Emmanuil M. Braverman

Emmanuil M. Braverman


Thursday, June 25, 1931

Passed away: 

Tuesday, April 26, 1977

Emmanuil Braverman, in full Emmanuil Markovich Braverman, started his postgraduate studies at the Institute of Automation and Remote Control (IARC, the USSR Academy of Sciences) in 1960. His academic supervisor was M.A. Aizerman. Before that, he worked in the Tsvetmetavtomatika Design Bureau, after graduating from Moscow Power Engineering Institute in 1955.

Braverman defended his candidate’s dissertation in 1963; his doctoral dissertation, in 1967.

Since the beginning of his research at IARC, Braverman was actively involved in pattern recognition problems, both in theory and applications. For the following 15 years, he became one of the main ideologists of pattern recognition technologies in the Institute and in the USSR. Braverman authored the geometric approach to pattern recognition and the famous “compactness hypothesis,” the subject of heated discussions in 1961 and 1962. The well-known “mighty trio,” Aizerman—Braverman—Rozonoer, created the method of potential functions in recognition theory. Their works on the method of potential functions have become classical in machine learning and are included in many textbooks on pattern recognition. Potential function-based algorithms can be used not only in recognition problems but also in a wide class of complex multidimensional function reconstruction problems, e.g., static object identification during normal operation. Braverman generalized this problem to the case of a dynamic object described by a differential equation.

He proposed many original ideas for the successful application of potential function-based algorithms. For example, note the so-called “second potential”: the potential function is used in the original receptor field to make similar patterns close in the receptor space when they are shifted or insignificantly transformed on the field.

Braverman significantly contributed to automatic classification (pattern recognition without a teacher, also known as self-training or cluster analysis). The problem of automatic classification as a problem of self-learning was pioneered by F. Rosenblatt in 1957. Just three years later, Braverman published a paper proposing a geometric analysis approach to the analysis of recognition devices (including the perceptron). He demonstrated the disadvantages of the perceptron as a self-learning device. Only the compactness hypothesis with its clear geometric interpretation explained the fundamental possibility of self-learning. As a result, this approach became primary in formulating automatic classification problems and, moreover, developing and theoretically investigating their solution algorithms. The convergence of iterative automatic classification algorithms is much more difficult to study compared to that of similar pattern recognition algorithms (with a teacher): the classical stochastic approximation technique becomes inapplicable due to the nonconvex functional. In 1965, Braverman graduated from the Department of Mechanics and Mathematics, Moscow State University (MSU). Subsequently, he developed a new method for examining a large class of random processes based on the semi-martingales theory; the method involved the knowledge accumulated at MSU. In 1966, Braverman published a paper, where he adopted this method to establish the convergence of a recurrence automatic classification algorithm, for the first time in the world.

Braverman together with I.B. Muchnik developed new areas in pattern recognition (the linguistic approach to complex object recognition) and data analysis (a class of extreme parameter grouping methods). Braverman’s R&D results in pattern recognition and related problems (automatic classification, extreme grouping, coupling matrix diagonalization, etc.) were systematized in the monograph Strukturnye metody obrabotki empiricheskikh dannykh (Structural Methods of Empirical Data Processing), Moscow: Nauka, 1983. (It was published after Braverman’s death in coauthorship with I.B. Muchnik.)

In 1968—69, Braverman began to study mathematical descriptions of economic systems. Initially, he used equilibrium economic-mathematical models of exchange; subsequently, complex classes of models for nonequilibrium economic situations. His first paper on an economic system model with nonequilibrium prices was written in 1969 but published only in 1972 (journal Economic and Mathematical Methods) due to the resistance of Soviet classics of mathematical economics.

In 1969, Braverman began part-time teaching and scientific activities as Professor at the Department of Engineering Cybernetics, Moscow Institute of Steel and Alloys. (At that time, the Department was headed by S.V. Emelyanov, Corresponding Member of the USSR Academy of Sciences.) Note his series of lectures on mathematical models of economic systems read in the Institute. In 1976, Braverman published his monograph Matematicheskie modeli planirovaniya i upravleniya v ekonomicheskikh sistemakh (Mathematical Models of Planning and Control in Economic Systems), Moscow: Nauka. It is still used as a textbook in many Russian universities and institutes. Braverman’s many-years research on economic and mathematical models was presented in the monograph Neravnovesnye modeli ekonomicheskikh system (Nonequilibrium Models of Economic Systems), Moscow: Nauka, 1981 (coauthor M.I. Levin).

Braverman’s main books are as follows:

  1. Strukturnye metody obrabotki empiricheskikh dannykh (Structural Processing Methods for Empirical Data), Moscow: Nauka, 1983. — 464 p. (coauthor I.B. Muchnik);
  2. Neravnovesnye modeli ekonomicheskikh sistem (Nonequilibrium Models of Economic Systems), Moscow: Nauka, 1981. — 304 p. (coauthor M.I. Levin);
  3. Matematicheskie modeli planirovaniya v ekonomicheskikh sistemakh (Mathematical Models of Planning in Economic Systems), Moscow: Nauka, 1976. — 368 p.;
  4. Obuchenie mashiny klassifikatsii ob”ektov (Teaching a Machine to Classify Objects), Moscow: Nauka, 1971. — 192 p. (coauthor A.G. Arkad’ev);
  5. Metod potentsial’nykh funktsii v teorii obucheniya mashin (The Method of Potential Functions in the Theory of Machine Learning), Moscow: Nauka, 1970. — 384 p. (coauthors M.A. Aizerman and L.I. Rozonoer);
  6. Teaching Computers to Recognize Patterns. Academic Press, 1967 (coauthor A. G. Arkadev);
  7. Computers and Pattern Recognition. Thompson Book Company, 1967 (coauthor A. G. Arkadev);
  8. Training Pattern-Recognition Machines. Foreign Technology Division, 1966;
  9. Zeichenerkennung und maschinelles Lernen. Oldenbourg, 1966 (coauthor A. G. Arkadev);
  10. Obuchenie mashiny raspoznavaniyu obrazov (Teaching a Machine to Recognize Patterns), Moscow, 1964. — 110 p. (coauthor A.G. Arkad’ev).

Many of them are presented in the Institute’s database:

Some of Braverman’s papers are available at Math-Net.Ru:

1. E. M. Braverman, I. B. Muchnik, A. L. Chernyavsky, An Approximating Approach to Solution of Sets of Structural Regression Equations, Avtomat. i Telemekh., 1978, 11,  120—128    ; Autom. Remote Control39:11 (1979), 1677—1685.
2. E. M. Braverman, M. I. Levin, Identification of Effective States in Networks of Industrial Elements. III, Avtomat. i Telemekh., 1978, 9,  90—101      ; Autom. Remote Control39:9 (1979), 1335—1345.
3. E. M. Braverman, M. I. Levin, Identification of Effective States in Networks of Industrial Elements. II, Avtomat. i Telemekh., 1978, 7,  79—86.    
4. E. M. Braverman, M. I. Levin, Identification of Effective States in Networks of Industrial Elements. I, Avtomat. i Telemekh., 1978, 6,  67—82      ; Autom. Remote Control39:6 (1978), 833—847.
5. E. M. Braverman, S. M. Meerkov, E. S. Pyatnitskii, Conditions for Applicability of the Method of Harmonic Balance to Systems with a Hysteresis Nonlinearity (in the Case of the Filter Hypothesis), Avtomat. i Telemekh., 1976, 11,  16—27      ; Autom. Remote Control37:11 (1976), 1640—1650.
6. E. M. Braverman, A Model of Consumer Choice with Prices Fixed, Avtomat. i Telemekh., 1976, 5,  100—111      ; Autom. Remote Control37:5 (1976), 729—740.
7. E. M. Braverman, B. M. Litvakov, I. B. Muchnik, S. G. Novikov, Stratified Sampling in the Organization of Empirical Data Collection, Avtomat. i Telemekh., 1975, 10,  65—78      ; Autom. Remote Control36:10 (1975), 1629—1641.
8. E. M. Braverman, Economic States of a Network of Production Units, Avtomat. i Telemekh., 1975, 3,  88—94    ; Autom. Remote Control36:3 (1975), 431—436.
9. E. M. Braverman, S. M. Meerkov, E. S. Pyatnitskii, A Small Parameter in the Problem of Justifying the Harmonic Balance Method (in the Case of the Filter Hypothesis). II, Avtomat. i Telemekh., 1975, 2,  5—12    ; Autom. Remote Control36:2 (1975), 189—196.
10. E. M. Braverman, S. M. Meerkov, E. S. Pyatnitskii, A Small Parameter in the Problem of Justifying the Harmonic Balance Method (in the Case of the Filter Hypothesis). I, Avtomat. i Telemekh., 1975, 1,  5—21    ; Autom. Remote Control36:1 (1975), 1—16.


The list of his papers in Avtomatika i Telemekhanika can be found at:

For their English versions, see the microfilm collection of Automation and Remote Control:

Articles about E.M. Braverman

  E.M. Braverman (obituary), Avtomat. i Telemekh., 1978, no. 3, 192.

Also, see the Wikipedia page devoted to Braverman: