Persons Chernov (Chernoff Faces) is a scheme of a visual representation of multifactorial data in the form of a human face. Each part of the face: nose, eyes, mouth - is the value of a specific variable assigned to this part (only 18).

The main idea is that for a person it is very natural to look at the face, because all people do it every day. Therefore, the analysis of the data is obtained by a form of "naturalistic". It is easy to compare and easily identify deviations. Even blondes will be able to produce a multifactor analysis of a significant amount of data.

In 1981, Bernard Flouri and Hans Riedwyl (Bernhard Flury and Hans Riedwyl) improved the concept and added Chernov's asymmetry. Thus, the number of variables has doubled - to 36.

So, each person is an array of 18 elements, each of which takes a value from 0 to 1. The value corresponds to the appearance of the corresponding part of the person. The parameters of the objects under study are given to these values. Extremes of real data will be adopted as 0 and 1. Everything else - lying in this interval. The resulting array is constructed face.

Here are the parameters set by the face:

1. Eyes size
2. Pipple size
3. Position pupil
4. Tilt eye
5. Horizontal Eyes Position
6. Vertical position of the eye
7. Bending eyebrows
8. The density of eyebrows
9. Horizontal position of eyebrows
10. Vertical eyebrows position
11. Upper border of hair
12. Lower border of hair
13. Personal face
14. Darkness of hair
15. Tilt hair hatching
16. RTA size
17. Bending of the mouth

The difficulty lies in the correct comparison of the studied variables with parts of the face. In case of error, important patterns may remain unnoticed.

Fluuri provides an example of a successful multifactor analysis with persons. He analyzed 100 real and 100 fake banknotes in the parameters of the size of the boundaries, indents and diagonals. That's what happened:

Fake banknotes were clearly stated in a separate group. Thus, the analysis made it possible to identify differing groups of objects.

Asymmetry allows us to consider objects in progress. The second example shows various factors in patients to which treatment was applied. The left side of the person shows the values \u200b\u200bof the parameters before, and the right - after treatment.

See how the status of the parameters has changed. You can easily understand who and how much it became better, not even delight in the essence of the parameters studied.

Article Graphical Representation of Multivariate Data by Means of Asymmetrical Faces (by Bernard Flury and Hans Riedwyl) can be read on JStor

If you do not have it, I can send you to you in exchange for an interesting link, which I still do not know.

Persons Chernova "is to coding the values \u200b\u200bof various variables in the characteristics or features of the human face. An example of such a" face "is shown in Fig.16.2.

Fig. 16.2."Face Chernova"

For each observation, a separate "face" is drawn. On each "face" relative values \u200b\u200bof variables are presented as forms and sizes of individual features (for example, the length and width of the nose, the size of the eye, the size of the pupil, the angle between the eyebrows).

Analysis of the information using such a method of display is based on human ability to intuitively find similarities and differences in facial features.

In fig. 16.3 presents a data set, each record of which is expressed in the form of "Face Chernov".

Fig. 16.3.An example of a multidimensional image image with the help of "Chernov's Persons"

Before using the visualization methods, it is necessary:

• Analyze whether all the data should be depicted or some part of them.
• Select sizes, proportions and scale images.
• Select a method that can most brightly display patterns inherent in data set.

Many modern data analysis tools make it possible to build hundreds of types of various graphs and diagrams. Therefore, the choice of the visualization method, if it is independently implemented by the user, is not as simple and easy, as it may seem at first glance. The presence of a large number of visualization tools presented in the instrument that the user applies may even cause confusion.

The same information can be submitted using various means. In order for the visualization tool to perform its main purpose - to provide information in a simple and accessible form to human perception - it is necessary to adhere to the laws of compliance with the selected content of the content of the displayed information and its functional purpose. In other words, you need to make it so that when looking at a visual presentation of information, it was possible to immediately identify patterns in the source data and to make a solution based on them.

Among the two-dimensional and three-dimensional funds are the most widely known linear graphs, linear, column, circular sectoral and vector diagrams.

With help linear graphic You can display the tendency, transfer changes to any sign in time. To compare several rows of numbers, such graphs are applied to the same coordinate axes.

Histogram Apply to compare values \u200b\u200bfor a certain period or ratio of values.

Circular diagrams Use if it is necessary to display the ratio of parts and the whole, i.e. To analyze the composition or structure of phenomena. Composite parts are depicted by sectors of the circle. Sectors are recommended to be placed according to their value: at the top - the largest, the rest - on the movement of the clockwise in order to reduce their magnitude. Circular diagrams are also used to display the results of factor analysis if the actions of all factors are unidirectional. In this case, each factor is displayed as one of the sectors of the circle.

The selection of this or that means of visualization depends on the task set (for example, you need to define the data structure or the process dynamics) and on the nature of the data set.

Fig. 16.1. Data set in Cartesian coordinates and in parallel coordinates

"Persons Chernova"

The main idea of \u200b\u200bpresenting information in "Persons Chernova" is to coding the values \u200b\u200bof various variables in the characteristics or features of the human face. An example of such a "face" is shown in Fig.16.2.

Fig. 16.2. "Face Chernova"

For each observation, a separate "face" is drawn. On each "face" relative values \u200b\u200bof variables are presented as forms and sizes of individual features (for example, the length and width of the nose, the size of the eye, the size of the pupil, the angle between the eyebrows).

Analysis of the information using such a method of display is based on human ability to intuitively find similarities and differences in facial features.

In fig. 16.3 presents a data set, each record of which is expressed in the form of "Face Chernov".

Fig. 16.3. An example of a multidimensional image image with the help of "Chernov's Persons"

Before using the visualization methods, it is necessary:

∙ Analyze whether to depict all the data or Some parts of them.

∙ Select sizes, proportions and scale images.

∙ Select a method that can most brightly display patterns inherent in data set.

Many modern data analysis tools make it possible to build hundreds of types of various graphs and diagrams. Therefore, the choice of the visualization method, if it is independently implemented by the user, is not as simple and easy, as it may seem at first glance. The presence of a large number of visualization tools presented in the instrument that the user applies may even cause confusion.

The same information can be submitted using various means. In order for the visualization tool to perform its main purpose - to provide information in a simple and accessible form to human perception - it is necessary to adhere to the laws of compliance with the selected content of the content of the displayed information and its functional purpose. In other words, you need to make it so that when looking at a visual presentation of information, it was possible to immediately identify patterns in the source data and to make a solution based on them.

Among the two-dimensional and three-dimensional funds are the most widely known linear graphs, linear, column, circular sectoral and vector diagrams.

With help linear graphicyou can display the tendency, transfer changes to any sign in time. To compare several rows of numbers, such graphs are applied to the same coordinate axes.

The histogram is used to compare the values \u200b\u200bfor a certain period or the ratio of values.

Circular diagramsuse if it is necessary to display the ratio of parts and the whole, i.e. To analyze the composition or structure of phenomena. Composite parts are depicted by sectors of the circle. Sectors are recommended to be placed according to their value: at the top - the largest, the rest - on the movement of the clockwise in order to reduce their magnitude. Circular diagrams are also used to display the results of factor analysis if the actions of all factors are unidirectional. In this case, each factor is displayed as one of the sectors of the circle.

The selection of this or that means of visualization depends on the task set (for example, you need to define the data structure or the process dynamics) and on the nature of the data set.

Quality of visualization

Modern analytical means, including Data Mining, are unthinkable without high-quality visualization. As a result of the use of visualization tools, visual and expressive, clear and simple images should be obtained, due to the use of a variety of means: colors, contrast, borders, proportions, scale, etc.

Due to the growth of rendering requirements, as well as the need to compare them among themselves, in recent years a number of the principles of the qualitative visual presentation of information have been formed.

Taffeta principles (TUFTE "S PRINCIPLES) of the graphic view of high quality data says:

∙ provide the user the largest number of ideas in the shortest time, with the smallest amount of ink on the lowest space;

∙ speak the truth about the data.

IN The basic principles of the layout of the visual means of presenting information are described:

1. Principle of conciseness.

2. The principle of generalization and unification.

3. The principle of the accent on the basic semantic elements.

4. The principle of autonomy.

5. Principle of structurality.

6. Principle of statality.

7. The principle of using familiar associations and stereotypes.

The principle of conciseness suggests that the visualization means must contain only those elements that are needed to report to the user of essential information, an accurate understanding of its value or adoption (with a probability of not lower than the permissible value) of the corresponding optimal solution.

In addition to the principles designated above, the visualization means must have a high reliability and speed, which will arrange a user on the basis of this solution.

Presentation of spatial characteristics

A separate direction of visualization is a visual representation of the spatial characteristics of objects. In most cases, such funds allocate individual regions on the map and denote them in various colors depending on the value of the analyzed indicator.

In fig. 16.4 An example of such visualization in the Mineset medium, which is, in this case, the tool of the Visual Data Mining is given. The map is presented as a graphical interface that displays the data in the form of a three-dimensional landscape of arbitrarily defined and positioned forms (columnar charts, each with individual height and color). This method allows to visually show the quantitative and relational characteristics of spatial-oriented data and quickly identify trends in them.

Fig. 16.4. Mineset. Landscaping visualizer

Main trends in visualization

As already noted, with the help of visualization tools, important business objectives are supported, among which is the decision-making process. In this regard, there is a need to transition of visualization to a better level, which is characterized by the emergence of absolutely new means of visualization and views on its functions, as well as the development of a number of trends in this area.

Among the main trends in the visualization of Philip Rosem (Philip Russom) allocates:

1. Development of complex types of diagrams.

Most data visualizations are based on standard type diagrams (sector charts, scattering schedules, etc.). These methods are at the same time the oldest, most elementary and distributed. In recent years, the list of types of diagrams supported by the instrumental means of visualization has significantly expanded. Since the needs of users are very diverse, visualization tools support the most different types of diagrams. For example, it is known that business users prefer sector charts and histograms, while scientists arrange more visualization in the form of scattering graphs and constellation diagrams. Users working with geospatial data are stronger interested in maps and other three-dimensional data views. Electronic instrumental panels, in turn, are more popular among managers using business analytical technologies to control the performance of the company. Such users need visual visualization in the form of "speedometers", "Thermometers" and "Traffic lights".

Figure creation tools and presentation graphics are mainly designed to visualize data. However, such visualization capabilities are usually built into many different other programs and systems - in reporting and OLAP tools, tools for Text Mining and Data Mining, as well as in CRM applications and business management applications. To create built-in visualization, many suppliers implement visualization functionality in the form of a component embedded in various tools, applications, programs and web pages (including toolbar and personalized portal pages).

2. Increasing the level of interaction with user visualization.

More recently, most of the visualization tools was static charts intended solely for viewing. Now dynamic charts are widely used, already themselves are a user interface, in which the user can directly and interactively manipulate visualization by selecting a new presentation of information.

For example, the basic interaction allows the user to rotate the diagram or change its type in search of the most complete presentation of the data. In addition, the user can change visual properties - for example, fonts, colors and frames. In the visualizations of complex type (scattering charts or constellation charts), the user can choose information points with the mouse and move them, thereby easier to understand the data presentation.

More advanced data visualization methods often include a diagram or any other visualization as an integral level. The user can deepen (Drill Down) in visualization, exploring the details

summarized data, or delved into OLAP, Data Mining or other complex technologies.

Comfortable interaction allows the user to change the visualization to find alternative data interpretations. Interaction with visualization involves the minimum user interface in its complexity, in which the user can manage the data representation, simply "click" on the visualization elements, dragging and placing data objects views or choosing the menu items. OLAP or DATA Mining tools turn directly interaction with visualization into one of the stages of iterative data analysis. Text Mining or document management tools give such direct interaction the nature of the navigation mechanism that helps the user explore the document libraries.

Visual queryit is the most modern form of complex user interaction with data. In it, the user can, for example, to see the extreme information points of the scattering schedule, choose their mouse and receive new visualations representing these points. The data visualization application generates the appropriate query language, manages the acceptance of the database request and visually represent the resulting set. The user can focus on the analysis without being distracted by the compilation of the request.

3. An increase in the size and complexity of the data structures represented by visualization.

The elementary sector diagram or histogram visualizes simple sequences of numerical information points. However, new enhanced types of diagrams are able to visualize thousands of such points and even complex data structures - for example, neural networks.

For example, OLAP tools (as well as tools for generating requests and issuing reports) have long been supported charts for their online reports. New visualization programs update content due to periodically recurring data reading. In fact, users of visualization programs tracking linear processes (stock market fluctuations, computer systems, seismograms, utility grids, etc.), need to load data in real time or close to it.

Users of Data Mining tools usually analyze very large sets of numerical data. Traditional types of business charts (sector diagrams and histograms) do not cope with the presentation of thousands of information points. Therefore, the Data Mining tools almost always support a kind of data visualization form capable of reflecting the structures and patterns of the data under study, in accordance with the analytical approach that is used in the instrument.

In addition to the fact that the visualization supports the processing of structured data, it is also key to representing the schemes of so-called unstructured data, such as text documents, i.e.

ChernOff Faces) - Displays multidimensional data in the form of a human face, its individual parts. People easily recognize faces and dismissed small changes without difficulty.

For each observation, a separate "face" is drawn, where the relative values \u200b\u200bof the selected variables are presented as the shapes and dimensions of individual features (for example, the nose length, the angle between the eyebrows, the width of the face). Thus, the observer can identify the visual characteristics of objects for each configuration of the values.

Parameters face

For example, 18 parameters can be used: the size of the eye, the size of the pupil, the position of the pupil, the slope of the eye, the horizontal position of the eye, the vertical position of the eye, the bending of the eyebrows, the density of the eyebrows, horizontal eyebrows, the vertical position of the eyebrows, the upper border of the hair, the lower border of the hair, Facial rubber, dark hair, hair hatching, nose, mouth size, mouth bending.

In 1981, Bernard Flury and Hans Riedwyl (Bernhard Flury and Hans Riedwyl) improved the concept and added Chernov asymmetry to people, which allowed to increase twice the number of variables (up to 36).

The use of Persons Chernov

Persons Chernov found wide application for analyzing the situation in various fields. This method allows you to quickly assess the state of multifactorial systems (10-30-dimensional sets), using the innate human ability to quickly evaluate changes represented by a person in many respects: assessment of treatment methods, array of statistical data, assessing the regime on nuclear power plants, in

It is easy to recognize individuals and without difficulty perceive small changes in it.

For each observation, a separate "face" is drawn, where the relative values \u200b\u200bof the selected variables are presented as the shapes and dimensions of individual features (for example, the nose length, the angle between the eyebrows, the width of the face). Thus, the observer can identify the visual characteristics of objects for each configuration of the values.

Parameters face

For example, 18 parameters can be used: the size of the eye, the size of the pupil, the position of the pupil, the slope of the eye, the horizontal position of the eye, the vertical position of the eye, the bending of the eyebrows, the density of the eyebrows, horizontal eyebrows, the vertical position of the eyebrows, the upper border of the hair, the lower border of the hair, Facial rubber, dark hair, hair hatching, nose, mouth size, mouth bending.

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Excerpt characterizing the face of Chernova

"Are you to Count Cyril Vladimirovich, Ma Chere?" - said the count from the dining room, coming out also in the front. "If he is better, Call Pierre to me to dine." After all, he had a dancer with children. Call necessarily MA Chere. Well, let's see how this will differ in Taras. He says that Count Orlova has no such lunch, which we will have.

- Mon Cher Boris, [Dear Boris,] - said Princess Anna Mikhailovna, son, when the coach of the Rostova Countess, in which they sat, drove along the elusive straw street and drove to the wide courtyard of Cyril Kirill Vladimirovich Duffle. "Mon Cher Boris," said his mother, pulling her hand from under the old salop and timidly and affectionate movement laying her on his son's hand, "be affectionable, be careful." Count Kirill Vladimirovich is still your godfather, and your future fate depends on it. Remember it, Mon Cher, be mil, how can you be ...
- If I knew that something would come out of this, except humiliation ... - the son answered coldly. - But I promised you and do it for you.
Despite the fact that whose coach was standing at the entrance, the Swiss, looking for a mother with her son (who, without ordering reports, rightly entered the glass Songs between the two rows of statues in the niches), significantly watched on the old salop, asked who they It pleases, princed or graph, and, having learned that the graph, said that their shiny is not worse and their begging is not accepted.
"We can leave," said the Son in French.
- MON AMI! [My friend!] - said Mother to a pleading voice, again fading his son, as if this touch could calm down or excite him.
Boris fell silent and, without removing the sheel, looked at his mother.
- Blue, - Anna Mikhailovna said with a gentle voice, turning to the Swiss, - I know that Cyrill Cyril Vladimirovich is very sick ... I then arrived ... I am a relative ... I will not disturb, dove ... but I would just need to see Prince Vasily Sergeevich: After all, he stands here. Follows, please.
The Swiss sullenly jerked the sneaker up and turned away.
"Princess Drubetskaya for the prince of Vasily Sergeyevich," he shouted from the top and from under the protrusion of the staircase looking to the waiter in stockings, shoes and phrak.
The mother placed the folds of his painted silk dress, looked into a whole venetian mirror in the wall and cheerfully in his stopped shoes went up the carpet of the staircase.
- MON CHER, VOUE M "Avez Promis, [My friend, you promised me," She turned again to his son, touching his arms.
Son, lowering his eyes, calmly walked behind her.
They entered the hall, from which one door led in the chambers, allotted by Prince Vasill.
While the mother with his son, coming to the middle of the room, intended to ask the way at the old waiter who jumped at their entrance, one of the doors turned the bronze handle and Prince Vasily in a velvet fur coat, with one star, at home, came out, Watching a beautiful black-haired man. This man was the famous St. Petersburg Dr. Lorrain.
- C "EST DONC POSITIF? [So, this is true?] - said the prince.
- Mon Prince, "Errare Humanum Est", Mais ... [Prince, a man is mistaken.] - answered the doctor, riding and uttering Latin words by French reprimand.
- C "EST BIEN, C" EST BIEN ... [Well, good ...]
Noticing Anna Mikhailovna with his son, Prince Vasily Pokhiloma let go of the doctor and silently, but with an question of question, approached them. The son noticed how suddenly the deep bitterness was expressed in the eyes of his mother, and smiled slightly.