I have this SVD decomposition of the document
I've read this page, but I don't understand how can I compute the best feature for document separation.
I know that:
S x Vt gives me relation between documents and features
U x S gives me relation between terms and features
But what is the key for the best feature selection?
SVD is concerned only with inputs, and not with their labels. In other words, it can be seen as an unsupervised technique. As such, it cannot tell you what features are good for separation, without making any further assumptions.
What it does tell you, is what 'basis vectors' are more important then others, in terms of reconstructing the original data using only a subset of the basis vectors.
Nevertheless, you can think about LSA in the following manner (this is only interpretation, the math is what important): A document is generated by a mixture of topics. Each topic is represented by a vector of length n, which tells you how likely is each word in this topic. For example, if the topic is sports, then words like football or game are more likely than bestseller or movie. These topic-vectors are the columns of U. In order to generate a document (a column of A), you take a linear combination of topics. The coefficients of the linear combination are the columns of Vt - each column tells you what proportion of topics to take in order to generate a document. In addition, each topic has an overall 'gain' factor, which tells you how much this topic is important in your set of documents (maybe you have just one document about sports out of 1000 total documents). These are the singular values == the diagonal of S. If you throw away the smaller ones, you can represent your original matrix A with less topics, and small amount of information lost. Of course, 'small' is a matter of application.
One drawback of LSA is that it is not entirely clear how to interpret the numbers - they are not probabilities, for example. It makes sense to have "0.5" units of sports in a document, but what does it mean to have "-1" units?
Related
I have been searching and attempting to implement a word embedding model to predict similarity between words. I have a dataset made up 3,550 company names, the idea is that the user can provide a new word (which would not be in the vocabulary) and calculate the similarity between the new name and existing ones.
During preprocessing I got rid of stop words and punctuation (hyphens, dots, commas, etc). In addition, I applied stemming and separated prefixes with the hope to get more precision. Then words such as BIOCHEMICAL ended up as BIO CHEMIC which is the word divided in two (prefix and stem word)
The average company name length is made up 3 words with the following frequency:
The tokens that are the result of preprocessing are sent to word2vec:
#window: Maximum distance between the current and predicted word within a sentence
#min_count: Ignores all words with total frequency lower than this.
#workers: Use these many worker threads to train the model
#sg: The training algorithm, either CBOW(0) or skip gram(1). Default is 0s
word2vec_model = Word2Vec(prepWords,size=300, window=2, min_count=1, workers=7, sg=1)
After the model included all the words in the vocab , the average sentence vector is calculated for each company name:
df['avg_vector']=df2.apply(lambda row : avg_sentence_vector(row, model=word2vec_model, num_features=300, index2word_set=set(word2vec_model.wv.index2word)).tolist())
Then, the vector is saved for further lookups:
##Saving name and vector values in file
df.to_csv('name-submission-vectors.csv',encoding='utf-8', index=False)
If a new company name is not included in the vocab after preprocessing (removing stop words and punctuation), then I proceed to create the model again and calculate the average sentence vector and save it again.
I have found this model is not working as expected. As an example, calculating the most similar words pet is getting the following results:
ms=word2vec_model.most_similar('pet')
('fastfood', 0.20879755914211273)
('hammer', 0.20450574159622192)
('allur', 0.20118337869644165)
('wright', 0.20001833140850067)
('daili', 0.1990675926208496)
('mgt', 0.1908089816570282)
('mcintosh', 0.18571510910987854)
('autopart', 0.1729743778705597)
('metamorphosi', 0.16965581476688385)
('doak', 0.16890916228294373)
In the dataset, I have words such as paws or petcare, but other words are creating relationships with pet word.
This is the distribution of the nearer words for pet:
On the other hand, when I used the GoogleNews-vectors-negative300.bin.gz, I could not add new words to the vocab, but the similarity between pet and words around was as expected:
ms=word2vec_model.most_similar('pet')
('pets', 0.771199643611908)
('Pet', 0.723974347114563)
('dog', 0.7164785265922546)
('puppy', 0.6972636580467224)
('cat', 0.6891531348228455)
('cats', 0.6719794869422913)
('pooch', 0.6579219102859497)
('Pets', 0.636363685131073)
('animal', 0.6338439583778381)
('dogs', 0.6224827170372009)
This is the distribution of the nearest words:
I would like to get your advice about the following:
Is this dataset appropriate to proceed with this model?
Is the length of the dataset enough to allow word2vec "learn" the relationships between the words?
What can I do to improve the model to make word2vec create relationships of the same type as GoogleNews where for instance word pet is correctly set among similar words?
Is it feasible to implement another alternative such as fasttext considering the nature of the current dataset?
Do you know any public dataset that can be used along with the current dataset to create those relationships?
Thanks
3500 texts (company names) of just ~3 words each is only around 10k total training words, with a much smaller vocabulary of unique words.
That's very, very small for word2vec & related algorithms, which rely on lots of data, and sufficiently-varied data, to train-up useful vector arrangements.
You may be able to squeeze some meaningful training from limited data by using far more training epochs than the default epochs=5, and far smaller vectors than the default size=100. With those sorts of adjustments, you may start to see more meaningful most_similar() results.
But, it's unclear that word2vec, and specifically word2vec in your averaging-of-a-name's-words comparisons, is matched to your end goals.
Word2vec needs lots of data, doesn't look at subword units, and can't say anything about word-tokens not seen during training. An average-of-many-word-vectors can often work as an easy baseline for comparing multiword texts, but might also dilute some word's influence compared to other methods.
Things to consider might include:
Word2vec-related algorithms like FastText that also learn vectors for subword units, and can thus bootstrap not-so-bad guess vectors for words not seen in training. (But, these are also data hungry, and to use on a small dataset you'd again want to reduce vector size, increase epochs, and additionally shrink the number of buckets used for subword learning.)
More sophisticated comparisons of multi-word texts, like "Word Mover's Distance". (That can be quite expensive on longer texts, but for names/titles of just a few words may be practical.)
Finding more data that's compatible with your aims for a stronger model. A larger database of company names might help. If you just want your analysis to understand English words/roots, more generic training texts might work too.
For many purposes, a mere lexicographic comparison - edit distances, count of shared character-n-grams – may be helpful too, though it won't detect all synonyms/semantically-similar words.
Word2vec does not generalize to unseen words.
It does not even work well for wards that are seen but rare. It really depends on having many many examples of word usage. Furthermore a you need enough context left and right, but you only use company names - these are too short. That is likely why your embeddings perform so poorly: too little data and too short texts.
Hence, it is the wrong approach for you. Retraining the model with the new company name is not enough - you still only have one data point. You may as well leave out unseen words, word2vec cannot work better than that even if you retrain.
If you only want to compute similarity between words, probably you don't need to insert new words in your vocabulary.
By eye, I think you can also use FastText without the need to stem the words. It also computes vectors for unknown words.
From FastText FAQ:
One of the key features of fastText word representation is its ability
to produce vectors for any words, even made-up ones. Indeed, fastText
word vectors are built from vectors of substrings of characters
contained in it. This allows to build vectors even for misspelled
words or concatenation of words.
FastText seems to be useful for your purpose.
For your task, you can follow FastText supervised tutorial.
If your corpus proves to be too small, you can build your model starting from availaible pretrained vectors (pretrainedVectors parameter).
I need some point of view to know if what I am doing is good or wrong or if there is better way to do it.
I have 10 000 elements. For each of them I have like 500 features.
I am looking to measure the separability between 2 sets of those elements. (I already know those 2 groups I don't try to find them)
For now I am using svm. I train the svm on 2000 of those elements, then I look at how good the score is when I test on the 8000 other elements.
Now I would like to now which features maximize this separation.
My first approach was to test each combination of feature with the svm and follow the score given by the svm. If the score is good those features are relevant to separate those 2 sets of data.
But this takes too much time. 500! possibility.
The second approach was to remove one feature and see how much the score is impacted. If the score changes a lot that feature is relevant. This is faster, but I am not sure if it is right. When there is 500 feature removing just one feature don't change a lot the final score.
Is this a correct way to do it?
Have you tried any other method ? Maybe you can try decision tree or random forest, it would give out your best features based on entropy gain. Can i assume all the features are independent of each other. if not please remove those as well.
Also for Support vectors , you can try to check out this paper:
http://axon.cs.byu.edu/Dan/778/papers/Feature%20Selection/guyon2.pdf
But it's based more on linear SVM.
You can do statistical analysis on the features to get indications of which terms best separate the data. I like Information Gain, but there are others.
I found this paper (Fabrizio Sebastiani, Machine Learning in Automated Text Categorization, ACM Computing Surveys, Vol. 34, No.1, pp.1-47, 2002) to be a good theoretical treatment of text classification, including feature reduction by a variety of methods from the simple (Term Frequency) to the complex (Information-Theoretic).
These functions try to capture the intuition that the best terms for ci are the
ones distributed most differently in the sets of positive and negative examples of
ci. However, interpretations of this principle vary across different functions. For instance, in the experimental sciences χ2 is used to measure how the results of an observation differ (i.e., are independent) from the results expected according to an initial hypothesis (lower values indicate lower dependence). In DR we measure how independent tk and ci are. The terms tk with the lowest value for χ2(tk, ci) are thus the most independent from ci; since we are interested in the terms which are not, we select the terms for which χ2(tk, ci) is highest.
These techniques help you choose terms that are most useful in separating the training documents into the given classes; the terms with the highest predictive value for your problem. The features with the highest Information Gain are likely to best separate your data.
I've been successful using Information Gain for feature reduction and found this paper (Entropy based feature selection for text categorization Largeron, Christine and Moulin, Christophe and Géry, Mathias - SAC - Pages 924-928 2011) to be a very good practical guide.
Here the authors present a simple formulation of entropy-based feature selection that's useful for implementation in code:
Given a term tj and a category ck, ECCD(tj , ck) can be
computed from a contingency table. Let A be the number
of documents in the category containing tj ; B, the number
of documents in the other categories containing tj ; C, the
number of documents of ck which do not contain tj and D,
the number of documents in the other categories which do
not contain tj (with N = A + B + C + D):
Using this contingency table, Information Gain can be estimated by:
This approach is easy to implement and provides very good Information-Theoretic feature reduction.
You needn't use a single technique either; you can combine them. Term-Frequency is simple, but can also be effective. I've combined the Information Gain approach with Term Frequency to do feature selection successfully. You should experiment with your data to see which technique or techniques work most effectively.
If you want a single feature to discriminate your data, use a decision tree, and look at the root node.
SVM by design looks at combinations of all features.
Have you thought about Linear Discriminant Analysis (LDA)?
LDA aims at discovering a linear combination of features that maximizes the separability. The algorithm works by projecting your data in a space where the variance within classes is minimum and the one between classes is maximum.
You can use it reduce the number of dimensions required to classify, and also use it as a linear classifier.
However with this technique you would lose the original features with their meaning, and you may want to avoid that.
If you want more details I found this article to be a good introduction.
Usually one wants to get a feature from a text by using the bag of words approach, counting the words and calculate different measures, for example tf-idf values, like this: How to include words as numerical feature in classification
But my problem is different, I want to extract a feature vector from a single word. I want to know for example that potatoes and french fries are close to each other in the vector space, since they are both made of potatoes. I want to know that milk and cream also are close, hot and warm, stone and hard and so on.
What is this problem called? Can I learn the similarities and features of words by just looking at a large number documents?
I will not make the implementation in English, so I can't use databases.
hmm,feature extraction (e.g. tf-idf) on text data are based on statistics. On the other hand, you are looking for sense (semantics). Therefore no such a method like tf-idef will work for you.
In NLP exists 3 basic levels:
morphological analyses
syntactic analyses
semantic analyses
(higher number represents bigger problems :)). Morphology is known for majority languages. Syntactic analyses is a bigger problem (it deals with things like what is verb, noun in some sentence,...). Semantic analyses has the most challenges, since it deals with meaning which is quite difficult to represent in machines, have many exceptions and are language-specific.
As far as I understand you want to know some relationships between words, this can be done via so-called dependency tree banks, (or just treebank): http://en.wikipedia.org/wiki/Treebank . It is a database/graph of sentences where a word can be considered as a node and relationship as arc. There is good treebank for czech language and for english there will be also some, but for many 'less-covered' languages it can be a problem to find one ...
user1506145,
Here is a simple idea that I have used in the past. Collect a large number of short documents like Wikipedia articles. Do a word count on each document. For the ith document and the jth word let
I = the number of documents,
J = the number of words,
x_ij = the number of times the jth word appears in the ith document, and
y_ij = ln( 1+ x_ij).
Let [U, D, V] = svd(Y) be the singular value decomposition of Y. So Y = U*D*transpose(V)), U is IxI, D is diagonal IxJ, and V is JxJ.
You can use (V_1j, V_2j, V_3j, V_4j) as a feature vector in R^4 for the jth word.
I am surprised the previous answers haven't mentioned word embedding. Word embedding algorithm can produce word vectors for each word a given dataset. These algorithms can nfer word vectors from the context. For instance, by looking at the context of the following sentences we can say that "clever" and "smart" is somehow related. Because the context is almost the same.
He is a clever guy
He is a smart guy
A co-occurrence matrix can be constructed to do this. However, it is too inefficient. A famous technique designed for this purpose is called Word2Vec. It can be studied from the following papers.
https://arxiv.org/pdf/1411.2738.pdf
https://arxiv.org/pdf/1402.3722.pdf
I have been using it for Swedish. It is quite effective in detecting similar words and completely unsupervised.
A package could be find in gensim and tensorflow.
I have question regarding the particular Naive Bayse algorithm that is used in document classification. Following is what I understand:
construct some probability of each word in the training set for each known classification
given a document we strip all the words that it contains
multiply together the probabilities of the words being present in a classification
perform (3) for each classification
compare the result of (4) and choose the classification with the highest posterior
What I am confused about is the part when we calculate the probability of each word given training set. For example for a word "banana", it appears in 100 documents in classification A, and there are totally 200 documents in A, and in total 1000 words appears in A. To get the probability of "banana" appearing under classification A do I use 100/200=0.5 or 100/1000=0.1?
I believe your model will more accurately classify if you count the number of documents the word appears in, not the number of times the word appears in total. In other words
Classify "Mentions Fruit":
"I like Bananas."
should be weighed no more or less than
"Bananas! Bananas! Bananas! I like them."
So the answer to your question would be 100/200 = 0.5.
The description of Document Classification on Wikipedia also supports my conclusion
Then the probability that a given document D contains all of the words W, given a class C, is
http://en.wikipedia.org/wiki/Naive_Bayes_classifier
In other words, the document classification algorithm Wikipedia describes tests how many of the list of classifying words a given document contains.
By the way, more advanced classification algorithms will examine sequences of N-words, not just each word individually, where N can be set based on the amount of CPU resources you are willing to dedicate to the calculation.
UPDATE
My direct experience is based on short documents. I would like to highlight research that #BenAllison points out in the comments that suggests my answer is invalid for longer documents. Specifically
One weakness is that by considering only the presence or absence of terms, the BIM ignores information inherent in the frequency of terms. For instance, all things being equal, we would expect that if 1 occurrence of a word is a good clue that a document belongs in a class, then 5 occurrences should be even more predictive.
A related problem concerns document length. As a document gets longer, the number of distinct words used, and thus the number of values of x(j) that equal 1 in the BIM, will in general increase.
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.1529
What does dimensionality reduction mean exactly?
I searched for its meaning, I just found that it means the transformation of raw data into a more useful form. So what is the benefit of having data in useful form, I mean how can I use it in a practical life (application)?
Dimensionality Reduction is about converting data of very high dimensionality into data of much lower dimensionality such that each of the lower dimensions convey much more information.
This is typically done while solving machine learning problems to get better features for a classification or regression task.
Heres a contrived example - Suppose you have a list of 100 movies and 1000 people and for each person, you know whether they like or dislike each of the 100 movies. So for each instance (which in this case means each person) you have a binary vector of length 100 [position i is 0 if that person dislikes the i'th movie, 1 otherwise ].
You can perform your machine learning task on these vectors directly.. but instead you could decide upon 5 genres of movies and using the data you already have, figure out whether the person likes or dislikes the entire genre and, in this way reduce your data from a vector of size 100 into a vector of size 5 [position i is 1 if the person likes genre i]
The vector of length 5 can be thought of as a good representative of the vector of length 100 because most people might be liking movies only in their preferred genres.
However its not going to be an exact representative because there might be cases where a person hates all movies of a genre except one.
The point is, that the reduced vector conveys most of the information in the larger one while consuming a lot less space and being faster to compute with.
You're question is a little vague, but there's an interesting statistical technique that may be what you're thinking off called Principal Component Analysis which does something similar (and incidentally plotting the results from which was my first real world programming task)
It's a neat, but clever technique which is remarkably widely applicable. I applied it to similarities between protein amino acid sequences, but I've seen it used for analysis everything from relationships between bacteria to malt whisky.
Consider a graph of some attributes of a collection of things where one has two independent variables - to analyse the relationship on these one obviously plots on two dimensions and you might see a scatter of points. if you've three variable you can use a 3D graph, but after that one starts to run out of dimensions.
In PCA one might have dozens or even a hundred or more independent factors, all of which need to be plotted on perpendicular axis. Using PCA one does this, then analyses the resultant multidimensional graph to find the set of two or three axis within the graph which contain the largest amount of information. For example the first Principal Coordinate will be a composite axis (i.e. at some angle through n-dimensional space) which has the most information when the points are plotted along it. The second axis is perpendicular to this (remember this is n-dimensional space, so there's a lot of perpendiculars) which contains the second largest amount of information etc.
Plotting the resultant graph in 2D or 3D will typically give you a visualization of the data which contains a significant amount of the information in the original dataset. It's usual for the technique to be considered valid to be looking for a representation that contains around 70% of the original data - enough to visualize relationships with some confidence that would otherwise not be apparent in the raw statistics. Notice that the technique requires that all factors have the same weight, but given that it's an extremely widely applicable method that deserves to be more widely know and is available in most statistical packages (I did my work on an ICL 2700 in 1980 - which is about as powerful as an iPhone)
http://en.wikipedia.org/wiki/Dimension_reduction
maybe you have heard of PCA (principle component analysis), which is a Dimension reduction algorithm.
Others include LDA, matrix factorization based methods, etc.
Here's a simple example. You have a lot of text files and each file consists some words. There files can be classified into two categories. You want to visualize a file as a point in a 2D/3D space so that you can see the distribution clearly. So you need to do dimension reduction to transfer a file containing a lot of words into only 2 or 3 dimensions.
The dimensionality of a measurement of something, is the number of numbers required to describe it. So for example the number of numbers needed to describe the location of a point in space will be 3 (x,y and z).
Now lets consider the location of a train along a long but winding track through the mountains. At first glance this may appear to be a 3 dimensional problem, requiring a longitude, latitude and height measurement to specify. But this 3 dimensions can be reduced to one if you just take the distance travelled along the track from the start instead.
If you were given the task of using a neural network or some statistical technique to predict how far a train could get given a certain quantity of fuel, then it will be far easier to work with the 1 dimensional data than the 3 dimensional version.
It's a technique of data mining. Its main benefit is that it allows you to produce a visual representation of many-dimensional data. The human brain is peerless at spotting and analyzing patterns in visual data, but can process a maximum of three dimensions (four if you use time, i.e. animated displays) - so any data with more than 3 dimensions needs to somehow compressed down to 3 (or 2, since plotting data in 3D can often be technically difficult).
BTW, a very simple form of dimensionality reduction is the use of color to represent an additional dimension, for example in heat maps.
Suppose you're building a database of information about a large collection of adult human beings. It's also going to be quite detailed. So we could say that the database is going to have large dimensions.
AAMOF each database record will actually include a measure of the person's IQ and shoe size. Now let's pretend that these two characteristics are quite highly correlated. Compared to IQs shoe sizes may be easy to measure and we want to populate the database with useful data as quickly as possible. One thing we could do would be to forge ahead and record shoe sizes for new database records, postponing the task of collecting IQ data for later. We would still be able to estimate IQs using shoe sizes because the two measures are correlated.
We would be using a very simple form of practical dimension reduction by leaving IQ out of records initially. Principal components analysis, various forms of factor analysis and other methods are extensions of this simple idea.