Spark now has two machine learning libraries - Spark MLlib and Spark ML. They do somewhat overlap in what is implemented, but as I understand (as a person new to the whole Spark ecosystem) Spark ML is the way to go and MLlib is still around mostly for backward compatibility.
My question is very concrete and related to PCA. In MLlib implementation there seems to be a limitation of the number of columns
spark.mllib supports PCA for tall-and-skinny matrices stored in row-oriented format and any Vectors.
Also, if you look at the Java code example there is also this
The number of columns should be small, e.g, less than 1000.
On the other hand, if you look at ML documentation, there are no limitations mentioned.
So, my question is - does this limitation also exists in Spark ML? And if so, why the limitation and is there any workaround to be able to use this implementation even if the number of columns is large?
PCA consists in finding a set of decorrelated random variables that you can represent your data with, sorted in decreasing order with respect to the amount of variance they retain.
These variables can be found by projecting your data points onto a specific orthogonal subspace. If your (mean-centered) data matrix is X, this subspace is comprised of the eigenvectors of X^T X.
When X is large, say of dimensions n x d, you can compute X^T X by computing the outer product of each row of the matrix by itself, then adding all the results up. This is of course amenable to a simple map-reduce procedure if d is small, no matter how large n is. That's because the outer product of each row by itself is a d x d matrix, which will have to be manipulated in main memory by each worker. That's why you might run into trouble when handling many columns.
If the number of columns is large (and the number of rows not so much so) you can indeed compute PCA. Just compute the SVD of your (mean-centered) transposed data matrix and multiply it by the resulting eigenvectors and the inverse of the diagonal matrix of eigenvalues. There's your orthogonal subspace.
Bottom line: if the spark.ml implementation follows the first approach every time, then the limitation should be the same. If they check the dimensions of the input dataset to decide whether they should go for the second approach, then you won't have problems dealing with large numbers of columns if the number of rows is small.
Regardless of that, the limit is imposed by how much memory your workers have, so perhaps they let users hit the ceiling by themselves, rather than suggesting a limitation that may not apply for some. That might be the reason why they decided not to mention the limitation in the new docs.
Update: The source code reveals that they do take the first approach every time, regardless of the dimensionality of the input. The actual limit is 65535, and at 10,000 they issue a warning.
Related
I have a dataset of 590000 records after preprocessing and i wanted to find clusters out of it and it contains string data (for now assume i have only one column with 590000 unique values in dataset). Also i am using custom defined distance measure and needed to calculate the distance matrix of size 590000*590000. Using some partition logic i created the distance matrix but cannot merge those partitions into one big distance matrix due to memory constarints. Does anyone have any sort of idea to resolve it ?? I picked DBSCAN for it. Is there any way to use deep learning methodologies?? any other ideas
Use a manageable sample first.
Because I doubt the results will be good enough to warrant any effort on scaling a method that does not work anyway.
The problem:
Suppose I have a group of around 1,000,000 short documents D (no more than 50 words each), and I want to let users to supply a document from the same group D, and and get the top K similar documents from D.
My approach:
My first approach was to preprocess the group D by applying simple tf-idf, and after I have vector for each document, which is extremely sparse, to use a simple nearest neighbours algorithm based on cosine similarity.
Then, on query time, to justuse my static nearest neighbours table which its size is 1,000,000 x K, without any further calculations.
After applying tf-idf, I got vectors in size ~200,000, which means now I have a very sparse table (that can be stored efficiently in memory using sparse vectors) in size 1,000,000 x 200,000.
However, calculating the nearest neighbours model took me more than one day, and still haven't finished.
I tried to lower the vectors dimension by applying HashingTF, that utilizes the hasing trick, instead, so I can set the dimension to a constant one (in my case, i used 2^13 for uninfied hashing), but still I get the same bad performance.
Some technical information:
I use Spark 2.0 for the tf-idf calculation, and sklearn NearestNeighbours on the collected data.
Is thier any more efficient way to achieve that goal?
Thanks in advance.
Edit:
I had an idea to try a LSH based approximation similarity algorithm like those implemented in spark as described here, but could not find one that supports the 'cosine' similarity metric.
There were some requirements for the algorithm on the relation between training instances and the dimensions of your vectors , but you can try DIMSUM.
You can find the paper here.
i got a facebook-list of user-ids from following page:
Stanford Facebook-Data
If you look at the facebook_combined data, you can see that it is a list of user-connections (edges). So for instance user 0 has something to do with user 1,2,3 and so on.
Now my work is to find clusters in the dataset.
In the first step i used node.js to read the file and save the data in an array like this:
array=[[0,1],[0,2], ...]
In the second step i used a k-means plugin for node.js to cluster the data:
Cluster-Plugin
But i dont know if the result is right, because now i get clusters of edges and not clusters of users.
UPDATE:
I am trying out a markov implementation for node js. The Markov Plugin however needs an adjacency matrix to build clusters. I implemented an algorithm with java to save the matrix in a file.
Maybe you got any other suggestion how i could get clusters out of edges.
K-means assumes your input data issue an R^d vector space.
In fact, it requires the data to be this way, because it computes means as cluster centers, hence the name k-means.
So if you want to use k-means, then you need
One row per datapoint (not an edge list)
A fixed dimensionality data space where the mean is a useful center (usually, you should have continuous attributes, on binary data the mean does not make too much sense) and where least-squares is a meaningful optimization criterion (again, on binary data, least-squares does not have a strong theoretical support)
On your Faceboook data, you could try some embedding, but I'd have doubts about the trustworthiness.
I have more than 10^8 records stored in elasticSearch. Now I want to clustering them by writing a hierarchical algorithm or using PIC based on spark MLlib.
However, I can't use some efficient algorithm like K-means because every record is stored in the form of
{mainID:[subId1,subId2,subId3,...]}
which obviously is not in euclidean space.
I need to calculate the distance of every pair of records which will take a very LONG time I guess (10^8 * 10^8). I know the cartesian product in spark to do such computing , but there will appear the duplicated ones like (mainID1,mainID2) and (mainID2,mainID1), which is not suitable to PIC.
Does anyone know a better way to cluster these records? Or any method to delete the duplicated ones in the result RDD of cartesian product?
Thanks A lot!
First of all, don't take the full Cartesian product:
select where a.MainID > b.MainID
This doesn't reduce the complexity, but it does save about 2x in generation time.
That said, consider your data "shape" and select the clustering algorithm accordingly. K-means, HC, and PIC have three different applications. You know K-means already, I'm sure.
PIC basically finds gaps in the distribution of distances. It's great for well-defined sets (clear boundaries), even when those curl around each other or nest. However, if you have a tendril of connecting points (like a dumbbell with a long, thin bar), PIC will not separate the obvious clusters.
HC is great for such sets, and is a good algorithm in general. Most HC algorithms have an "understanding" of density, and tend to give clusterings that fit human cognition's interpretation. However, HC tends to be slow.
I strongly suggest that you consider a "seeded" algorithm: pick a random subset of your points, perhaps
sqrt(size) * dim
points, where size is the quantity of points (10^8) and dim is the number of dimensions. For instance, your example has 5 dimensions, so take 5*10^4 randomly selected points. Run the first iterations on those alone, which will identify centroids (K-means), eigenvectors (PIC), or initial hierarchy (HC). With those "seeded" values, you can now characterize each of the candidate clusters with 2-3 parameters. Classifying the remaining 10^8 - 5*10^4 points against 3 parameters is a lot faster, being O(size) time instead of O(size^2).
Does that get you moving toward something useful?
I have a trading strategy on the foreign exchange market that I am attempting to improve upon.
I have a huge table (100k+ rows) that represent every possible trade in the market, the type of trade (buy or sell), the profit/loss after that trade closed, and 10 or so additional variables that represent various market measurements at the time of trade-opening.
I am trying to find out if any of these 10 variables are significantly related to the profits/losses.
For example, imagine that variable X ranges from 50 to -50.
The average value of X for a buy order is 25, and for a sell order is -25.
If most profitable buy orders have a value of X > 25, and most profitable sell orders have a value of X < -25 then I would consider the relationship of X-to-profit as significant.
I would like a good starting point for this. I have installed RapidMiner 5 in case someone can give me a specific recommendation for that.
A Decision Tree is perhaps the best place to begin.
The tree itself is a visual summary of feature importance ranking (or significant variables as phrased in the OP).
gives you a visual representation of the entire
classification/regression analysis (in the form of a binary tree),
which distinguishes it from any other analytical/statistical
technique that i am aware of;
decision tree algorithms require very little pre-processing on your data, no normalization, no rescaling, no conversion of discrete variables into integers (eg, Male/Female => 0/1); they can accept both categorical (discrete) and continuous variables, and many implementations can handle incomplete data (values missing from some of the rows in your data matrix); and
again, the tree itself is a visual summary of feature importance ranking
(ie, significant variables)--the most significant variable is the
root node, and is more significant than the two child nodes, which in
turn are more significant than their four combined children. "significance" here means the percent of variance explained (with respect to some response variable, aka 'target variable' or the thing
you are trying to predict). One proviso: from a visual inspection of
a decision tree you cannot distinguish variable significance from
among nodes of the same rank.
If you haven't used them before, here's how Decision Trees work: the algorithm will go through every variable (column) in your data and every value for each variable and split your data into two sub-sets based on each of those values. Which of these splits is actually chosen by the algorithm--i.e., what is the splitting criterion? The particular variable/value combination that "purifies" the data the most (i.e., maximizes the information gain) is chosen to split the data (that variable/value combination is usually indicated as the node's label). This simple heuristic is just performed recursively until the remaining data sub-sets are pure or further splitting doesn't increase the information gain.
What does this tell you about the "importance" of the variables in your data set? Well importance is indicated by proximity to the root node--i.e., hierarchical level or rank.
One suggestion: decision trees handle both categorical and discrete data usually without problem; however, in my experience, decision tree algorithms always perform better if the response variable (the variable you are trying to predict using all other variables) is discrete/categorical rather than continuous. It looks like yours is probably continuous, in which case in would consider discretizing it (unless doing so just causes the entire analysis to be meaningless). To do this, just bin your response variable values using parameters (bin size, bin number, and bin edges) meaningful w/r/t your problem domain--e.g., if your r/v is comprised of 'continuous values' from 1 to 100, you might sensibly bin them into 5 bins, 0-20, 21-40, 41-60, and so on.
For instance, from your Question, suppose one variable in your data is X and it has 5 values (10, 20, 25, 50, 100); suppose also that splitting your data on this variable with the third value (25) results in two nearly pure subsets--one low-value and one high-value. As long as this purity were higher than for the sub-sets obtained from splitting on the other values, the data would be split on that variable/value pair.
RapidMiner does indeed have a decision tree implementation, and it seems there are quite a few tutorials available on the Web (e.g., from YouTube, here and here). (Note, I have not used the decision tree module in R/M, nor have i used RapidMiner at all.)
The other set of techniques i would consider is usually grouped under the rubric Dimension Reduction. Feature Extraction and Feature Selection are two perhaps the most common terms after D/R. The most widely used is PCA, or principal-component analysis, which is based on an eigen-vector decomposition of the covariance matrix (derived from to your data matrix).
One direct result from this eigen-vector decomp is the fraction of variability in the data accounted for by each eigenvector. Just from this result, you can determine how many dimensions are required to explain, e.g., 95% of the variability in your data
If RapidMiner has PCA or another functionally similar dimension reduction technique, it's not obvious where to find it. I do know that RapidMiner has an R Extension, which of course let's you access R inside RapidMiner.R has plenty of PCA libraries (Packages). The ones i mention below are all available on CRAN, which means any of the PCA Packages there satisfy the minimum Package requirements for documentation and vignettes (code examples). I can recommend pcaPP (Robust PCA by Projection Pursuit).
In addition, i can recommend two excellent step-by-step tutorials on PCA. The first is from the NIST Engineering Statistics Handbook. The second is a tutorial for Independent Component Analysis (ICA) rather than PCA, but i mentioned it here because it's an excellent tutorial and the two techniques are used for the similar purposes.