.osintegrators.com/whitepapers/MongoHadoopWP/index.html
Without knowing more, it's hard to tell. You might want to try both. Post your results if you do!