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Paper:
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Text Classification based on Word Subspace with Term-Frequency

Text classification has become indispensable due to the rapid increase of text in digital form. Over the past three decades, efforts have been made to approach this task using various learning algorithms and statistical models based on bag-of-words (BOW) features. Despite its simple implementation, BOW features lack semantic meaning representation. To solve this problem, neural networks started to be employed to learn word vectors, such as the word2vec. Word2vec embeds word semantic structure into vectors, where the angle between vectors indicates the meaningful similarity between words. To measure the similarity between texts, we propose the novel concept of word subspace, which can represent the intrinsic variability of features in a set of word vectors. Through this concept, it is possible to model text from word vectors while holding semantic information. To incorporate the word frequency directly in the subspace model, we further extend the word subspace to the term-frequency (TF) weighted word subspace. Based on these new concepts, text classification can be performed under the mutual subspace method (MSM) framework. The validity of our modeling is shown through experiments on the Reuters text database, comparing the results to various state-of-art algorithms.

Introduction
Text classification has become an indispensable task due to the rapid growth in the number of texts in digital form available online. It aims to classify different texts, also called documents, into a fixed number of predefined categories, helping to organize data, and making easier for users to find the desired information. Over the past three decades, many methods based on machine learning and statistical models have been applied to perform this task, such as latent semantic analysis (LSA), support vector machines (SVM), and multinomial naive Bayes (MNB).
The first step in utilizing such methods to categorize textual data is to convert the texts into a vector representation. One of the most popular text representation models is the bag-of-words model BIBREF0 , which represents each document in a collection as a vector in a vector space. Each dimension of the vectors represents a term (e.g., a word, a sequence of words), and its value encodes a weight, which can be how many times the term occurs in the document.
Despite showing positive results in tasks such as language modeling and classification BIBREF1 , BIBREF2 , BIBREF3 , the BOW representation has limitations: first, feature vectors are commonly very high-dimensional, resulting in sparse document representations, which are hard to model due to space and time complexity. Second, BOW does not consider the proximity of words and their position in the text and consequently cannot encode the words semantic meanings.
To solve these problems, neural networks have been employed to learn vector representations of words BIBREF4 , BIBREF5 , BIBREF6 , BIBREF7 . In particular, the word2vec representation BIBREF8 has gained attention. Given a training corpus, word2vec can generate a vector for each word in the corpus that encodes its semantic information. These word vectors are distributed in such a way that words from similar contexts are represented by word vectors with high correlation, while words from different contexts are represented by word vectors with low correlation.
One crucial aspect of the word2vec representation is that arithmetic and distance calculation between two word vectors can be performed, giving information about their semantic relationship. However, rather than looking at pairs of word vectors, we are interested in studying the relationship between sets of vectors as a whole and, therefore, it is desirable to have a text representation based on a set of these word vectors.
To tackle this problem, we introduce the novel concept of word subspace. It is mathematically defined as a low dimensional linear subspace in a word vector space with high dimensionality. Given that words from texts of the same class belong to the same context, it is possible to model word vectors of each class as word subspaces and efficiently compare them in terms of similarity by using canonical angles between the word subspaces. Through this representation, most of the variability of the class is retained. Consequently, a word subspace can effectively and compactly represent the context of the corresponding text. We achieve this framework through the mutual subspace method (MSM) BIBREF9 .
The word subspace of each text class is modeled by applying PCA without data centering to the set of word vectors of the class. When modeling the word subspaces, we assume only one occurrence of each word inside the class.
However, as seen in the BOW approach, the frequency of words inside a text is an informative feature that should be considered. In order to introduce this feature in the word subspace modeling and enhance its performance, we further extend the concept of word subspace to the term-frequency (TF) weighted word subspace.
In this extension, we consider a set of weights, which encodes the words frequencies, when performing the PCA. Text classification with TF weighted word subspace can also be performed under the framework of MSM. We show the validity of our modeling through experiments on the Reuters database, an established database for natural language processing tasks. We demonstrate the effectiveness of the word subspace formulation and its extension, comparing our methods' performance to various state-of-art methods.
The main contributions of our work are:
The remainder of this paper is organized as follows. In Section "Related Work" , we describe the main works related to text classification. In Section "Word subspace" , we present the formulation of our proposed word subspace. In Section "Conventional text classification methods" , we explain how text classification with word subspaces is performed under the MSM framework. Then, we present the TF weighted word subspace extension in Section "TF weighted word subspace" . Evaluation experiments and their results are described in Section "Experimental Evaluation" . Further discussion is then presented in Section "Discussion" , and our conclusions are described in Section "Conclusions and Future Work" .

TF weighted word subspace
The word subspace formulation presented in Section "Word subspace" is a practical and compact way to represent sets of word vectors, retaining most of the variability of features. However, as seen in the BOW features, the frequency of words is relevant information that can improve the characterization of a text. To incorporate this information into the word subspace modeling, we propose an extension of the word subspace, called the term-frequency (TF) weighted word subspace.
Like the word subspace, the TF weighted word subspace is mathematically defined as a low-dimensional linear subspace in a word vector space with high dimensionality. However, a weighted version of the PCA BIBREF25 , BIBREF26 is utilized to incorporate the information given by the frequencies of words (term-frequencies). This TF weighted word subspace is equivalent to the word subspace if we consider all occurrences of the words.
Consider the set of word vectors $\lbrace {x}_c^k\rbrace _{k=1}^{N_c} \in \mathbb {R}^{p}$ , which represents each word in the context $c$ , and the set of weights $\lbrace \omega _i\rbrace _{i=1}^{N_c}$ , which represent the frequencies of the words in the context $c$ .
We incorporate these frequencies into the subspace calculation by weighting the data matrix ${X}$ as follows: 
$${\widetilde{X}}={X}{\Omega }^{1/2},$$   (Eq. 33) 
where ${X} \in \mathbb {R}^{p \times N_c}$ is a matrix containing the word vectors $\lbrace {x}_c^k\rbrace _{k=1}^{N_c}$ and ${\Omega }$ is a diagonal matrix containing the weights $\lbrace \omega _i\rbrace _{i=1}^{N_c}$ .
We then perform PCA by solving the SVD of the matrix ${\widetilde{X}}$ : 
$${\widetilde{X}}={AMB}^{\top },$$   (Eq. 34) 
where the columns of the orthogonal matrices ${A}$ and ${B}$ are, respectively, the left-singular vectors and right-singular vectors of the matrix ${\widetilde{X}}$ , and the diagonal matrix ${M}$ contains singular values of ${\widetilde{X}}$ .
Finally, the orthonormal basis vectors of the $m_c$ -dimensional TF weighted subspace ${W}$ are the column vectors in ${A}$ corresponding to the $m_c$ largest singular values in ${M}$ .
Text classification with TF weighted word subspace can also be performed under the framework of MSM. In this paper, we will refer to MSM with TF weighted word subspace as TF-MSM.

Experimental Evaluation
In this section we describe the experiments performed to demonstrate the validity of our proposed method and its extension. We used the Reuters-8 dataset without stop words from BIBREF27 aiming at single-label classification, which is a preprocessed format of the Reuters-21578. Words in the texts were considered as they appeared, without performing stemming or typo correction. This database has eight different classes with the number of samples varying from 51 to over 3000 documents, as can be seen in Table 1 .
To obtain the vector representation of words, we used a freely available word2vec model, trained by BIBREF8 , on approximately 100 billion words, which encodes the vector representation in $\mathbb {R}^{300}$ of over 3 million words from several different languages. Since we decided to focus on English words only, we filtered these vectors to about 800 thousand words, excluding all words with non-roman characters.
To show the validity of our word subspace representation for text classification and the proposed extension, we divided our experiment section into two parts: The first one aims to verify if sets of word vectors are suitable for subspace representation, and the second one puts our methods in practice in a text classification test, comparing our results with the conventional methods described in Section "Related Work" .

Evaluation of the word subspace representation
In this experiment, we modeled the word vectors from each class in the Reuters-8 database into a word subspace. The primary goal is to visualize how much of the text data can be represented by a lower dimensional subspace.
Subspace representations are very efficient in compactly represent data that is close to a normal distribution. This characteristic is due to the application of the PCA, that is optimal to find the direction with the highest variation within the data.
In PCA, the principal components give the directions of maximum variance, while their corresponding eigenvalues give the variance of the data in each of them. Therefore, by observing the distribution of the eigenvalues computed when performing PCA in the modeling of the subspaces, we can suggest if the data is suitable or not for subspace representation.
For each class, we normalized the eigenvalues by the largest one of the class. Fig. 2 shows the mean of the eigenvalues and the standard deviation among classes. It is possible to see that the first largest eigenvalues retain larger variance than the smallest ones. In fact, looking at the first 150 largest eigenvalues, we can see that they retain, on average, 86.37% of the data variance. Also, by observing the standard deviation, we can understand that the eigenvalues distribution among classes follows the same pattern, that is, most of the variance is in the first dimensions. This plot indicates that text data represented by vectors generated with word2vec is suitable for subspace representation.

Discussion
Given the observation of the eigenvalues distribution of word vectors, we could see that word vectors that belong to the same context, i.e., same class, are suitable for subspace representation. Our analysis showed that half of the word vector space dimensions suffice to represent most of the variability of the data in each class of the Reuters-8 database.
The results from the text classification experiment showed that subspace-based methods performed better than the text classification methods discussed in this work. Ultimately, our proposed TF weighted word subspace with MSM surpassed all the other methods. word2vec features are reliable tools to represent the semantic meaning of the words and when treated as sets of word vectors, they are capable of representing the content of texts. However, despite the fact that word vectors can be treated separately, conventional methods such as SVM and LSA may not be suitable for text classification using word vectors.
Among the conventional methods, LSA and SVM achieved about 86% and 89%, respectively, when using bag-of-words features. Interestingly, both methods had better performance when using binary weights. For LSA, we can see that despite the slight differences in the performance, tfidfBOW required approximations with smaller dimensions. SVM had the lowest accuracy rate when using the tfidfBOW features. One possible explanation for this is that TF-IDF weights are useful when rare words and very frequent words exist in the corpus, giving higher weights for rare words and lower weights for common words. Since we removed the stop words, the most frequent words among the training documents were not considered and, therefore, using TF-IDF weights did not improve the results.
Only MNB with tfBOW performed better than MSM. This result may be because tfBOW features encode the word frequencies, while MSM only considers a single occurrence of words. When incorporating the word frequencies with our TF weighted word subspace, we achieved a higher accuracy of 92.01%, performing better than MNB at a significance level of 95%.

Conclusions and Future Work
In this paper, we proposed a new method for text classification, based on the novel concept of word subspace under the MSM framework. We also proposed the term-frequency weighted word subspace which can incorporate the frequency of words directly in the modeling of the subspace by using a weighted version of PCA.
Most of the conventional text classification methods are based on the bag-of-words features, which are very simple to compute and had been proved to produce positive results. However, bag-of-words are commonly high dimensional models, with a sparse representation, which is computationally heavy to model. Also, bag-of-words fail to convey the semantic meaning of words inside a text. Due to these problems, neural networks started to be applied to generate a vector representation of words. Despite the fact that these representations can encode the semantic meaning of words, conventional methods do not work well when considering word vectors separately.
In our work, we focused on the word2vec representation, which can embed the semantic structure of words, rendering vector angles as a useful metric to show meaningful similarities between words. Our experiments showed that our word subspace modeling along with the MSM outperforms most of the conventional methods. Ultimately, our TF weighted subspace formulation resulted in significantly higher accuracy when compared to all conventional text classification methods discussed in this work. It is important to note that our method does not consider the order of the words in a text, resulting in a loss of context information. As a future work, we wish to extend our word subspace concept further in mainly two directions. First, we seek to encode word order, which may enrich the representation of context information. Second, we wish to model dynamic context change, enabling analysis of large documents, by having a long-short memory to interpret information using cues from different parts of a text.
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Question: Which dataset has been used in this work?

To answer the question, format your response as a `json` object with two fields:

"answer": A string providing a succinct answer to the question, in your own words.
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For instance, for the question "What baselines did the authors compare against?", a sample response might be:

{
  "answer": "BERT and RoBERTa."
  "evidence": ["We compare our approach against two baselines. In Table 1, we compare against BERT. In Table 2, we compare against RoBERTa. Our findings indicate that our approach improves over both baeslines..."]
}

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To repeat, the question is: Which dataset has been used in this work?

Answer JSON object:
{"answer": "The Reuters-8 dataset (with stop words removed)", "evidence": ["In this section we describe the experiments performed to demonstrate the validity of our proposed method and its extension. We used the Reuters-8 dataset without stop words from BIBREF27 aiming at single-label classification, which is a preprocessed format of the Reuters-21578. Words in the texts were considered as they appeared, without performing stemming or typo correction. This database has eight different classes with the number of samples varying from 51 to over 3000 documents, as can be seen in Table 1 ."]}