How to compare bubble charts programmatically? - statistics

1.) I have data points for a bubble chart of age vs weight [['<15 yr', 30], ['<25 yr', 60], ...]
2.) I also have 4 or 5 canned models for overweight population, malnutrition, etc.
How to tell (programmatically) if a given set of data matches any of the pre-determined models.
What specific math or statistics literature I need to look for direction.

In statistics this is usually studied using a Goodness of fit test. Any good statistics book should cover this topic. This question might be a good candidate for stats.stackexchange.com

Related

Number of training samples for text classification tas

Suppose you have a set of transcribed customer service calls between customers and human agents, where on average each call's length is 7 minutes. Customers will mostly call because of issues they have with the product. Let's assume that a human can assign one label per axis per call:
Axis 1: What was the problem from the customer's perspective?
Axis 2: What was the problem from the agent's perspective?
Axis 3: Could the agent resolve the customer's issue?
Based on the manually labeled texts you want to train a text classifier that shall predict a label for each call for each of the three axes. But the labeling of recordings takes time and costs money. On the other hand you need a certain amount of training data to get good prediction results.
Given the above assumptions, how many manually labeled training texts would you start with? And how do you know that you need more labeled training texts?
Maybe you've worked on a similar task before and can give some advice.
UPDATE (2018-01-19): There's no right or wrong answer to my question. Ok, ideally, somebody worked on exactly the same task, but that's very unlikely. I'll leave the question open for one more week and then accept the best answer.
This would be tricky to answer but I will try my best based on my experience.
In the past, I have performed text classification on 3 datasets; the number in the bracket indicates how big my dataset was: restaurant reviews (50K sentences), reddit comments (250k sentences) and developer comments from issue tracking systems (10k sentences). Each of them had multiple labels as well.
In each of the three cases, including the one with 10k sentences, I achieved an F1 score of more than 80%. I am stressing on this dataset specifically because I was told by some that the size is less for this dataset.
So, in your case, assuming you have atleast 1000 instances (calls that include conversation between customer and agent) of average 7 minute calls, this should be a decent start. If the results are not satisfying, you have the following options:
1) Use different models (MNB, Random Forest, Decision Tree, and so on in addition to whatever you are using)
2) If point 1 gives more or less similar results, check the ratio of instances of all the classes you have (the 3 axis you are talking about here). If they do not share a good ratio, get more data or try out the different balancing techniques if you cannot get more data.
3) Another way would be to classify them at a sentence level than message or conversation level to generate more data and individual labels for sentences rather than message or the conversation itself.

interpretation of SVD for text mining topic analysis

Background
I'm learning about text mining by building my own text mining toolkit from scratch - the best way to learn!
SVD
The Singular Value Decomposition is often cited as a good way to:
Visualise high dimensional data (word-document matrix) in 2d/3d
Extract key topics by reducing dimensions
I've spent about a month learning about the SVD .. I must admit much of the online tutorials, papers, university lecture slides, .. and even proper printed textbooks are not that easy to digest.
Here's my understanding so far: SVD demystified (blog)
I think I have understood the following:
Any (real) matrix can be decomposed uniquely into 3 multiplied
matrices using SVD, A=U⋅S⋅V^T
S is a diagonal matrix of singular values, in descending order of magnitude
U and V^T are matrices of orthonormal vectors
I understand that we can reduce the dimensions by filtering out less significant information by zero-ing the smaller elements of S, and reconstructing the original data. If I wanted to reduce dimensions to 2, I'd only keep the 2 top-left-most elements of the diagonal S to form a new matrix S'
My Problem
To see the documents projected onto the reduced dimension space, I've seen people use S'⋅V^T. Why? What's the interpretation of S'⋅V^T?
Similarly, to see the topics, I've seen people use U⋅S'. Why? What's the interpretation of this?
My limited school maths tells me I should look at these as transformations (rotation, scale) ... but that doesn't help clarify it either.
** Update **
I've added an update to my blog explanation at SVD demystified (blog) which reflects the rationale from one of the textbooks I looked at to explain why S'.V^T is a document view, and why U.S' is a word view. Still not really convinced ...

PredictionIO for Content Recommendation e.g. Tweets

I recently installed PredictionIO.
What I'd like to achieve is: I'd like to categorize content on the words included in the text. But how can I import data like raw Tweets to PredictionIO? Is it possible to let PredictionIO run over the content and find strong words and to sort them in categories?
What I'd like to get is something like this: Query for Boston Red Sox --> keywords that should appear would be: baseball, Boston, sports, ...
So I'll add on a little to what Thomas said. He's right, it all depends whether or not you have labels associated to your tweets. If your data is labeled then this will be a Text Classification problem. Look at this for more detailed info:
If you're instead looking to cluster, or group, a set of unlabeled observations then, as Thomas said, your best bet is to incorporate LDA into the works. Look at the latter documentation for more information, but basically once you run the LDA model you'll obtain an object of type DistributedLDAModel which has a method topicDistributions which gives you, for each tweet, a vector where each component is associated to a topic, and the component entry gives you the probability that the tweet belongs to that topic. You can cluster by assigning each tweet the topic with highest probability.
You also have access to a matrix of size MxN, where M is the number of words in your vocabulary, and N is the number of topics, or clusters, you wish to discover in your data. You can roughly interpret the ij th entry of this Topics Matrix as the probability that the word i appears in a document given that the document belongs to topic j. Another rule you could use for clustering is to treat each word vector associated to your tweets as a vector of counts. Then, you can interpret the ij entry of the product of your word matrix (tweets as rows, words as columns) and the Topics Matrix returned by LDA as the probability that tweet i belongs to topic j (this follows under certain assumptions, feel free to ask if you want more details). Again now you assign tweet i to the topic associated to the largest numerical value in row i of the resulting matrix. You can even use this clustering rule for assigning topics to incoming observations once you have used your original set of tweets for topic discovery!
Now, for data processing, you can still use the Text Classification reference for transforming your Tweets to word count vectors via the DataSource and Preparator components. As for importing your data, if you have the tweets saved locally on a file, you can use PredictionIO's Python SDK to import your data. An example is also given in the classification reference.
Feel free to ask any questions if anything isn't clear, and good luck!
So, really depends on if you have labelled data.
For example:
Baseball :: "I love Boston Red Sox #GoRedSox"
Sports :: "Woohoo! I love sports #winning"
Boston :: "Baseball time at Fenway Park. Red Sox FTW!"
...
Then you would be able to train a model to classifying Tweets against these keywords. You might be interested in templates for MLlib Naive Bayes, Decision Trees.
If you don't have labelled data (really, who wants to manually label Tweets) you might be able to use approaches such as Topic Modeling (e.g., LDA).
I don't think there is a template for LDA but being an active open source project it wouldn't surprise me if someone has already implemented this so might be a good idea to ask on PredictionIO user or dev forums.

Systematic threshold for cosine similarity with TF-IDF weights

I am running an analysis of several thousand (e.g., 10,000) text documents. I have computed TF-IDF weights and have a matrix with pairwise cosine similarities. I want to treat the documents as a graph to analyze various properties (e.g., the path length separating groups of documents) and to visualize the connections as a network.
The problem is that there are too many similarities. Most are too small to be meaningful. I see many people dealing with this problem by dropping all similarities below a particular threshold, e.g., similarities below 0.5.
However, 0.5 (or 0.6, or 0.7, etc.) is an arbitrary threshold, and I'm looking for techniques that are more objective or systematic to get rid of tiny similarities.
I'm open to many different strategies. For example, is there a different alternative to tf-idf that would make most of the small similarities 0? Other methods to keep only significant similarities?
In short, take the average cosine value of an initial clustering or even all of the initial sentences and accept or reject clusters based on something akin to the following.
One way to look at the problem is to try and develop a score based on a distance from the mean similarity (1.5 standard deviations (86th percentile if the data were normal) tends to mark an outlier with 3 (99.9th percentile) being an extreme outlier), taking the high end for good measure. I cannot remember where, but this idea has had traction in other forums and formed the basis for my similarity.
Keep in mind that the data is not likely to be normally distributed.
average(cosine_similarities)+alpha*standard_deviation(cosine_similarities)
In order to obtain alpha, you could use the Wu Palmer score or another score as described by NLTK. Strong similarities with Wu Palmer should lead to a larger range of acceptance while lower Wu Palmer scores should lead to a more strict acceptance. Therefore, taking 1-Wu Palmer score would be adviseable. You can even use this method for LSA or LDA groups. To be even more strict and take things close to 1.5 or more standard deviations, you could even try 1+Wu Palmer (the cream of the crop), re-find the ultimate K,find the new score, cluster, and repeat.
Beware though, this would mean finding the Wu Palmer of all relevant words and is quite a large computational problem. Also, 10000 documents is peanuts compared to most algorithms. The smallest I have seen for tweets was 15,000 and the 20 news groups set was 20,000 documents. I am pretty sure Alchemy API uses something akin to the 20 news groups set. They definitely use senti-wordnet.
The basic equation is not really mine so feel free to dig around for it.
Another thing to keep in mind is that the calculation is time intensive. It may be a good idea to use a student t value for estimating the expected value/mean wu-palmer score of SOV pairings and especially good if you try to take the entire sentence. Commons Math3 for java/scala includes the distribution as does scipy for python and R should already have something as well.
Xbar +/- tsub(alpha/2)*sample_std/sqrt(sample_size)
Note: There is another option with this weight. You could use an algorithm that adds or subtracts from this threshold until achieving the best result. This would likely not be related solely to the cosine importance but possibly to an inflection point or gap as with Tibshirani's gap statistic.

How to know one system is siginficantly better than another one?

I am studying lexical semantics. I have 65 pairs of synonyms with their sense relatedness. The dataset is derived from the paper:
Rubenstein, Herbert, and John B. Goodenough. "Contextual correlates of synonymy." Communications of the ACM 8.10 (1965): 627-633.
I extract sentences containing those synonyms, transfer the neighbouring words appearing in those sentences to vectors, calculate the cosine distance between different vectors, and finally get the Pearson correlation between the distances we calculate and the sense relatedness given by Rubenstein and Goodenough
I get the Pearson correlation for Method 1 is 0.79, and for Method 2 is 0.78, for example. How do I measure Method 1 is significantly better than Method 2 or not?
Well Strictly not a programming question, but since this question is unanswered in others stackexchange sites, i'll tell the approach i would take.
I would say there are other benchmarks to check your approaches on similar tasks. You can check how your method performs on those benchmarks and analyze the results. Some methods may capture similarity more while others relatedness and some both.
This is the link WordVec Demo which automatically scores your vectors and provides you the results.

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