LSA is one of the models (Dumais, 2004) which is often used in natural language processing tasks. The advantage of this method over other dimensionality reduction methods is that the dimensionality reduction considers the context of the text data. The main aim of the LSA model is to detect a relationship between text data and the words they contain. LSA assumes that words in the text data that are close by their meaning will occur in similar pieces of text, by the so-called distributional hypothesis. Also, the LSA model is a dimensionality reduction method, so it helps to reduce the dimensionality of huge text vectors. Suppose we have a text data X = { X 1 , X 2 , … , X N } and a bag of words is created. The bag of words is a list of words from all text data, excluding the words that do not satisfy the conditions defined by the various pre-processing filters. Each data item is described by the words obtained after the bag of words is created. According to the frequency of the words in the text data, a so-called text matrix is created: (1) x 11 x 12 ⋯ x 1 n x 21 x 22 ⋯ x 2 n ⋮ ⋮ ⋱ ⋮ x N 1 x N 2 ⋯ x N n , here x p l is the frequency of the lth word in the pth text, p = 1 , … , N, l = 1 , … , n. N is the number of the analysed texts, and n is the number of words in the bag of words. In the simplest case, the frequency value is equal to the number of words appeared in the text. Usually, in the literature, the relative frequency is used. In this case, the word frequency in the text is divided from the total appearance of the word overall text data. Each row of the matrix (1) is a text vector X p ′ ∈ R n , p = 1 , … , N, corresponding to a text which represents a numerical expression of the text. Given the text matrix, the mathematical technique (in the LSA model) called singular value decomposition is used to reduce the number of columns while preserving the similarity structure among rows. In such a way, the dimensionality reduction is performed, where the new dimensionality D of analysed data is obtained. Usually, two parameters influence the LSA model output: the number of expected dimensions and the exponent scaling feature component strengths. The exponent scaling feature helps to highlight the more important words in the list of the bag of words.

In the stage of a class assignment in our proposed approach, we used the similarity measure. The related works showed that the most common similarity measure used in text analysis is a cosine similarity distance. Other similarity measures such as Dice coefficient, overlap, etc. (Stefanovič et al., 2019) can also be used in text similarity detection. The performed primary research showed that there is no significant difference between usage of cosine and Dice coefficient in our model. The cosine similarity distance between text vectors X p ′ and Y ′ (in our case, Y ′ is the text vector that represents the most frequent words of each class) can be calculated using the formula (2): (2) cos ( X p ′ , Y ′ ) = X p ′ × Y ′ | X p ′ | × | Y ′ | , p = 1 , … , N .

Let’s say we have three words that describe our selected and analysed data class the best: “euros”, “lent”, “more”. The text data samples are given in Table 1. The text matrix (1) with relative word frequency is formed, and we want to find which of the texts X 1 , X 2 , X 3 is most similar to our three words presented as a text vector Y ′ = ( 1 , 1 , 1 ) that reflect the class context.

The cosine similarity distance is in the interval [ 0 , 1 ]. If the value of cosine similarity is equal to 1, it means that the texts are obviously the same, and vice versa, the value 0 means the two texts are completely different. As we can see in Table 1, the most similar text to our selected three words is the text X 2 and cosine distance is equal to 0.7746. The word “euros” appears two times and the word “more” once. The other text X 3 is close to X 2 , and the text X 1 is most dissimilar.

There are many methods applied in data science, most of them are used nowadays to solve data classification and clustering tasks. In our research, we pay attention to data clustering. Various clustering methods can be used (Aggarwal and Zhai, 2012), such as density-based clustering, hierarchical clustering, k-means, etc. In our proposed approach, we used SOM. SOM is one of the artificial neural network models proposed by Kohonen (2012). The main advantage of this method is that it not just clusters the data, but also shows the results in a visual form that can be interpreted much easier by a researcher. The SOM visual form can be presented in various ways (Stefanovič and Kurasova, 2011; Dzemyda and Kurasova, 2002) but the main aim of SOM is to preserve the topology of multidimensional data when they are transformed into a lower-dimensional space (usually two-dimensional). SOM can be applied in various fields such as data mining (López et al., 2019), text mining (Yoshioka and Dozono, 2018), and even in image analysis tasks (Licen et al., 2020; Aly and Almotairi, 2020). SOM can be used to cluster, classify, and visualize the data. SOM is a set of nodes connected via a rectangular or hexagonal topology. The rectangular topology of SOM is presented in Fig. 2.

The set of weights forms a vector M i j , i = 1 , … , k a , j = 1 , … , k b that is usually called a neuron or codebook vector, where k a is the number of columns, and k b is the number of rows of SOM. All texts of an analysed data are given to the SOM as text vectors. The learning process of the SOM algorithm starts from the initialization of the components of the vectors M i j , where they can be initialized at random, linear, or by the principal components. At each learning step, an input vector X p ′ is passed to the SOM. The vector X p ′ is compared to all neurons M i j . Usually, the Euclidean distance between this input vector X p ′ and each neuron M i j is calculated. The vector M w with the minimal Euclidean distance to X p ′ is designated as a neuron winner. All neuron components are adapted according to the learning rule: (3) M i j ( t + 1 ) = M i j ( t ) + h i j w ( X p ′ − M i j ( t ) ) , here t is the number of iteration, h i j w is a neighbouring function, w is a pair of indices of the neuron winner of vector X p ′ , p = 1 , … , N. The learning is repeated until the maximum number of iterations is reached. A lot of SOM visualization ways use colouring techniques to show the distance in the map. It shows how much the vectors of the neighbouring cells are close in the dimensionality space of the analysed data. The most popular one is based on the so-called unified distance matrix (u-matrix) (Ultsch and Siemon, 1989). SOM is coloured by the values of u-matrix elements. If the greyscale is used, a dark colour between the neurons corresponds to a large distance. A light colour between the neurons signifies that the codebook vectors are close to each other in the input space. Light areas can be thought of as clusters and dark areas as cluster separators.

Suppose we have a multi-label text data X = { X 1 , X 2 , … , X N }, where N is the number of data items. At least some of the data items X p , p = 1 , … , N are assigned to more than one class (for example, some data items have been assigned to one class, some – to two classes). First of all, the data must be pre-processed to avoid the artificial similarity between text data. Later, tokenization has to be performed. Tokenization is a way of separating text data into smaller units called tokens. In this research, tokens can be words, characters, punctuation signs, etc. Next, unnecessary tokens have to be removed from the texts. There are various pre-processing filters that can be applied, such as number removing, erase punctuation, case converting to lower or uppercase, the character length in the tokens, stop word lists, etc. In our previous research (Stefanovič and Kurasova, 2014), we analysed the influence of text data pre-processing filters on SOM clustering results. The experiment results showed that it is advisable to use filters to remove the numbers and leave the numbers inside the words, for example, “Covid-19”. Also, a case converting filter has to be chosen, it does not matter whether all tokens will be converted to the lower case or uppercase. It is preferable to use a stemming algorithm, which allows reducing the number of the same meaning words, for example: from “accepted”, “accepting”, “acceptable”, just one word “accept” will be included. The punctuation eraser filter must be used, too. One more important filter is the usage of the stop words list. This list has to include commonly used words of the analysed language. It is also desirable to include specific words that are often used in the texts in the domain under analysis. To avoid the high number of unimportant words in the text data, it is suggested selecting the tokens length filter. Usually, according to the previous research, the length of tokens that has to be selected is not less than three characters.

Then, all analysed text data has to be split into the subsets S 1 , S 2 , … , S C of each different class, where C is the number of classes in the analysed data. If the text is assigned to more than one class, the same text can be included in different subsets. For example, we have the text “Businesses affected by the COVID pandemic will receive financial support”, which belong to the “Pandemic” and “Finance” classes. In this case, the same text will be included in two subsets. After subsets are formed, the most frequent words lists W S 1 , W S 2 , … , W S C of each subset are found (the most frequent words). In the next step, text vectors of each different words lists W S z = ( w z 1 , w z 2 , … , w z T ), z = 1 , … , C are formed, where T is the selected number of words. The cosine similarity distance is calculated by Eq. (2), and a distance matrix is formed: (4) d 11 d 12 ⋯ d 1 C d 21 d 22 ⋯ d 2 C ⋮ ⋮ ⋱ ⋮ d N 1 d N 2 ⋯ d N C , here d p z is a cosine similarity distance value between pre-processed text vectors X p ′ and text vectors of words lists W S z , where p = 1 , … , N, z = 1 , … , C. LSA is used to reduce the dimensionality of the pre-processed text vectors. Without LSA usage, the dimensionality of the text matrix is usually very high (depends on the size of the analysed text data), so the dimensionality reduction helps SOM in better performance. After the LSA model, the data is fed to the SOM. The various parameters of the SOM can be selected, but considering our previous research (Stefanovic and Kurasova, 2014), we suggest using the Gaussian neighbouring function and linear learning rate. In the proposed approach, the SOM size needs to be chosen by the researcher, starting with the largest number and moving to the smallest one, reducing the size by the chosen step. Also, the parameter L has to be selected, which indicates the limit when the class assignment has to be done in a SOM cell. For example, we chose L = 80 %, and there is a SOM cell where 10 data items fall: 8 items belong to the first class, 1 item belongs to the second class, and 1 item belongs to the third class. In this case, the dominant class is the first class, and the new class assignment is possible because the limit L is satisfied. It means that in this SOM cell, the data items have to be assigned to the dominant class. The pseudocode of the new class assignment is presented in Algorithm 1. In the output of Algorithm 1, the adjusted text data classes are obtained. For simplicity, the pseudocode shows only the case of one or two classes. The proposed approach can be applied and used when text data has been assigned to more classes, in this case, just a few inspection conditions need to be added.

To perform the experimental investigation, the newly collected data has been used (LFND, 2021). The data is collected from public financial Lithuania news websites and stored in a database as texts. The analysed data is a set of text X 1 , X 2 , … , X N , where N = 12484. In cooperation with a company, whose main field is accounting and business management software development with more than 30 years of experience, the five experts from the financial department assigned all text data manually to 10 classes (Collective, Development, Finance, Industry, Innovation, International, Law enforcement, Pandemic, Politics, and Reliability). In the process of data class assignment, the rule was that each text data item could be assigned to no more than two classes. As mentioned before, the problem with the manual assignment of the class is that every expert can interpret the text differently (human factor). Another problem is that some text can be assigned to more than two classes, so it is difficult to decide which classes must be main. This imbalance can lead to inaccurate results in other steps, thus it is important to discover the ways to solve this problem. For instance, we have the text “The pandemic has had many financial consequences around the world”. This sentence could be assigned to the classes “International”, “Pandemic”, and “Finance”.

The token number distribution of unpre-processed text data is presented in Fig. 3. As we can see in Fig. 3, the majority of the text length is no more than 54 tokens. There are 2490 texts whose number of tokens is equal from 54 to 105, and there are just 202 texts that are longer than 105 tokens.

In this research, the multi-label text data is analysed, thus some texts belong to one or two classes. Suppose, we have a text that belongs to “Pandemic” and “Collective” classes, so this text will be considered as “Pandemic, and “Collective” at the same time. The data class distribution is presented in Fig. 4 (if data item has more than one class, it is presented in both classes). Because of the reason that this data is collected from a financial news website, the majority of the text belongs to the class “Finance”. The number of data items from the other classes is similar, except the number of classes “Industry”, “Development”, and “Collective” is larger. The smallest number of data items are from class “Politics”.

There are 6025 texts that got just one class assigned, and the rest 6459 of data items are assigned to two classes. The total number of tokens over all the data is equal to 438730 when the data is unpre-processed (59148 unique tokens) and, respectively, after pre-processing (filters are described in Subsection 3.4) overall number of tokens is equal to 254615 (22730 unique tokens). The most frequent words of each data class are presented in Fig. 5, which allows us to find which words represent each class the best.

As it was mentioned before, first of all, the text data has to be pre-processed. In our experimental investigation, we used the following pre-processing filters: removed numbers, tokens were converted to the lower case, used Lithuanian language snowball stemming algorithm (Jocas, 2020), erased punctuation, used smaller than three characters tokens’ length, and used the Lithuanian language stop words list. An example of SOM using the analysed data is presented in Fig. 6. An Orange data mining tool has been used for the visual presentation of SOM (Demšar et al., 2013). In this type of visualization, the circles show just the class label of the majority data items which fall in the one SOM cell, so some data items from other classes can be in the same cell as well. In this example, the selected size of the SOM is equal to 10 × 10 (it can be various depending on the researcher selection), but because of the u-matrix visualization, the additional cells are included in the SOM, which are used to represent the distance between clusters. The darker colours mean that the distance is larger than the light colour cells. As we can see, on the left side and the left top corner of the SOM, the blue colour dominates, indicating that the majority of the data is from class “Collective”. On the right side and the right top corner, “Finance” class data items are placed. On the top of the SOM, the light blue circles represent the data items that belong to the “Law enforcement” class. All other class members spread overall SOM, and the small clusters are formed.

There are a lot of various options that can be selected in the approach, so according to our previous research (Stefanovic and Kurasova, 2014), we choose the following SOM parameters by default: SOM size is equal to 40 × 40, and reduced by 5 until the SOM size is equal to 5 × 5; neighbouring function is Gaussian and learning rate is linear; iteration number equals to 100; the initial SOM neurons are generated at random. In the class assignment part, we used the cosine similarity distance, and the most frequent word lists of each class have 15 words. The primary research showed that the words overlap from different classes when selecting the high number of the most frequent word, so the final results can be worse. To determine which dimensionality has to be selected as an output of the LSA model, the research has been conducted, where the reduced dimensionality D varies from 10 to 50 by step 10, and the limit percent of new class assignment L = 90 %. The process described in Algorithm 1 has been performed, and after all the steps, each data item has been assigned to adjusted classes. As mentioned before, the experts have been asked to review the new data class assignments and mark one of the tags described in Table 2. All assigned tags have been calculated and used to evaluate the proposed approach.

First of all, the primary research has been performed to find out how the size of the SOM influences the number of new assignments. Thus, for simplicity, when using LSA, the dimensionality is reduced to D = 10, and the results are presented in Fig. 7. As we can see, in the beginning, when the SOM size is 40 × 40, the number of the “Accept” assignment is equal to 35. When reducing the SOM size, the “Accept” number is also decreasing. The “Decline” and “Possible” curves are similar enough. When the SOM size is 30 × 30, and 25 × 25, the number of “Decline” assignment is slightly larger.

In this experimental investigation, we will assume that if the new class assignments reviewed by experts are tagged as “Accept” and “Possible”, it will be considered as a correct new class assignment, and the data is not corrupted. In such a way, the correct assignment ratio can be calculated using the simple formula (5). The ratio can be expressed as percentages: (5) Correct assignment ratio = Accept + Possible Accept + Decline + Possible .

The same calculations have been performed using the approach with different reduced dimensionalities, and the overall correct assignment value is presented in Fig. 8. As we can see, using L = 90 %, the highest number of assignments (296 assignments) is obtained when D = 40. The highest correct assignment ratio is 89.61 %, obtained when D = 50, but the results are not significantly different from the case when D = 40. The worst result considering the number of assignments and correct assignment values is when the dimensionality equals 10. According to the obtained results, we select D = 40 in the following research, because of the highest number of assignments and almost the highest correct assignment ratio. To find out which limit L should be chosen, an experiment has been performed. The limit L has been changed from 95 % to 70 % by step 5 %. The total number of new class assignments has been calculated. Also, the counter has been used to determine how many times the same text has changed the class (one time, two times, three times, and four times) in overall steps of the SOM size reduction. The results are presented in Fig. 9.

As we can see, when the limit is equal to 90 %, 85 %, and 80 %, the number of assignments tends to decrease, so the selected limit is suitable. If the highest limit of 95 % is selected and the SOM size is 5 × 5, the data is clustered too much, so the number of assignments increases. Obviously, the limits L = 75 % and L = 70 % are not suitable for the analysed data because when the SOM size is 5 × 5, the number of new assignments highly increases. Also, overall steps of the SOM size reduction, some of the text data class has been changed even four times. The high number of new assignments indicates that data items are assigned to a new class in each step of the SOM size reduction. The new assignment becomes pointless, because usually, the text data class is continuously changed. A deeper analysis, when the limits are from 95 % to 80 %, has been performed, and the results are presented in Fig. 10. The correct assignment ratio in each step has shown that when the limit L = 95 %, only 5 of 70 assignments were “Decline”, the other assignments were “Accept” and “Possible”. If the limit L = 90 %, there 152 “Accept”, 31 “Decline”, and 113 texts are tagged as “Possible”. Almost all correct assignment ratios are higher than 85 %, and lower just when the SOM size is equal to 35 × 35, and 30 × 30. As we can see, when the limits are equal to L = 85 % and L = 80 %, the correct assignments ratio is near 80 %, only when the size of SOM is equal to 5 × 5, the ratio decreases to 39.13 % and 20.22 %, respectively.

A deeper analysis of the SOM size 5 × 5 has been performed to analyse why the correct assignment ratio decreases significantly. As we can see (Fig. 11), the highest number of “Decline” is when trying to assign the “Law enforcement” class. The analysis of texts where a class is assigned incorrectly showed that one of the common reasons influencing the results is some specific words in the Lithuanian texts. For example, the word “research” can often be found in law enforcement and innovation context texts. The word “research” can indicate some criminal situations, law enforcement investigations, but also it could refer to the scientific research context in the class of “Innovation”. One of the problem solutions is to include such words in the stop word list, but it is possible that this word can be useful in some situations.

The correct assignment ratio per all steps of the SOM size reduction is obtained and presented in Fig. 12. As we can see, with each reduction of the SOM size, the correct assignments are gradually decreasing, but the number of assignments is increasing. When the limit percent L = 80 % is selected, the correct assignments ratio is equal to 76.46 %, and the number of assignments is 1546, which means that approximately 13 % of the data items class has been changed. In this case, the 364 of 1546 multi-label text data class has been assigned incorrectly. The rest of the assigned classes have been tagged as “Accept” (619), and “Possible” equal to 563. The highest correct assignments ratio is obtained when the limit is equal to 95 %, but just 70 times text data class have been changed. The ratio value is high, so these class assignments are indisputably correct.

The experimental investigation has shown that the optimal limit percent is equal to 85 % because the correct assignments ratio is more than 82 %, where just 155 of 865 assignments were incorrect. The best way to improve the results of the proposed approach could be manually prepared keywords of an analysed data for each class. By selecting not overlapping words between different classes, the new class assignment ratio could be higher.

The comprehensively experimental investigation has been performed using one Lithuanian multi-label text data, and the usability of the proposed approach has been experimentally proved. The analysed data has been chosen because of the following reasons: the data size (the usage of the proposed approach with higher amount of text data); the text data is not in the English language (the English language usually is suitable for various methods and is structurally simpler); the data must be multi-label (one data item belongs to more than one class). The same level experimental investigation using other multi-label text data has not been performed, because data with similar properties have not been found. Usually, all of the data in the various freely accessed databases are of small size or artificially made. Primary research has shown that the chosen language does not significantly influence the obtained results, the concept of the model remains the same. Therefore, the proposed approach can be used to adjust multi-label text data classes in any language. There is also a limitation on how many classes need to have one item of the analysed data.

When analysing other data with other properties, for example, text data that have more classes, different language and different lengths of text, the selected parameters used in the proposed approach should be tuned according to the specificity of text data. For example, an English stemming algorithm should be used to analyse an English text, and if the text is much longer, the frequency of words included may also be higher than three, etc. Different pre-processed data may affect the parameters of the LSA and SOM algorithms (reduced data dimensionality may be higher, while SOM size reduction starts with smaller/larger SOM size). Each newly proposed approach has its limitations and threats, but the results of the experimental study are promising and will be used in future work on classification tasks.