according to paper which written by chawla, et al (2002)
the best perfomance of balancing data is combining undersampling with SMOTE.
I’ve tried to combine my dataset using under-sampling and SMOTE,
but I am bit confuse about the attribute for under-sampling.
In weka there is Resample to decrease the majority class.
there is a attribute in Resample
biasToUniformClass -- Whether to use bias towards a uniform class. A value of 0 leaves the class distribution as-is, a value of 1 ensures the class distribution is uniform in the output data.
I use value 0 and the data in majority class is down so the minority do and when I use value 1, the data in majority decrease but in minority class, the data is up.
I try to use value 1 for that attribute, but I don't using smote to increase the instances of minority class because the data is already balance and the result is good too.
so, is that the same as I combine the SMOTE and under-sampling or I still have to try with value 0 in that attribute and do the SMOTE ?
For undersampling, see the EasyEnsemble algorithm (a Weka implementation was developed by Schubach, Robinson, and Valentini).
The EasyEnsemble algorithm allows you to split the data into a certain number of balanced partitions. To achieve this balance, set the numIterations parameter equal to:
(# of majority instances) / (# minority instances) = numIterations
For example, if there are 30 total instances with 20 in the majority class and 10 in the minority class, set the numIterations parameter equal to 2 (i.e., 20 majority instances / 10 instances equals 2 balanced partitions). These 2 partitions should each contain 20 instances; each has the same 10 minority instances along with a different 10 instances from the majority class.
The algorithm then trains classifiers on each of the balanced partitions,
and at test time, ensembles the batch of classifiers trained on each of the balanced partitions for prediction.
Related
I am using ArangoDB and I am trying to build a graph-based recommender system with it.
The data model just contains users, items and ratings (edges).
Therefore want to calculate the affinity of a user to a movie with the katz measure.
Eventually I want to do this:
Get all (or a certain number of) paths between a user and a item
For all of these paths do the following:
Multiply each edge's rating with a damping factor (e.g. 0.7)
Sum up all calculated values within a path
Calculate the average of all calculated path values
The result is some kind of affinity between a user and an item, weighted with the intermediary ratings and damped by a defined factor.
I was trying to realize something like that in AQL but it was either wrong or much too slow. How could a algorithm like this look in AQL?
From a performance point of view there might be better choices for graph based recommender systems. If someone has a suggestion (e.g. Item Rank or other algorithms), it would also be nice to get some ideas here.
I love this topic but sometimes I get to my borders.
In the following, #start and #end are parameters representing the two endpoints; for simplicity, I've assumed that:
the maximum admissible path length is 10000
"rates" is the name of the "edges" collection
"rating" is the name of the property giving a weight to an edge
the "damping" factor is as per the requirements
FOR v,e,p IN 0..10000 OUTBOUND #start rates
OPTIONS {uniqueVertices: "path"}
FILTER v._id==#end
LET r = AVERAGE(p.edges[*].rating) * 0.7
COLLECT AGGREGATE avg = AVERAGE(r)
RETURN avg
I would like to know how can I estimate the growth (how much the size increasez in a period of time) of an index of App engine Search API (FTS) based on the number of entities inserted and amount of information. For this I would like to know basically how is the index size calculated (on what does it depend). Specifically:
When inserting new entities, is the growth (size) influenced by the number of previous existing entities? (ie. is the growth exponential)? For ex. if I have 1000 entities and I insert 10, the index will grow with X bytes. But if I have 100000 entities and insert 10, will it increase with X or much more than X (exponentially, let' say 10*X) ?
Does the number of fields (properties) influences the size exponentially? For ex. if I have entity A with 2 fields and entity B with 4 fields (let's say identical in values, for mathematical simplicity) will the size increase, when adding entity B, twice as that of entity A or much more than that?
What other means can I use to find statistical information; do I have other tools in the cloud console of app engine, or can I do this programmatically ?
Thank you.
You can check the size of a given index by running the code below.
from google.appengine.api import search
for index in search.get_indexes(fetch_schema=True):
logging.info("index %s", index.storage_usage)
# pseudo code
amount_of_items_to_add = 100
x = 0
for x <= amount_of_items_to_add:
search_api_insert_insert(data)
x+=1
#rerun for loop to see how much the size increased
for index in search.get_indexes(fetch_schema=True):
logging.info("index %s", index.storage_usage)
This code is obviously not a complete working example, but you should be able to build a simple method that takes some data inserts it into the search api and returns how much the used storage increased.
I have run a number of tests for different number of entities and different number of indexed properties per entity and it seams thst the estimated growth of the index reported by the api is not exponential it is linear.
But the most interesting fact to know is that although the size reported is realtime almost, after deleting documents from the index, it may take 12, 24 even 36 hours to update.
One approach to split the data into two disjoint sets, one for training and one for tests is taking the first 80% as the training set and the rest as the test set. Is there another approach to split the data into training and test sets?
** For example, I have a data contains 20 attributes and 5000 objects. Therefore, I will take 12 attributes and 1000 objects as my training data and 3 attributes from the 12 attributes as test set. Is this method correct?
No, that's invalid. You would always use all features in all data sets. You split by "objects" (examples).
It's not clear why you are taking just 1000 objects and trying to extract a training set from that. What happened to the other 4000 you threw away?
Train on 4000 objects / 20 features. Cross-validate on 500 objects / 20 features. Evaluate performance on the remaining 500 objects/ 20 features.
If your training produces a classifier based on 12 features, it could be (very) hard to evaluate its performances on a test set based only on a subset of these features (your classifier is expecting 12 inputs and you'll give only 3).
Feature/attribute selection/extraction is important if your data contains many redundant or irrelevant features. So you could identify and use only the most informative features (maybe 12 features) but your training/validation/test sets should be based on the same number of features (e.g. since you're mentioning weka Why do I get the error message 'training and test set are not compatible'?).
Remaining on a training/validation/test split (holdout method), a problem you can face is that the samples might not be representative.
For example, some classes might be represented with very few instance or even with no instances at all.
A possible improvement is stratification: sampling for training and testing within classes. This ensures that each class is represented with approximately equal proportions in both subsets.
However, by partitioning the available data into fixed training/test set, you drastically reduce the number of samples which can be used for learning the model. An alternative is cross validation.
Why would one use kmedoids algoirthm rather then kmeans? Is it only the fact that
the number of metrics that can be used in kmeans is very limited or is there something more?
Is there an example of data, for which it makes much more sense to choose the best representatives
of cluster from the data rather then from R^n?
The problem with k-means is that it is not interpretable. By interpretability i mean the model should also be able to output the reason that why it has resulted a certain output.
lets take an example.
Suppose there is food review dataset which has two posibility that there is a +ve review or a -ve review so we can say we will have k= 2 where k is the number of clusters. Now if you go with k-means where in the algorithm the third step is updation step where you update your k-centroids based on the mean distance of the points that lie in a particular cluster. The example that we have chosen is text problem, so you would also apply some kind of text-featured vector schemes like BagOfWords(BOW), word2vec. now for every review you would get the corresponding vector. Now the generated centroid c_i that you will get after running the k-means would be the mean of the vectors present in that cluster. Now with that centroid you cannot interpret much or rather i should say nothing.
But for same problem you apply k-medoids wherein you choose your k-centroids/medoids from your dataset itself. lets say you choose x_5 point from your dataset as first medoid. From this your interpretability will increase beacuse now you have the review itself which is termed as medoid/centroid. So in k-medoids you choose the centroids from your dataset itself.
This is the foremost motivation of introducing k-mediods
Coming to the metrics part you can apply all the metrics that you apply for k-means
Hope this helps.
Why would we use k-medoids instead of k-means in case of (squared) Euclidean distance?
1. Technical justification
In case of relatively small data sets (as k-medoids complexity is greater) - to obtain a clustering more robust to noise and outliers.
Example 2D data showing that:
The graph on the left shows clusters obtained with K-medoids (sklearn_extra.cluster.KMedoids method in Python with default options) and the one on the right with K-means for K=2. Blue crosses are cluster centers.
The Python code used to generate green points:
import numpy as np
import matplotlib.pyplot as plt
rng = np.random.default_rng(seed=32)
a = rng.random((6,2))*2.35 - 3*np.ones((6,2))
b = rng.random((50,2))*0.25 - 2*np.ones((50,2))
c = rng.random((100,2))*0.5 - 1.5*np.ones((100,2))
d = rng.random((7,2))*0.55
points = np.concatenate((a, b, c, d))
plt.plot(points[:,0],points[:,1],"g.", markersize=8, alpha=0.3) # green points
2. Business case justification
Here are some example business cases showing why we would prefer k-medoids. They mostly come down to the interpretability of the results and the fact that in k-medoids the resulting cluster centers are members of the original dataset.
2.1 We have a recommender engine based only on user-item preference data and want to recommend to the user those items (e.g. movies) that other similar people enjoyed. So we assign the user to his/her closest cluster and recommend top movies that the cluster representant (actual person) watched. If the cluster representant wasn't an actual person we wouldn't possess the history of actually watched movies to recommend. Each time we'd have to search additionally e.g. for the closest person from the cluster. Example data: classic MovieLens 1M Dataset
2.2 We have a database of patients and want to pick a small representative group of size K to test a new drug with them. After clustering the patients with K-medoids, cluster representants are invited to the drug trial.
Difference between is that in k-means centroids(cluster centrum) are calculated as average of vectors containing in the cluster, and in k-medoids the medoid (cluster centrum) is record from dataset closest to centroid, so if you need to represent cluster centrum by record of your data you use k-medoids, otherwise i should use k-means (but concept of these algorithms are same)
The K-Means algorithm uses a Distance Function such as Euclidean Distance or Manhattan Distance, which are computed over vector-based instances. The K-Medoid algorithm instead uses a more general (and less constrained) distance function: aka pair-wise distance function.
This distinction works well in contexts like Complex Data Types or relational rows, where the instances have a high number of dimensions.
High dimensionality problem
In standard clustering libraries and the k-means algorithms, the distance computation phase can spend a lot of time scanning the entire vector of attributes that belongs to an instance; for instance, in the context of documents clustering, using the standard TF-IDF representation. During the computation of the cosine similarity, the distance function scans all the possible words that appear in the whole collection of documents. Which in many cases can be composed by millions of entries. This is why, in this domain, some authors [1] suggests to restrict the words considered to a subset of N most frequent word of that language.
Using K-Kedoids there is no need to represent and store the documents as vectors of word frequencies.
As an alternative representation for the documents is possible to use the set of words appearing at least twice in the document; and as a distance measure, there can be used Jaccard Distance.
In this case, vector representation is long as the number of words in your dictionary.
Heterogeneousity and Complex Data Types.
There are many domains where is considerably better to abstract the implementation of an instance:
Graph's nodes clustering;
Car driving behaviour, represented as GPS routes;
Complex data type allows the design of ad-hoc distance measures which can fit better with the proper data domain.
[1] Christopher D. Manning, Prabhakar Raghavan, and Hinrich Schütze. 2008. Introduction to Information Retrieval. Cambridge University Press, New York, NY, USA.
Source: https://github.com/eracle/Gap
I am working in a chemistry/biology project. We are building a web-application for fast matching of the user's experimental data with predicted data in a reference database. The reference database will contain up to a million entries. The data for one entry is a list (vector) of tuples containing a float value between 0.0 and 20.0 and an integer value between 1 and 18. For instance (7.2394 , 2) , (7.4011, 1) , (9.9367, 3) , ... etc.
The user will enter a similar list of tuples and the web-app must then return the - let's say - top 50 best matching database entries.
One thing is crucial: the search algorithm must allow for discrepancies between the query data and the reference data because both can contain small errors in the float values (NOT in the integer values). (The query data can contain errors because it is derived from a real-life experiment and the reference data because it is the result of a prediction.)
Edit - Moved text to answer -
How can we get an efficient ranking of 1 query on 1 million records?
You should add a physicist to the project :-) This is a very common problem to compare functions e.g. look here:
http://en.wikipedia.org/wiki/Autocorrelation
http://en.wikipedia.org/wiki/Correlation_function
In the first link you can read: "The SEQUEST algorithm for analyzing mass spectra makes use of autocorrelation in conjunction with cross-correlation to score the similarity of an observed spectrum to an idealized spectrum representing a peptide."
An efficient linear scan of 1 million records of that type should take a fraction of a second on a modern machine; a compiled loop should be able to do it at about memory bandwidth, which would transfer that in a two or three milliseconds.
But, if you really need to optimise this, you could construct a hash table of the integer values, which would divide the job by the number of integer bins. And, if the data is stored sorted by the floats, that improves the locality of matching by those; you know you can stop once you're out of tolerance. Storing the offsets of each of a number of bins would give you a position to start.
I guess I don't see the need for a fancy algorithm yet... describe the problem a bit more, perhaps (you can assume a fairly high level of chemistry and physics knowledge if you like; I'm a physicist by training)?
Ok, given the extra info, I still see no need for anything better than a direct linear search, if there's only 1 million reference vectors and the algorithm is that simple. I just tried it, and even a pure Python implementation of linear scan took only around three seconds. It took several times longer to make up some random data to test with. This does somewhat depend on the rather lunatic level of optimisation in Python's sorting library, but that's the advantage of high level languages.
from cmath import *
import random
r = [(random.uniform(0,20), random.randint(1,18)) for i in range(1000000)]
# this is a decorate-sort-undecorate pattern
# look for matches to (7,9)
# obviously, you can use whatever distance expression you want
zz=[(abs((7-x)+(9-y)),x,y) for x,y in r]
zz.sort()
# return the 50 best matches
[(x,y) for a,x,y in zz[:50]]
Can't you sort the tuples and perform binary search on the sorted array ?
I assume your database is done once for all, and the positions of the entries is not important. You can sort this array so that the tuples are in a given order. When a tuple is entered by the user, you just look in the middle of the sorted array. If the query value is larger of the center value, you repeat the work on the upper half, otherwise on the lower one.
Worst case is log(n)
If you can "map" your reference data to x-y coordinates on a plane there is a nifty technique which allows you to select all points under a given distance/tolerance (using Hilbert curves).
Here is a detailed example.
One approach we are trying ourselves which allows for the discrepancies between query and reference is by binning the float values. We are testing and want to offer the user the choice of different bin sizes. Bin sizes will be 0.1 , 0.2 , 0.3 or 0.4. So binning leaves us with between 50 and 200 bins, each with a corresponding integer value between 0 and 18, where 0 means there was no value within that bin. The reference data can be pre-binned and stored in the database. We can then take the binned query data and compare it with the reference data. One approach could be for all bins, subtract the query integer value from the reference integer value. By summing up all differences we get the similarity score, with the the most similar reference entries resulting in the lowest scores.
Another (simpler) search option we want to offer is where the user only enters the float values. The integer values in both query as reference list can then be set to 1. We then use Hamming distance to compute the difference between the query and the reference binned values. I have previously asked about an efficient algorithm for that search.
This binning is only one way of achieving our goal. I am open to other suggestions. Perhaps we can use Principal Component Analysis (PCA), as described here