I experience a strange situation when running Mahout K-means:
Using the a pre-selected set of initial centroids, I run K-means on a SequenceFile generated by lucene.vector. The run is for testing purposes, so the file is small (around 10MB~10000 vectors).
When K-means is executed with a single mapper (the default considering the Hadoop split size which in my cluster is 128MB), it reaches a given clustering result in 2 iterations (Case A).
However, I wanted to test if there would be any improvement/deterioration in the algorithm's execution speed by firing more mapping tasks (the Hadoop cluster has in total 6 nodes).
I therefore set the -Dmapred.max.split.size parameter to 5242880 bytes, in order to make mahout fire 2 mapping tasks (Case B).
I indeed succeeded in starting two mappers, but the strange thing was that the job finished after 5 iterations instead of 2, and that even at the first assignment of points to clusters, the mappers made different choices compared to the single-map execution . What I mean is that after close inspection of the clusterDump for the first iteration for both two cases, I found that in case B some points were not assigned to their closest cluster.
Could this behavior be justified by the existing K-means Mahout implementation?
From a quick look at the sources, I see two problems with the Mahout k-means implementation.
First of all, the way the S0, S1, S2 statistics are kept is probably not numerically stable for large data sets. Oh, and since k-means actually does not even use S2, it is also unnecessary slow. I bet a good implementation can beat this version of k-means by a factor of 2-5 at least.
For small data sets split onto multiple machines, there seems to be an error in the way they compute their means. Ouch. This will amplify if the reducer is applied to more than one input, in particular when the partitions are small. To be more verbose, the cluster mean apparently is initialized with the previous mean instead of the 0 vector. Now if you if you reduce 't' copies of it, the resulting vector will be off by 't' times the previous mean.
Initialization of AbstractCluster:
setS1(center.like());
Update of the mean:
getS1().assign(x, Functions.PLUS);
Merge of multiple copies of a cluster:
setS1(getS1().plus(cl.getS1()));
Finalization to new center:
setCenter(getS1().divide(getS0()));
So with this approach, the center will be offset from the proper value by the previous center times t / n where t is the number of splits, and n the number of objects.
To fix the numerical instability (which arises whenever the data set is not centered on the 0 vector), I recommend replacing the S1 statistic by the true mean, not S0*mean. Both S1 and S2 can be incrementally updated at little cost using the incremental mean formula which AFAICT was used in the original "k-means" publication by MacQueen (which actually is an online kmeans, while this is Lloyd style batch iterations). Well, for an incremental k-means you obviously need the updatable mean vector anyway... I believe the formula was also discussed by Knuth in his essential books. I'm surprised that Mahout does not seem to use it. It's fairly cheap (just a few CPU instructions more, no additional data, so it all happens in the CPU cache line) and gives you extra precision when you are dealing with large data sets.
Related
Originally in my df, I had my BMI in numeric format(1-5), which I recoded (underweigh to obese), factored and choose a specific reference using relevel (Normal, originally 3). Then did a logistic regression: y~ BMI+other covariates. My questions are the following :
1- When I plug my logistic in tbl_regression, the levels have undesired orders (underweight, obese1, obese 2, overweight) . Is there a way to rearrange the levels the way I want to (underweight, overweight, obese 1, obese 2)?
2- I used tbl_regression on a small data set which went ok. My new model, however, is based on 3M observation and 13 variables (the database is 1Gb). This time my tbl_regression is taking about 1h to process and out put the table, which is not normal since I have a fast laptop. Is there a way to make this more efficient ? I tried keeping the model only while using tbl_regression and removed the database, but it is still hellishly long. I tried with the trial data and it was ok..
1 - I recommend using contrasts() to set the reference level. The relevel() function just moves a factor level to the first position. Examples here Is there a way to relevel a variable in gtsummary after generating the beautiful table?
2 - I suspect with such a large model, the confidence interval calculation is what is slowing you down. If you see a big difference in the computation times of summary() and broom::tidy() with the CI calculation compared to tbl_regression(), please create an illustrative example (that anyone can run locally) and it can be looked into further.
So, I understand that in general one should use coalesce() when:
the number of partitions decreases due to a filter or some other operation that may result in reducing the original dataset (RDD, DF). coalesce() is useful for running operations more efficiently after filtering down a large dataset.
I also understand that it is less expensive than repartition as it reduces shuffling by moving data only if necessary. My problem is how to define the parameter that coalesce takes (idealPartionionNo). I am working on a project which was passed to me from another engineer and he was using the below calculation to compute the value of that parameter.
// DEFINE OPTIMAL PARTITION NUMBER
implicit val NO_OF_EXECUTOR_INSTANCES = sc.getConf.getInt("spark.executor.instances", 5)
implicit val NO_OF_EXECUTOR_CORES = sc.getConf.getInt("spark.executor.cores", 2)
val idealPartionionNo = NO_OF_EXECUTOR_INSTANCES * NO_OF_EXECUTOR_CORES * REPARTITION_FACTOR
This is then used with a partitioner object:
val partitioner = new HashPartitioner(idealPartionionNo)
but also used with:
RDD.filter(x=>x._3<30).coalesce(idealPartionionNo)
Is this the right approach? What is the main idea behind the idealPartionionNo value computation? What is the REPARTITION_FACTOR? How do I generally work to define that?
Also, since YARN is responsible for identifying the available executors on the fly is there a way of getting that number (AVAILABLE_EXECUTOR_INSTANCES) on the fly and use that for computing idealPartionionNo (i.e. replace NO_OF_EXECUTOR_INSTANCES with AVAILABLE_EXECUTOR_INSTANCES)?
Ideally, some actual examples of the form:
Here 's a dataset (size);
Here's a number of transformations and possible reuses of an RDD/DF.
Here is where you should repartition/coalesce.
Assume you have n executors with m cores and a partition factor equal to k
then:
The ideal number of partitions would be ==> ???
Also, if you can refer me to a nice blog that explains these I would really appreciate it.
In practice optimal number of partitions depends more on the data you have, transformations you use and overall configuration than the available resources.
If the number of partitions is too low you'll experience long GC pauses, different types of memory issues, and lastly suboptimal resource utilization.
If the number of partitions is too high then maintenance cost can easily exceed processing cost. Moreover, if you use non-distributed reducing operations (like reduce in contrast to treeReduce), a large number of partitions results in a higher load on the driver.
You can find a number of rules which suggest oversubscribing partitions compared to the number of cores (factor 2 or 3 seems to be common) or keeping partitions at a certain size but this doesn't take into account your own code:
If you allocate a lot you can expect long GC pauses and it is probably better to go with smaller partitions.
If a certain piece of code is expensive then your shuffle cost can be amortized by a higher concurrency.
If you have a filter you can adjust the number of partitions based on a discriminative power of the predicate (you make different decisions if you expect to retain 5% of the data and 99% of the data).
In my opinion:
With one-off jobs keep higher number partitions to stay on the safe side (slower is better than failing).
With reusable jobs start with conservative configuration then execute - monitor - adjust configuration - repeat.
Don't try to use fixed number of partitions based on the number of executors or cores. First understand your data and code, then adjust configuration to reflect your understanding.
Usually, it is relatively easy to determine the amount of raw data per partition for which your cluster exhibits stable behavior (in my experience it is somewhere in the range of few hundred megabytes, depending on the format, data structure you use to load data, and configuration). This is the "magic number" you're looking for.
Some things you have to remember in general:
Number of partitions doesn't necessarily reflect
data distribution. Any operation that requires shuffle (*byKey, join, RDD.partitionBy, Dataset.repartition) can result in non-uniform data distribution. Always monitor your jobs for symptoms of a significant data skew.
Number of partitions in general is not constant. Any operation with multiple dependencies (union, coGroup, join) can affect the number of partitions.
Your question is a valid one, but Spark partitioning optimization depends entirely on the computation you're running. You need to have a good reason to repartition/coalesce; if you're just counting an RDD (even if it has a huge number of sparsely populated partitions), then any repartition/coalesce step is just going to slow you down.
Repartition vs coalesce
The difference between repartition(n) (which is the same as coalesce(n, shuffle = true) and coalesce(n, shuffle = false) has to do with execution model. The shuffle model takes each partition in the original RDD, randomly sends its data around to all executors, and results in an RDD with the new (smaller or greater) number of partitions. The no-shuffle model creates a new RDD which loads multiple partitions as one task.
Let's consider this computation:
sc.textFile("massive_file.txt")
.filter(sparseFilterFunction) // leaves only 0.1% of the lines
.coalesce(numPartitions, shuffle = shuffle)
If shuffle is true, then the text file / filter computations happen in a number of tasks given by the defaults in textFile, and the tiny filtered results are shuffled. If shuffle is false, then the number of total tasks is at most numPartitions.
If numPartitions is 1, then the difference is quite stark. The shuffle model will process and filter the data in parallel, then send the 0.1% of filtered results to one executor for downstream DAG operations. The no-shuffle model will process and filter the data all on one core from the beginning.
Steps to take
Consider your downstream operations. If you're just using this dataset once, then you probably don't need to repartition at all. If you are saving the filtered RDD for later use (to disk, for example), then consider the tradeoffs above. It takes experience to become familiar with these models and when one performs better, so try both out and see how they perform!
As others have answered, there is no formula which calculates what you ask for. That said, You can make an educated guess on the first part and then fine tune it over time.
The first step is to make sure you have enough partitions. If you have NO_OF_EXECUTOR_INSTANCES executors and NO_OF_EXECUTOR_CORES cores per executor then you can process NO_OF_EXECUTOR_INSTANCES*NO_OF_EXECUTOR_CORES partitions at the same time (each would go to a specific core of a specific instance).
That said this assumes everything is divided equally between the cores and everything takes exactly the same time to process. This is rarely the case. There is a good chance that some of them would be finished before others either because of locallity (e.g. the data needs to come from a different node) or simply because they are not balanced (e.g. if you have data partitioned by root domain then partitions including google would probably be quite big). This is where the REPARTITION_FACTOR comes into play. The idea is that we "overbook" each core and therefore if one finishes very quickly and one finishes slowly we have the option of dividing the tasks between them. A factor of 2-3 is generally a good idea.
Now lets take a look at the size of a single partition. Lets say your entire data is X MB in size and you have N partitions. Each partition would be on average X/N MBs. If N is large relative to X then you might have very small average partition size (e.g. a few KB). In this case it is usually a good idea to lower N because the overhead of managing each partition becomes too high. On the other hand if the size is very large (e.g. a few GB) then you need to hold a lot of data at the same time which would cause issues such as garbage collection, high memory usage etc.
The optimal size is a good question but generally people seem to prefer partitions of 100-1000MB but in truth tens of MB probably would also be good.
Another thing you should note is when you do the calculation how your partitions change. For example, lets say you start with 1000 partitions of 100MB each but then filter the data so each partition becomes 1K then you should probably coalesce. Similar issues can happen when you do a groupby or join. In such cases both the size of the partition and the number of partitions change and might reach an undesirable size.
I am working on a MATLAB implementation of an adaptive Matrix-Vector Multiplication for very large sparse matrices coming from a particular discretisation of a PDE (with known sparsity structure).
After a lot of pre-processing, I end up with a number of different blocks (greater than, say, 200), for which I want to calculate selected entries.
One of the pre-processing steps is to determine the (number of) entries per block I want to calculate, which gives me an almost perfect measure of the amount of time each block will take (for all intents and purposes the quadrature effort is the same for each entry).
Thanks to https://stackoverflow.com/a/9938666/2965879, I was able to make use of this by ordering the blocks in reverse order, thus goading MATLAB into starting with the biggest ones first.
However, the number of entries differs so wildly from block to block, that directly running parfor is limited severely by the blocks with the largest number of entries, even if they are fed into the loop in reverse.
My solution is to do the biggest blocks serially (but parallelised on the level of entries!), which is fine as long as the overhead per iterand doesn't matter too much, resp. the blocks don't get too small. The rest of the blocks I then do with parfor. Ideally, I'd let MATLAB decide how to handle this, but since a nested parfor-loop loses its parallelism, this doesn't work. Also, packaging both loops into one is (nigh) impossible.
My question now is about how to best determine this cut-off between the serial and the parallel regime, taking into account the information I have on the number of entries (the shape of the curve of ordered entries may differ for different problems), as well as the number of workers I have available.
So far, I had been working with the 12 workers available under a the standard PCT license, but since I've now started working on a cluster, determining this cut-off becomes more and more crucial (since for many cores the overhead of the serial loop becomes more and more costly in comparison to the parallel loop, but similarly, having blocks which hold up the rest are even more costly).
For 12 cores (resp. the configuration of the compute server I was working with), I had figured out a reasonable parameter of 100 entries per worker as a cut off, but this doesn't work well when the number of cores isn't small anymore in relation to the number of blocks (e.g 64 vs 200).
I have tried to deflate the number of cores with different powers (e.g. 1/2, 3/4), but this also doesn't work consistently. Next I tried to group the blocks into batches and determine the cut-off when entries are larger than the mean per batch, resp. the number of batches they are away from the end:
logical_sml = true(1,num_core); i = 0;
while all(logical_sml)
i = i+1;
m = mean(num_entr_asc(1:min(i*num_core,end))); % "asc" ~ ascending order
logical_sml = num_entr_asc(i*num_core+(1:num_core)) < i^(3/4)*m;
% if the small blocks were parallelised perfectly, i.e. all
% cores take the same time, the time would be proportional to
% i*m. To try to discount the different sizes (and imperfect
% parallelisation), we only scale with a power of i less than
% one to not end up with a few blocks which hold up the rest
end
num_block_big = num_block - (i+1)*num_core + sum(~logical_sml);
(Note: This code doesn't work for vectors num_entr_asc whose length is not a multiple of num_core, but I decided to omit the min(...,end) constructions for legibility.)
I have also omitted the < max(...,...) for combining both conditions (i.e. together with minimum entries per worker), which is necessary so that the cut-off isn't found too early. I thought a little about somehow using the variance as well, but so far all attempts have been unsatisfactory.
I would be very grateful if someone has a good idea for how to solve this.
I came up with a somewhat satisfactory solution, so in case anyone's interested I thought I'd share it. I would still appreciate comments on how to improve/fine-tune the approach.
Basically, I decided that the only sensible way is to build a (very) rudimentary model of the scheduler for the parallel loop:
function c=est_cost_para(cost_blocks,cost_it,num_cores)
% Estimate cost of parallel computation
% Inputs:
% cost_blocks: Estimate of cost per block in arbitrary units. For
% consistency with the other code this must be in the reverse order
% that the scheduler is fed, i.e. cost should be ascending!
% cost_it: Base cost of iteration (regardless of number of entries)
% in the same units as cost_blocks.
% num_cores: Number of cores
%
% Output:
% c: Estimated cost of parallel computation
num_blocks=numel(cost_blocks);
c=zeros(num_cores,1);
i=min(num_blocks,num_cores);
c(1:i)=cost_blocks(end-i+1:end)+cost_it;
while i<num_blocks
i=i+1;
[~,i_min]=min(c); % which core finished first; is fed with next block
c(i_min)=c(i_min)+cost_blocks(end-i+1)+cost_it;
end
c=max(c);
end
The parameter cost_it for an empty iteration is a crude blend of many different side effects, which could conceivably be separated: The cost of an empty iteration in a for/parfor-loop (could also be different per block), as well as the start-up time resp. transmission of data of the parfor-loop (and probably more). My main reason to throw everything together is that I don't want to have to estimate/determine the more granular costs.
I use the above routine to determine the cut-off in the following way:
% function i=cutoff_ser_para(cost_blocks,cost_it,num_cores)
% Determine cut-off between serial an parallel regime
% Inputs:
% cost_blocks: Estimate of cost per block in arbitrary units. For
% consistency with the other code this must be in the reverse order
% that the scheduler is fed, i.e. cost should be ascending!
% cost_it: Base cost of iteration (regardless of number of entries)
% in the same units as cost_blocks.
% num_cores: Number of cores
%
% Output:
% i: Number of blocks to be calculated serially
num_blocks=numel(cost_blocks);
cost=zeros(num_blocks+1,2);
for i=0:num_blocks
cost(i+1,1)=sum(cost_blocks(end-i+1:end))/num_cores + i*cost_it;
cost(i+1,2)=est_cost_para(cost_blocks(1:end-i),cost_it,num_cores);
end
[~,i]=min(sum(cost,2));
i=i-1;
end
In particular, I don't inflate/change the value of est_cost_para which assumes (aside from cost_it) the most optimistic scheduling possible. I leave it as is mainly because I don't know what would work best. To be conservative (i.e. avoid feeding too large blocks to the parallel loop), one could of course add some percentage as a buffer or even use a power > 1 to inflate the parallel cost.
Note also that est_cost_para is called with successively less blocks (although I use the variable name cost_blocks for both routines, one is a subset of the other).
Compared to the approach in my wordy question I see two main advantages:
The relatively intricate dependence between the data (both the number of blocks as well as their cost) and the number of cores is captured much better with the simulated scheduler than would be possible with a single formula.
By calculating the cost for all possible combinations of serial/parallel distribution and then taking the minimum, one cannot get "stuck" too early while reading in the data from one side (e.g. by a jump which is large relative to the data so far, but small in comparison to the total).
Of course, the asymptotic complexity is higher by calling est_cost_para with its while-loop all the time, but in my case (num_blocks<500) this is absolutely negligible.
Finally, if a decent value of cost_it does not readily present itself, one can try to calculate it by measuring the actual execution time of each block, as well as the purely parallel part of it, and then trying to fit the resulting data to the cost prediction and get an updated value of cost_it for the next call of the routine (by using the difference between total cost and parallel cost or by inserting a cost of zero into the fitted formula). This should hopefully "converge" to the most useful value of cost_it for the problem in question.
I have to check performance of various clustering algos using different performance operators in rapidminer. For that I want to know the following things:
what does cluster number index value shows which is output of cluster count performance operator?
what does small and large value of avg within cluster distance and avg. within centroid distance mean in terms of good and bad clustering?
I also want to check other indexes value like Dunn index,Jaccard index, Fowlkes–Mallows for various clustering algos. but rapidminer don't have any operator for this, what to do for that. I don't have experience with R.
I have copied part of the answer I gave on the Rapid-I forum
The cluster number index is the count of clusters - pointless you might say but when used with DBSCAN, it can be quite interesting http://rapidminernotes.blogspot.co.uk/2010/12/counting-clusters.html
The avg within cluster and centroid distances are hard to interpret - one thing to search for is "elbow criterion" in this context. As the number of clusters varies, note how the validity measure changes and look for an "elbow" that marks the point where the natural progression of the measure dominates the structure.
R has many validity measures and it's worth investing some time because you can always call the R process from RapidMiner which makes it easier to work out what is going on.
I am clustering a large set of points. Throughout the iterations, I want to avoid re-computing cluster properties if the assigned points are the same as the previous iteration. Each cluster keeps the IDs of its points. I don't want to compare them element wise, comparing the sum of the ID vector is risky (a small ID can be compensated with a large one), may be I should compare the sum of squares? Is there a hashing method in Matlab which I can use with confidence?
Example data:
a=[2,13,14,18,19,21,23,24,25,27]
b=[6,79,82,85,89,111,113,123,127,129]
c=[3,9,59,91,99,101,110,119,120,682]
d=[11,57,74,83,86,90,92,102,103,104]
So the problem is that if I just check the sum, it could be that cluster d for example, looses points 11,103 and gets 9,105. Then I would mistakenly think that there has been no change in the cluster.
This is one of those (very common) situations where the more we know about your data and application the better we are able to help. In the absence of better information than you provide, and in the spirit of exposing the weakness of answers such as this in that absence, here are a couple of suggestions you might reject.
One appropriate data structure for set operations is a bit-set, that is a set of length equal to the cardinality of the underlying universe of things in which each bit is set on or off according to the things membership of the (sub-set). You could implement this in Matlab in at least two ways:
a) (easy, but possibly consuming too much space): define a matrix with as many columns as there are points in your data, and one row for each cluster. Set the (cluster, point) value to true if point is a member of cluster. Set operations are then defined by vector operations. I don't have a clue about the relative (time) efficiency of setdiff versus rowA==rowB.
b) (more difficult): actually represent the clusters by bit sets. You'll have to use Matlab's bit-twiddling capabilities of course, but the pain might be worth the gain. Suppose that your universe comprises 1024 points, then you'll need an array of 16 uint64 values to represent the bit set for each cluster. The presence of, say, point 563 in a cluster requires that you set, for the bit set representing that cluster, bit 563 (which is probably bit 51 in the 9th element of the set) to 1.
And perhaps I should have started by writing that I don't think that this is a hashing sort of a problem, it's a set sort of a problem. Yeah, you could use a hash but then you'll have to program around the limitations of using a screwdriver on a nail (choose your preferred analogy).
If I understand correctly, to hash the ID's I would recommend using the matlab Java interface to use the Java hashing algorithms
http://docs.oracle.com/javase/1.4.2/docs/api/java/security/MessageDigest.html
You'll do something like:
hash = java.security.MessageDigest.getInstance('SHA');
Hope this helps.
I found the function
DataHash on FEX it is quiet fast for vectors and the strcmp on the keys is a lot faster than I expected.