Since K-means cannot handle categorical variables directly, I want to know if it is correct to convert International Standard Industrial Classification of All Economic Activities or ISIC into double data types to cluster it using K-means along with other financial and transactional data? Or shall I try other techniques such as one hot encoding?
The biggest assumption is that ISIC codes are categorical not numeric variables since code “2930” refers to “Manufacture of parts and accessories for motor vehicles” and not money, kilos, feet, etc., but there is a sort of pattern in such codes since they are not assigned randomly and have a hierarchy for instance 2930 belongs to Section C “Manufacturing” and Division 29 “Manufacture of motor vehicles, trailers and semi-trailers”.
As you want to use standard K-Means, you need your data has a geometric meaning. Hence, if your mapping of the codes into the geometric space is linear, you will not get any proper clustering result. As the distance of the code does not project in their value. For example code 2930 is as close to code 2931 as code 2929. Therefore, you need a nonlinear mapping for the categorical space to the geometric space to using the standard k-mean clustering.
One solution is using from machine learning techniques similar to word-to-vec (for vectorizing words) if you have enough data for co-occurrences of these codes.
Clustering is all about distance measurement.
Discretizing numeric variable to categorical is a partial solution. As earlier highlighted, the underlying question is how to measure the distance for a discretized variable with other discretized variable and numeric variable?
In literature, there are several unsupervised algorithms for treating mixed data. Take a look at the k-prototypes algorithm and the Gower distance.
The k-prototypes in R is given in clustMixType package. The Gower distance in R is given in the function daisy in the cluster package. If using Python, you can look at this post
Huang, Z. (1997). Clustering large data sets with mixed numeric and categorical values. Paper presented at the Proceedings of the 1st Pacific-Asia Conference on Knowledge Discovery and Data Mining,(PAKDD).
Gower, J. C. (1971). A general coefficient of similarity and some of its properties. Biometrics, 857-871.
K-means is designed to minimize the sum of squares.
Does minimizing the sum of squares make sense for your problem? Probably not!
While 29, 2903 and 2930 are supposedly all related 2899 likely is not very much related to 2900. Hence, a least squares approach will produce undesired results.
The method is really designed for continuous variables of the same type and scale. One-hot encoded variables cause more problems than they solve - these are a naive hack to make the function "run", but the results are statistically questionable.
Try to figure out what he right thing to do is. It's probably not least squares here.
I have a pair of word and semantic types of those words. I am trying to compute the relatedness measure between these two words using semantic types, for example: word1=king, type1=man, word2=queen, type2=woman
we can use gensim word_vectors.most_similar to get 'queen' from 'king-man+woman'. However, I am looking for similarity measure between vector represented by 'king-man+woman' and 'queen'.
I am looking for a solution to above (or)
way to calculate vector that is representative of 'king-man+woman' (and)
calculating similarity between two vectors using vector values in gensim (or)
way to calculate simple mean of the projection weight vectors(i.e king-man+woman)
You should look at the source code for the gensim most_similar() method, which is used to propose answers to such analogy questions. Specifically, when you try...
sims = wv_model.most_similar(positive=['king', 'woman'], negative=['man'])
...the top result will (in a sufficiently-trained model) often be 'queen' or similar. So, you can look at the source code to see exactly how it calculates the target combination of wv('king') - wv('man') + wv('woman'), before searching all known vectors for those closest vectors to that target. See...
https://github.com/RaRe-Technologies/gensim/blob/5f6b28c538d7509138eb090c41917cb59e4709af/gensim/models/keyedvectors.py#L486
...and note that the local variable mean is the combination of the positive and negative values provided.
You might also find other methods there useful, either directly or as models for your own code, such as distances()...
https://github.com/RaRe-Technologies/gensim/blob/5f6b28c538d7509138eb090c41917cb59e4709af/gensim/models/keyedvectors.py#L934
...or n_similarity()...
https://github.com/RaRe-Technologies/gensim/blob/5f6b28c538d7509138eb090c41917cb59e4709af/gensim/models/keyedvectors.py#L1005
Source:- https://machinelearningmastery.com/k-nearest-neighbors-for-machine-learning/
This page has a section quoting the following passage:-
Best Prepare Data for KNN
Rescale Data: KNN performs much better if all of the data has the same scale. Normalizing your data to the range [0, 1] is a good idea. It may also be a good idea to standardize your data if it has a Gaussian
distribution.
Address Missing Data: Missing data will mean that the distance between samples cannot be calculated. These samples could be excluded or the missing values could be imputed.
Lower Dimensionality: KNN is suited for lower dimensional data. You can try it on high dimensional data (hundreds or thousands of input variables) but be aware that it may not perform as well as other techniques. KNN can benefit from feature selection that reduces the dimensionality of the input feature space.
Please, can someone explain the Second point, i.e. Address Missing Data, in detail?
Missing data in this context means that some samples do not have all the existing features.
For example:
Suppose you have a database with age and height for a group of individuals.
This would mean that for some persons either the height or the age is missing.
Now, why this affects KNN?
Given a test sample
KNN finds the samples that are closer to it (Aka: the students with similar age and height).
KNN does this to make some inference about the test sample based on its nearest neighbors.
If you want to find these neighbors you must be able to compute the distance between samples. To compute the distance between 2 samples you must have all the features for these 2 samples.
If some of them are missing you won't be able to compute distance.
So implicitly you would be lossing the samples with missing data
I'm training a corpus consisting of 200000 reviews into positive and negative reviews using a Naive Bayes model, and I noticed that performing TF-IDF actually reduced the accuracy (while testing on test set of 50000 reviews) by about 2%. So I was wondering if TF-IDF has any underlying assumptions on the data or model that it works with, i.e. any cases where accuracy is reduced by the use of it?
The IDF component of TF*IDF can harm your classification accuracy in some cases.
Let suppose the following artificial, easy classification task, made for the sake of illustration:
Class A: texts containing the word 'corn'
Class B: texts not containing the word 'corn'
Suppose now that in Class A, you have 100 000 examples and in class B, 1000 examples.
What will happen to TFIDF? The inverse document frequency of corn will be very low (because it is found in almost all documents), and the feature 'corn' will get a very small TFIDF, which is the weight of the feature used by the classifier. Obviously, 'corn' was THE best feature for this classification task. This is an example where TFIDF may reduce your classification accuracy. In more general terms:
when there is class imbalance. If you have more instances in one class, the good word features of the frequent class risk having lower IDF, thus their best features will have a lower weight
when you have words with high frequency that are very predictive of one of the classes (words found in most documents of that class)
You can heuristically determine whether the usage of IDF on your training data decreases your predictive accuracy by performing grid search as appropriate.
For example, if you are working in sklearn, and you want to determine whether IDF decreases the predictive accuracy of your model, you can perform a grid search on the use_idf parameter of the TfidfVectorizer.
As an example, this code would implement the gridsearch algorithm on the selection of IDF for classification with SGDClassifier (you must import all the objects being instantiated first):
# import all objects first
X = # your training data
y = # your labels
pipeline = Pipeline([('tfidf',TfidfVectorizer()),
('sgd',SGDClassifier())])
params = {'tfidf__use_idf':(False,True)}
gridsearch = GridSearch(pipeline,params)
gridsearch.fit(X,y)
print(gridsearch.best_params_)
The output would be either:
Parameters selected as the best fit:
{'tfidf__use_idf': False}
or
{'tfidf__use_idf': True}
TF-IDF as far as I understand is a feature. TF is term frequency i.e. frequency of occurence in a document. IDF is inverse document frequncy i.e frequency of documents in which the term occurs.
Here, the model is using the TF-IDF info in the training corpus to estimate the new documents. For a very simple example, Say a document with word bad has pretty high term frequency of word bad in training set will sentiment label as negative. So, any new document containing bad will be more likely to be negative.
For the accuracy you can manaually select training corpus which contains mostly used negative or positive words. This will boost the accuracy.
What is an algorithm to compare multiple sets of numbers against a target set to determine which ones are the most "similar"?
One use of this algorithm would be to compare today's hourly weather forecast against historical weather recordings to find a day that had similar weather.
The similarity of two sets is a bit subjective, so the algorithm really just needs to diferentiate between good matches and bad matches. We have a lot of historical data, so I would like to try to narrow down the amount of days the users need to look through by automatically throwing out sets that aren't close and trying to put the "best" matches at the top of the list.
Edit:
Ideally the result of the algorithm would be comparable to results using different data sets. For example using the mean square error as suggested by Niles produces pretty good results, but the numbers generated when comparing the temperature can not be compared to numbers generated with other data such as Wind Speed or Precipitation because the scale of the data is different. Some of the non-weather data being is very large, so the mean square error algorithm generates numbers in the hundreds of thousands compared to the tens or hundreds that is generated by using temperature.
I think the mean square error metric might work for applications such as weather compares. It's easy to calculate and gives numbers that do make sense.
Since your want to compare measurements over time you can just leave out missing values from the calculation.
For values that are not time-bound or even unsorted, multi-dimensional scatter data it's a bit more difficult. Choosing a good distance metric becomes part of the art of analysing such data.
Use the pearson correlation coefficient. I figured out how to calculate it in an SQL query which can be found here: http://vanheusden.com/misc/pearson.php
In finance they use Beta to measure the correlation of 2 series of numbers. EG, Beta could answer the question "Over the last year, how much would the price of IBM go up on a day that the price of the S&P 500 index went up 5%?" It deals with the percentage of the move, so the 2 series can have different scales.
In my example, the Beta is Covariance(IBM, S&P 500) / Variance(S&P 500).
Wikipedia has pages explaining Covariance, Variance, and Beta: http://en.wikipedia.org/wiki/Beta_(finance)
Look at statistical sites. I think you are looking for correlation.
As an example, I'll assume you're measuring temp, wind, and precip. We'll call these items "features". So valid values might be:
Temp: -50 to 100F (I'm in Minnesota, USA)
Wind: 0 to 120 Miles/hr (not sure if this is realistic but bear with me)
Precip: 0 to 100
Start by normalizing your data. Temp has a range of 150 units, Wind 120 units, and Precip 100 units. Multiply your wind units by 1.25 and Precip by 1.5 to make them roughly the same "scale" as your temp. You can get fancy here and make rules that weigh one feature as more valuable than others. In this example, wind might have a huge range but usually stays in a smaller range so you want to weigh it less to prevent it from skewing your results.
Now, imagine each measurement as a point in multi-dimensional space. This example measures 3d space (temp, wind, precip). The nice thing is, if we add more features, we simply increase the dimensionality of our space but the math stays the same. Anyway, we want to find the historical points that are closest to our current point. The easiest way to do that is Euclidean distance. So measure the distance from our current point to each historical point and keep the closest matches:
for each historicalpoint
distance = sqrt(
pow(currentpoint.temp - historicalpoint.temp, 2) +
pow(currentpoint.wind - historicalpoint.wind, 2) +
pow(currentpoint.precip - historicalpoint.precip, 2))
if distance is smaller than the largest distance in our match collection
add historicalpoint to our match collection
remove the match with the largest distance from our match collection
next
This is a brute-force approach. If you have the time, you could get a lot fancier. Multi-dimensional data can be represented as trees like kd-trees or r-trees. If you have a lot of data, comparing your current observation with every historical observation would be too slow. Trees speed up your search. You might want to take a look at Data Clustering and Nearest Neighbor Search.
Cheers.
Talk to a statistician.
Seriously.
They do this type of thing for a living.
You write that the "similarity of two sets is a bit subjective", but it's not subjective at all-- it's a matter of determining the appropriate criteria for similarity for your problem domain.
This is one of those situation where you are much better off speaking to a professional than asking a bunch of programmers.
First of all, ask yourself if these are sets, or ordered collections.
I assume that these are ordered collections with duplicates. The most obvious algorithm is to select a tolerance within which numbers are considered the same, and count the number of slots where the numbers are the same under that measure.
I do have a solution implemented for this in my application, but I'm looking to see if there is something that is better or more "correct". For each historical day I do the following:
function calculate_score(historical_set, forecast_set)
{
double c = correlation(historical_set, forecast_set);
double avg_history = average(historical_set);
double avg_forecast = average(forecast_set);
double penalty = abs(avg_history - avg_forecast) / avg_forecast
return c - penalty;
}
I then sort all the results from high to low.
Since the correlation is a value from -1 to 1 that says whether the numbers fall or rise together, I then "penalize" that with the percentage difference the averages of the two sets of numbers.
A couple of times, you've mentioned that you don't know the distribution of the data, which is of course true. I mean, tomorrow there could be a day that is 150 degree F, with 2000km/hr winds, but it seems pretty unlikely.
I would argue that you have a very good idea of the distribution, since you have a long historical record. Given that, you can put everything in terms of quantiles of the historical distribution, and do something with absolute or squared difference of the quantiles on all measures. This is another normalization method, but one that accounts for the non-linearities in the data.
Normalization in any style should make all variables comparable.
As example, let's say that a day it's a windy, hot day: that might have a temp quantile of .75, and a wind quantile of .75. The .76 quantile for heat might be 1 degree away, and the one for wind might be 3kmh away.
This focus on the empirical distribution is easy to understand as well, and could be more robust than normal estimation (like Mean-square-error).
Are the two data sets ordered, or not?
If ordered, are the indices the same? equally spaced?
If the indices are common (temperatures measured on the same days (but different locations), for example, you can regress the first data set against the second,
and then test that the slope is equal to 1, and that the intercept is 0.
http://stattrek.com/AP-Statistics-4/Test-Slope.aspx?Tutorial=AP
Otherwise, you can do two regressions, of the y=values against their indices. http://en.wikipedia.org/wiki/Correlation. You'd still want to compare slopes and intercepts.
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If unordered, I think you want to look at the cumulative distribution functions
http://en.wikipedia.org/wiki/Cumulative_distribution_function
One relevant test is Kolmogorov-Smirnov:
http://en.wikipedia.org/wiki/Kolmogorov-Smirnov_test
You could also look at
Student's t-test,
http://en.wikipedia.org/wiki/Student%27s_t-test
or a Wilcoxon signed-rank test http://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test
to test equality of means between the two samples.
And you could test for equality of variances with a Levene test http://www.itl.nist.gov/div898/handbook/eda/section3/eda35a.htm
Note: it is possible for dissimilar sets of data to have the same mean and variance -- depending on how rigorous you want to be (and how much data you have), you could consider testing for equality of higher moments, as well.
Maybe you can see your set of numbers as a vector (each number of the set being a componant of the vector).
Then you can simply use dot product to compute the similarity of 2 given vectors (i.e. set of numbers).
You might need to normalize your vectors.
More : Cosine similarity