Data Representation in Machine Learning

In implementing most of the machine learning algorithms, we represent each data point with a feature vector as the input. A vector is basically an array of numerics, or in physics, an object with magnitude and direction. How do we represent our business data in terms of a vector?

Primitive Feature Vector

Whether the data are measured observations, or images (pixels), free text, factors, or shapes, they can be categorized into four following types:

  1. Categorical data
  2. Binary data
  3. Numerical data
  4. Graphical data

The most primitive representation of a feature vector looks like this:

Screen Shot 2019-09-15 at 3.58.09 PM
A typical feature vector. (Source: https://www.researchgate.net/publication/318740904_Chat_Detection_in_an_Intelligent_Assistant_Combining_Task-oriented_and_Non-task-oriented_Spoken_Dialogue_Systems/figures?lo=1)

Numerical Data

Numerical data can be represented as individual elements above (like Tweet GRU, Query GRU), and I am not going to talk too much about it.

Categorical Data

However, for categorical data, how do we represent them? The first basic way is to use one-hot encoding:

Screen Shot 2019-09-15 at 4.02.51 PM
One-hot encoding of categorical data (Source: https://developers.google.com/machine-learning/data-prep/transform/transform-categorical)

For each type of categorical data, each category has an integer code. In the figure above, each color has a code (0 for red, 1 for orange etc.) and they will eventually be transformed to the feature vector on the right, with vector length being the total number of categories found in the data, and the element will be filled with 1 if it is of that category. This allows a natural way of dealing with missing data (with all elements 0) and multi-category (with multiple non-zeros).

In natural language processing, the bag-of-words model is often used to represent free-text data, which is the one-hot encoding above with words as the categories. It is a good way as long as the order of the words does not matter.

Binary Data

For binary data, it can be easily represented by one element, either 1 or 0.

Graphical Data

Graphical data are best represented in terms of graph Laplacian and adjacency matrix. Refer to a previous blog article for more information.

Shortcomings

A feature vector can be a concatenation of various features in terms of all these types except graphical data.

However, such representation that concatenates all the categorical, binary, and numerical fields has a lot of shortcomings:

  1. Data with different categories are often seen as orthogonal, i.e., perfectly dissimilar.  It ignores the correlation between different variables. However, it is a very big assumption.
  2. The weights of different fields are not considered.
  3. Sometimes if the numerical values are very large, it outweighs other categorical data in terms of influence in computation.
  4. Data are very sparse, costing a lot of memory waste and computing time.
  5. It is unknown whether some of the data are irrelevant.

Modifying Feature Vectors

In light of the shortcomings, to modify the feature factors, there are three main ways of dealing with this:

  1. Rescaling: rescaling all of some of the elements, or reweighing, to adjust the influence from different variables.
  2. Embedding: condensing the information into vectors of smaller lengths.
  3. Sparse coding: deliberately extend the vectors to a larger length.

Rescaling

Rescaling means rescaling all or some of the elements in the vectors. Usually there are two ways:

  1. Normalization: normalizing all the categories of one feature to having the sum of 1.
  2. Term frequency-inverse document frequency (tf-idf): weighing the elements so that the weights are heavier if the frequency is higher and it appears in relatively few documents or class labels.

Embedding

Embedding means condensing a sparse vector to a smaller vector. Many sparse elements disappear and information is encoded inside the elements. There are rich amount of work on this.

  1. Topic models: finding the topic models (latent Dirichlet allocation (LDA),  structural topic models (STM) etc.) and encode the vectors with topics instead;
  2. Global dimensionality reduction algorithms: reducing the dimensions by retaining the principal components of the vectors of all the data, e.g., principal component analysis (PCA), independent component analysis (ICA), multi-dimensional scaling (MDS) etc;
  3. Local dimensionality reduction algorithms: same as the global, but these are good for finding local patterns, where examples include t-Distributed Stochastic Neighbor Embedding (tSNE) and Uniform Manifold Approximation and Projection (UMAP);
  4. Representation learned from deep neural networks: embeddings learned from encoding using neural networks, such as auto-encoders, Word2Vec, FastText, BERT etc.
  5. Mixture Models: Gaussian mixture models (GMM), Dirichlet multinomial mixture (DMM) etc.
  6. Others: Tensor decomposition (Schmidt decomposition, Jennrich algorithm etc.), GloVe etc.

Sparse Coding

Sparse coding is good for finding basis vectors for dense vectors.

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Summarizing Text Summarization

There are many tasks in natural language processing that are challenging. This blog entry is on text summarization, which briefly summarizes the survey article on this topic. (arXiv:1707.02268) The authors of the article defined the task to be

Automatic text summarization is the task of producing a concise and fluent summary while preserving key information content and overall meaning.

There are basically two approaches to this task:

  • extractive summarization: identifying important sections of the text, and extracting them; and
  • abstractive summarization: producing summary text in a new way.

Most algorithmic methods developed are of the extractive type, while most human writers summarize using abstractive approach. There are many methods in extractive approach, such as identifying given keywords, identifying sentences similar to the title, or wrangling the text at the beginning of the documents.

How do we instruct the machines to perform extractive summarization? The authors mentioned about two representations: topic and indicator. In topic representations, frequencies, tf-idf, latent semantic indexing (LSI), or topic models (such as latent Dirichlet allocation, LDA) are used. However, simply extracting these sentences out with these algorithms may not generate a readable summary. Employment of knowledge bases or considering contexts (from web search, e-mail conversation threads, scientific articles, author styles etc.) are useful.

In indicator representation, the authors mentioned the graph methods, inspired by PageRank. (see this) “Sentences form vertices of the graph and edges between the sentences indicate how similar the two sentences are.” And the key sentences are identified with ranking algorithms. Of course, machine learning methods can be used too.

Evaluation on the performance on text summarization is difficult. Human evaluation is unavoidable, but with manual approaches, some statistics can be calculated, such as ROUGE.

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Generative Adversarial Networks

Recently I have been drawn to generative models, such as LDA (latent Dirichlet allocation) and other topic models. In deep learning, there are a few examples, such as FVBN (fully visible belief networks), VAE (variational autoencoder), RBM (restricted Boltzmann machine) etc. Recently I have been reading about GAN (generative adversarial networks), first published by Ian Goodfellow and his colleagues and collaborators. Goodfellow published his talk in NIPS 2016 on arXiv recently.

Yesterday I attended an event at George Mason University organized by Data Science DC Meetup Group. Jennifer Sleeman talked about GAN. It was a very good talk.

In GAN, there are two important functions, namely, the discriminator (D), and the generator (G). As a generative model, the distribution of training data, all labeled positive, can be thought of the distribution that the generator was trained to produce. The discriminator discriminates the data with positive labels and those with negative labels. Then the generator tries to generate data, probably from noises, which should be negative, to fake the discriminator to see it as positive. This process repeats iteratively, and eventually the generator is trained to produce data that are close to the distribution of the training data, and the discriminator will be confused to classify the generated data as positive with probability \frac{1}{2}. The intuition of this competitive game is from minimax game in game theory. The formal algorithm is described in the original paper as follow:

gan_algorithm

The original paper discussed about that the distribution of final generated data identical to that of the training data being the optimal for the model, and argued using the Jensen-Shannon (JS) divergence. Ferenc Huszár discussed in his blog about the relations between maximum likelihood, Kullback-Leibler (KL) divergence, and Jensen-Shannon (JS) divergence.

I have asked the speaker a few questions about the concepts of GAN as well.

GAN is not yet a very sophisticated framework, but it already found a few industrial use. Some of its descendants include LapGAN (Laplacian GAN), and DCGAN (deep convolutional GAN). Applications include voice generation, image super-resolution, pix2pix (image-to-image translation), text-to-image synthesis, iGAN (interactive GAN) etc.

Adversarial training is the coolest thing since sliced bread.” – Yann LeCun

16427477_10105464843466738_3344635019272539994_n

 

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Author-Topic Models in gensim

Recently, gensim, a Python package for topic modeling, released a new version of its package which includes the implementation of author-topic models.

The most famous topic model is undoubtedly latent Dirichlet allocation (LDA), as proposed by David Blei and his colleagues. Such a topic model is a generative model, described by the following directed graphical models:

lda_pic

In the graph, \alpha and \beta are hyperparameters. \theta is the topic distribution of a document, z is the topic for each word in each document, \phi is the word distributions for each topic, and w is the generated word for a place in a document.

There are models similar to LDA, such as correlated topic models (CTM), where \phi is generated by not only \beta but also a covariance matrix \Sigma.

There exists an author model, which is a simpler topic model. The difference is that the words in the document are generated from the author for each document, as in the following graphical model. x is the author of a given word in the document.

author_pic

Combining these two, it gives the author-topic model as a hybrid, as shown below:

authortopic_pic

The new release of Python package, gensim, supported the author-topic model, as demonstrated in this Jupyter Notebook.

P.S.:

  • I am also aware that there is another topic model called structural topic model (STM), developed for the field of social science. However, there is no Python package supporting this, but an R package, called stm, is available for it. You can refer to their homepage too.
  • I may consider including author-topic model and STM in the next release of the Python package shorttext.

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Local and Global: Words and Topics

Word2Vec has hit the NLP world for a while, as it is a nice method for word embeddings or word representations. Its use of skip-gram model and deep learning made a big impact too. It has been my favorite toy indeed. However, even though the words do have a correlation across a small segment of text, it is still a local coherence. On the other hand, topic models such as latent Dirichlet allocation (LDA) capture the distribution of words within a topic, and that of topics within a document etc. And it provides a representation of a new document in terms of a topic.

In my previous blog entry, I introduced Chris Moody’s LDA2Vec algorithm (see: his SlideShare). Unfortunately, not many papers or blogs have covered this new algorithm too much despite its potential. The API is not completely well documented yet, although you can see its example from its source code on its Github. In its documentation, it gives an example of deriving topics from an array of random numbers, in its lda2vec/lda2vec.py code:

from lda2vec import LDA2Vec
n_words = 10
n_docs = 15
n_hidden = 8
n_topics = 2
n_obs = 300
words = np.random.randint(n_words, size=(n_obs))
_, counts = np.unique(words, return_counts=True)
model = LDA2Vec(n_words, n_hidden, counts)
model.add_categorical_feature(n_docs, n_topics, name='document id')
model.finalize()
doc_ids = np.arange(n_obs) % n_docs
loss = model.fit_partial(words, 1.0, categorical_features=doc_ids)

A more comprehensive example is in examples/twenty_newsgroup/lda.py .

Besides, LDA2Vec, there are some related research work on topical word embeddings too. A group of Australian and American scientists studied about the topic modeling with pre-trained Word2Vec (or GloVe) before performing LDA. (See: their paper and code) On the other hand, another group with Chinese and Singaporean scientists performs LDA, and then trains a Word2Vec model. (See: their paper and code) And LDA2Vec concatenates the Word2Vec and LDA representation, like an early fusion.

No matter what, representations with LDA models (or related topic modeling such as correlated topic models (CTM)) can be useful even outside NLP. I have found it useful at some intermediate layer of calculation lately.

proj3_lda20structure
Graphical Representations of LDA model. Source: http://salsahpc.indiana.edu/b649proj/images/proj3_LDA%20structure.png

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LDA2Vec: a hybrid of LDA and Word2Vec

Both LDA (latent Dirichlet allocation) and Word2Vec are two important algorithms in natural language processing (NLP). LDA is a widely used topic modeling algorithm, which seeks to find the topic distribution in a corpus, and the corresponding word distributions within each topic, with a prior Dirichlet distribution. Word2Vec is a vector-representation model, trained from RNN (recurrent neural network), to seek a continuous representation for words.

They are both very useful, but LDA deals with words and documents globally, and Word2Vec locally (depending on adjacent words in the training data). A LDA vector is so sparse that the users can interpret the topic easily, but it is inflexible. Word2Vec’s representation is not human-interpretable, but it is easy to use. In his slides, Chris Moody recently devises a topic modeling algorithm, called LDA2Vec, which is a hybrid of the two, to get the best out of the two algorithms.

Honestly, I never used this algorithm. I rarely talk about something I didn’t even try, but I want to raise awareness so that more people know about it when I come to use it. To me, it looks like concatenating two vectors with some hyperparameters, but  the source codes rejects this claim. It is a topic model algorithm.

There are not many blogs or papers talking about LDA2Vec yet. I am looking forward to learning more about it when there are more awareness.

lda2vec
Jupyter Notebook for LDA2Vec Demonstration [link]
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Computational Journalism

We “sensed” what has been the current hot issues in the past (and we still often do today.) Methods of “sensing,” or “detecting”, is now more sophisticated however as the computational technologies are now more advanced. The methods involved can be collected to a field called “computational journalism.”

Recently, there is a blog post by Jeiran about understanding the public impression about Iran using computational methods. She divided the question into the temporal and topical perspectives. The temporal perspective is about various time-varying patterns of the number of related news articles; the topical perspective is about the distribution of various topics, using latent Dirichlet allocation (LDA), and Bayes’ Theorem. The blog post is worth reading.

In February last year, there was a video clip online that Daeil Kim, a data scientist at New York Times, spoke at NYC Data Science Meetup. Honestly, I still have not watched it yet (but I think I should have.) What his work is also about computational journalism, on his algorithm, and LDA.

Of course, computational journalism is the application of natural language processing and machine learning on news articles… However, as a computational physicist has to know physics, a computational journalist has to know journalism. A data scientist has to be someone who knows the technology and the subject matter.

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Useful Python Packages

python
(Taken from http://latticeqcd.org/pythonorg/static/images/antigravity.png, adapted from http://xkcd.com/353/)

Python is the basic programming languages if one wants to work on data nowadays. Its popularity comes with its intuitive syntax, its support of several programming paradigms, and the package numpy (Numerical Python). Yes, if you asked which package is a “must-have” outside the standard Python packages, I would certainly name numpy.

Let me list some useful packages that I have found useful:

  1. numpy: Numerical Python. Its basic data type is ndarray, which acts like a vector with vectorized calculation support. It makes Python to perform matrix calculation efficiently like MATLAB and Octave. It supports a lot of commonly used linear algebraic algorithms, such as eigenvalue problems, SVD etc. It is the basic of a lot of other Python packages that perform heavy numerical computation. It is such an important package that, in some operating systems, numpy comes with Python as well.
  2. scipy: Scientific Python. It needs numpy, but it supports also sparse matrices, special functions, statistics, numerical integration…
  3. matplotlib: Graph plotting.
  4. scikit-learn: machine learning library. It contains a number of supervised and unsupervised learning algorithms.
  5. nltk: natural language processing. It provides not only basic tools like stemmers, lemmatizers, but also some algorithms like maximum entropy, tf-idf vectorizer etc. It provides a few corpuses, and supports WordNet dictionary.
  6. gensim: another useful natural language processing package with an emphasis on topic modeling. It mainly supports Word2Vec, latent semantic indexing (LSI), and latent Dirichlet allocation (LDA). It is convenient to construct term-document matrices, and convert them to matrices in numpy or scipy.
  7. networkx: a package that supports both undirected and directed graphs. It provides basic algorithms used in graphs.
  8. sympy: Symbolic Python. I am not good at this package, but I know mathics and SageMath are both based on it.
  9. pandas: it supports data frame handling like R. (I have not used this package as I am a heavy R user.)

Of course, if you are a numerical developer, to save you a good life, install Anaconda.

There are some other packages that are useful, such as PyCluster (clustering), xlrd (Excel files read/write), PyGame (writing games)… But since I have not used them, I would rather mention it in this last paragraph, not to endorse but avoid devaluing it.

Don’t forget to type in your IPython Notebook:

import antigravity

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