# Stochastic Diffusion Model for Analysis of Dynamics and Forecasting Events in News Feeds

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## Abstract

**:**

## 1. Introduction

## 2. Review of Research on Forecasting Events Based on Text Analysis

## 3. Materials and Methods

**N**text documents describing news feed events for a certain period of time with references to the dates of their occurrence. Then, using lexical and semantic methods of computational linguistics (removal of punctuation marks, stop words, bringing words to normal forms, lemmatization, creating a glossary of terms, etc.) [26,27,28,29], by means of the glossary of terms (words, n-grams, or objects of associative-semantic classes) of

**M**size, let us create a vector representation of a set of texts in information space with (which dimension will be

**R**). To improve the accuracy of text analysis and further clustering by semantic groups, you can use the approaches based on combining words that have a similar meaning in texts into associative-semantic classes, for example, using the word2vec algorithm.

^{M}**N**, and each element of the vector${x}_{k,i}$ describes the TF-IDF normalized frequency of the k-term (words, n-grams, or objects of associative-semantic classes) occurrence from the glossary into the i-document of the collection: $\mathrm{TFIDF}=\mathrm{TF}\ast \mathrm{IDF}=\frac{{\mathrm{n}}_{\mathrm{k}}}{{{\displaystyle \sum}}_{\mathrm{k}}{\mathrm{n}}_{\mathrm{k}}}\ast \mathrm{log}\frac{\mathrm{D}}{\mathrm{d}}$, where ${n}_{k}$ is the number of occurrences of the k-term in a document; $\sum}_{k}{n}_{k$ is the total number of terms in the document; D is the total number of documents in the collection; and d is the number of documents where this term is found. Using TF-IDF reduces the weight of commonly used terms, which are logically relevant, and finally increases the text clustering accuracy. Vectors ${X}_{i}$ form a matrix of

**N**by

**M**dimension: term—document:

_{i}is a document from the cluster;${\mu}_{p}$ is the centroid of cluster p; N

_{p}is the set of documents of cluster p. The centroid, i.e., the arithmetic mean vector of all vectors in a cluster (or a subgroup thereof), can be calculated as follows: ${\mu}_{p}=\frac{\sum {\mathrm{N}}_{\mathrm{p}}}{{D}_{p}}$, where${\mathrm{N}}_{\mathrm{p}}$is vector of a news item from cluster p;${D}_{p}$ is the number of news texts in the cluster. As the distance between vectors, we use the cosine metric (the cosine of angle between vectors):$d\left({\mathrm{y}}_{i},{\mathrm{z}}_{i}\right)=\frac{{\sum}_{i=1}^{n}({y}_{i}\ast {z}_{i})}{\sqrt{{\sum}_{i=1}^{n}{y}_{i}^{2}}\ast \sqrt{{\sum}_{i=1}^{n}{z}_{i}^{2}}}$, where ${y}_{i}$ is the coordinate value of the first vector;${z}_{i}$ is the coordinate value of the second vector (the larger the cosine of the angle between vectors, the higher the similarity of documents). Given that all the elements of vectors are positive numbers: $0\le d\left({\mathrm{y}}_{i},{\mathrm{z}}_{i}\right)\le 1$.

**X**). Then, we determine the values of cosines of angles between the centroid vectors and the predicted event vector for some point of time t. Then, we calculate their mean value. The mean value of the cosines at this point of time t will be the point on the numerical segment [0, 1], and in view of the change over time of the cluster’s structure, this point will perform movements (wandering) on the segment. Eventually this point may reach the given cosine value, which will be considered as the threshold of the event occurrence (let us call it l). We refer to the current value of the mean value of cosines as the information system state at a time (denote it as x

_{bs}_{0}). Probability of reaching the event threshold l will depend on the time t (i.e., in fact, we consider virtually random wandering of the point on segment [0, 1], which contains a trap in l, where the wandering point can eventually fall.

## 4. Results

#### 4.1. Deriving the Distribution Function for the Time Series Parameters, Which Describe Dynamics of the News Feed Content

#### 4.1.1. Plotting of Difference Schemes of Probabilities of State Transitions in Information Space. Deriving the Main Equation of the Model

_{i}(the information system state).

- $P\left(x-\epsilon ,h\right)$ is the probability that the system is in state (x − ε);
- $P\left(x,h\right)$ is the probability that it is in state x;
- $P\left(x+\xi ,h\right)$is the probability that it is in state (x + ξ).

^{2}+ ξ

^{2})/2τ before the second derivative for x, which accounts for the probability of an accidental state change. The condition (ε

^{2}+ ξ

^{2}) < (l − x

_{0})

^{2}must be met, which is all about the transition from initial state x

_{0}across the event reaching threshold (

**l**), which cannot occur faster than in one step τ. If (ε

^{2}+ ξ

^{2}) ≥ (l − x

_{0})

^{2}, the system crosses the event reaching threshold in one step.

#### 4.1.2. Formulating and Solving a Boundary Value Problem When Predicting News Events in the Information Space for Systems with Memory Implementation and Self-Organization

_{0}, then the integral $P\left(l,t\right)$ shown in Equation (9):

_{0}. This is why, in Equation (9), the first integral is calculated from the lower limit of 0 to the upper limit x

_{0}by using ${\rho}_{2}\left(x,t\right)$, and the second integral of x

_{0}to l by using ${\rho}_{1}\left(x,t\right)$. So, the Equation (9) determines the time dependence of the probability of the “survival” of the wandering point (that it will not fall into the trap).

#### 4.2. Experimental Testing of the Suggested Model for Forecasting News Feed Events

#### 4.2.1. Definition of the Parameters of the Event Forecasting Model Based on Changes in the Cluster Structure in the Information Space of News Feeds

**W**topical clusters (in our case,

**W**= 300, i.e., we have 299 topical cluster + one cluster containing all texts that were not included in 299 thematic clusters). Next, each of

**W**clusters is divided into 365 subgroups of text vectors by days of news publication. If there were no thematic news on a given day, the day subgroup of this cluster will contain an empty set of vectors. Thus, in each of cluster, news feed events for 2016 form time series that determine the model’s parameters.

**W**(i.e., we get

**W**centroids for each day). If there were no topical news on the given day, the day group of this cluster will contain an empty set of vectors, and the centroid forms an empty set.

**W**, we find the cosine values of the angles between the day centroid vectors ${C}_{j}\left(t\right)$and the vector of news N

_{i}of the textual description of the predicted event (these cosines are denoted as ${S}_{j}\left(t\right)=cos\left\{{C}_{j}\left(t\right);Ni\right\}$). If there are no news on the given day, the cosine metric will be equal to the empty set.

#### 4.2.2. Evaluation of the Value of Cosine Measure of the Event Occurrence Threshold in the Information Space of News Feeds

#### 4.2.3. Modelling of the Predicted Event Occurrence Probability Dependence on Time. Analysis of Modelling Results

#### 4.2.4. Assessment of the Accuracy and Reliability of Forecasts of the Implementation of Events in the News Feed, Obtained on the Basis of the Developed Model of the Dynamics of the News Feeds Content

_{p}

_{.}), which correspond to a given time. Determining the accuracy and reliability of forecasting an event in a news feed based on a single implementation observed is an ambiguous task, un the sense that an event can occur even at a very small value of probability and may not yet occur at a probability close to the figure of one, but there is no possibility of conducting a series of tests. To assess the accuracy and reliability of the proposed forecasting methodology, an evaluative analysis and comparison of the probabilities of the predicted (P

_{p.}) and random events (P

_{r}) occurrence may be conducted.

_{p.}) has already been described earlier.

_{r}). To determine P

_{p}, the vector representation of the predicted event was used to determine P

_{r}. It is also necessary to specify a certain vector, relative to which the change in the daytime centroids of the existing clusters will occur. Let us take as a basis that any event that occurs during the year can be largely random (their sum or superposition will also be random), then we can use the vector of the annual centroid of all the events of the year contained in the text corpus as the vector, with respect to which the cosine metric will be calculated and the model parameters ξ, ε, and ${x}_{0}$ will be determined.

_{p}) and random events (P

_{r}): $\%=\frac{1-{P}_{p.}}{1-{P}_{r.}}\xb7100\%$.

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Results of modelling the event threshold crossing for five news described in Table 2 (l = 0.5) for a simple diffusion model.

Cheap | Buy | Book | Case | Free | Delivery | Discount | |
---|---|---|---|---|---|---|---|

${S}_{1}$ | 0 | 1 | 1 | 1 | 0 | 0 | 1 |

${S}_{2}$ | 1 | 1 | 1 | 1 | 1 | 1 | 0 |

No. | Normalized News Text | Date of Event | Value of Parameter ε | Value of Parameter ξ | Initial State of System x_{0} 31 December 2016 |
---|---|---|---|---|---|

1. | {“id”:”9dc7c737-0359-418f-a809-28a4aa23b3bb”,”date”:1490774096000,”title”:”The head of the Ministry of Internal Affairs was killed after he identified theft for 10 billion”,”content”:”couple a week attempt on the life of Nikolai Volk write a statement dismissal own desire to refuse to sign inventory internal financial report information life killed the day before head of the Ministry of Internal Affairs of the Ministry of Internal Affairs Nikolay Volkov complained native department to steal an asset billion ruble force to sign blank document testimony native witness to check investigator IC Russia direct killer to look for authorised operative central directorate Criminal Investigation Department Ministry of Internal Affairs of Russia source editorial office report wolf to identify multi-billion dollar embezzlement assign a lot of internal check number of inventory suspicion to be confirmed establish an investigation person demand a high-ranking police officer signing an act verification of the Ministry of Internal Affairs RID allegedly no financial hole theft of the Ministry of Internal Affairs RID to be able to pay in time contractor owes many organizations previously the Ministry of Internal Affairs initiate a case the fact of fraud against the organization mariotrek responsible construction sanatorium ministry Olympics Sochi FSUE RID Ministry of Internal Affairs speak Customer service we are talking about fraud million rubles identification of the fact of involvement of the employee of the Ministry of Internal Affairs RID fraud the case is transferred to the Investigative Committee is known at the moment the Ministry of Internal Affairs should remain a Sochi builder at least one million rubles of the Ministry of Internal Affairs RID to be the defendant arbitration case lawsuit lawsuit Stroy Universal LLC debt million rubles Organization LLC Enterprise RTSPP RID owes a million to the Ministry of Internal Affairs Russia comment this situation refuse to remind the killer to pursue the goal of robbing the wolves take the portfolio money leave the place expensive phone cash money the killer is hiding car VAZ forget the place medical mask IC consider contract murder priority version death head of the Ministry of Internal Affairs RID ““,”url”:” https://life.ru/991216 “,”siteType”:”LIFE”} | 29 March 2017 (implementation term is 88 days) | 0.016 | 0.016 | 0.046 |

2. | {“id”:”3845f74e-c144-4ec3-9b8f-333e8e08b8ad”,”date”:1490776169000,”title”:”Tajikistan becomes the main foreign supplier of suicide bombers for ISIL “,”content”:”conclusion come author study war by suicide statistical analysis industry martyrdom Islamic state yoke publish international center fight terrorism Hague Netherlands period December year November year only suicide bomber yoke to control to load explosives Inghimashi machine fighter belt suicide bomber fight conventional weapons need to be blown up nearby enemy prima life live bomb house indicate foreign fighter mark author research general difficulty foreigner die quality suicide bomber to consider fifteen year mention Kuni accept Islamic tradition nickname associated place of origin prima life Al Muhajir similarly Al Ansari indicate foreigner indicate country of origin stay die quality drive car explosives originate country Tajikistan then go native Saudi Arabia Morocco Tunisia Russia further give the table indicate the exact figure suicide bomber yoke Tajikistan Saudi Arabia Morocco Tunisia Russia strange year numerous to immigrate the Salafi Tunisia to be a large foreign legion yoke to number about a thousand fighter go close thousand a native of the Wahhabi Kingdom of As Saud native to found follow the immigrant Jordan to rule the royal dynasty belong to the Hashemite clan to originate great-grandfather Prophet Muhammad it is possible therefore the list of the suicide bomber indicate the period only and Jordan Moroccan twelve month to go talk significantly Tajik perish Syria Iraq stroke attack to load explosives Ingimasi machine native foreign country celebrate representative International Center fighting terrorism number amazing consider soul population quantity of natives various country number of yoke prima life assume Tajik frequently direct to suicidal explosion minimum partly nationality Organization to prohibit Russia Supreme Court of the Russian Federation”,”url”:” https://life.ru/991022 “,”siteType”:”LIFE”} | 29 March 2017 (implementation term is 88 days) | 0.021 | 0.021 | 0.083 |

3. | {“id”:”5fbf3918-22cc-4ef3-8ad0-20ae2654286c”,”date”:1491441192000,”title”:”In the area of the attack on the employees of the Russian Guard in Astrakhan a firefight is going on “,”content”:”inform life source law enforcement agency Leninsky district Astrakhan to start a firefight crime figure presumably a few hours earlier to attack a Rosguard officer preliminary data special operation pass the area railway station Astrakhan specify the source remind today night three Rosguards get a gunshot wound attack several criminal declare the regional directorate of the ID of RF attack fighter Rosguard involved crime figure April kill police officer Astrakhan”,”url”:” https://life.ru/994664 “,”siteType”:”LIFE”} | 6 April 2017 (implementation term is 96 days) | 0.016 | 0.016 | 0.047 |

4. | {“id”:”c7584973-348d-417a-90c3-2199a4040558”,”date”:1491047117000,”title”:”NATO Does Not Intend to Fight with Russia for Abkhazia and South Ossetia”,”content”: “representative NATO South Caucasus William Lahue declare treaty organization fight Russia Abkhazia South Ossetia case joining Georgia North Atlantic Alliance Georgia must decide status territory clearly understand so far stay Russian army the fifth article Georgia use nobody want war Lahue report member alliance agree Georgia member NATO none term possible joining Georgia alliance call report Interfax slowly matter go forward future Georgia receive invitation know Lahue speech joining Georgia NATO depend parallel factor politics various country willingness Georgia”,”url”:” http://www.vesti.ru/doc.html?id=2872818 “,”siteType”:”VESTI”} | 1 April 2017 (implementation term is 91 days) | 0.011 | 0.011 | 0.036 |

5. | {“id”:”dacb1299-f6fa-4b25-a4cd-95795657cf4c”,”date”:1490474466000,”title”:”Syrian military liberated 195 settlements from IS * since January “,”content”:”number of settlement liberate January Syrian government army terrorist organization Islamic State yoke January reach report Saturday Russian center reconciliation feuding party Syria number of settlement liberate January year Syrian government troops armed formation international terrorist organization Islamic State increase be said bulletin publish web-site Ministry of Defense of the Russian Federation 24 h control government troops cross a square kilometer territory total difficulty liberate a square kilometer number of settlement join reconciliation process 24 h change message center reconciliation continue negotiations accession regime cessation of hostilities detachment armed opposition Aleppo province Damascus Ham Homs El Quneitr number of armed groups declare a cessation of hostilities compliance agreement armistice change terrorist organization forbid Russia”,”url”:” https://ria.ru/syria/20170325/1490808936.html “,”siteType”:”RIA”} | 25 March 2017 (implementation term is 84 days) | 0.016 | 0.016 | 0.060 |

Normalized Text of News | Date of Event | Value of Parameter ε | Value of Parameter ξ | Initial State of System x_{0} 31 December 2016 |
---|---|---|---|---|

{“id”:”85e74845-70da-434c-a602-497efa002de6”,”date”:1514753700000,”title”:” Roly-Poly Bun”,”content”:”grandmother of the gate speak a handful of two door grandfather the road to live to knead fry roll a winglet swept kneaded towards the window song all the more go to roll the floor half put a chimney sweeper sweep a threshold jump yarned scraped on to concoct sing chill chilled eat through take a distant yard porch bench butter scrape window lie scrape mudroom sour cream old man take a distant yard porch bench butter scrape up a window lie scrape mudroom sour cream old man hare box flour cornbin leave hare box flour cornbin leave old woman old woman old woman old woman Bun Bun Bun Bun Bun Bun bun”,”url”:”http://null.ru/null”,”siteType”:”Fictitious”} | implementation time is not known | 0.0022 | 0.0022 | 0.0076 |

**Table 4.**Values of accuracy and reliability of their determination for news from Table 2.

News Number | Accuracy ϒ % | $\mathbf{Deviation}\mathbf{Square}\mathbf{d}{\mathit{\sigma}}^{2}\mathit{\%}$ |
---|---|---|

1. | 79.5 | 16.0 |

2. | 74.0 | 2.3 |

3. | 79.2 | 13.7 |

4. | 73.0 | 6.3 |

5. | 72.0 | 12.3 |

Average value | $\overline{\Upsilon \%}$ = 75.5 | $\overline{\sigma \%}$ = ±3.2 |

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**MDPI and ACS Style**

Zhukov, D.; Andrianova, E.; Trifonova, O.
Stochastic Diffusion Model for Analysis of Dynamics and Forecasting Events in News Feeds. *Symmetry* **2021**, *13*, 257.
https://doi.org/10.3390/sym13020257

**AMA Style**

Zhukov D, Andrianova E, Trifonova O.
Stochastic Diffusion Model for Analysis of Dynamics and Forecasting Events in News Feeds. *Symmetry*. 2021; 13(2):257.
https://doi.org/10.3390/sym13020257

**Chicago/Turabian Style**

Zhukov, Dmitry, Elena Andrianova, and Olga Trifonova.
2021. "Stochastic Diffusion Model for Analysis of Dynamics and Forecasting Events in News Feeds" *Symmetry* 13, no. 2: 257.
https://doi.org/10.3390/sym13020257