The structure of the question is the following: first, I give the concept of collective recognition , further explain the different methods of collective classification, which I found, and at the end I bring my question. Who has already eaten a dog in this business and they may not need to explain what it is and what methods are there, you can just look at the headings of the methods I have cited and go to the question.
What is collective recognition / classification?
Collective (group) recognition means the use of multiple classifiers, each of which decides on the class of one entity, situation, image, and then merging and coordinating the decisions of individual classifiers with the help of an algorithm. The use of multiple classifiers, as a rule, leads to higher recognition accuracy and better indicators of computational efficiency.
Some approaches to combining classifier solutions:
based on the concept of competence areas of classifiers and the use of procedures to evaluate the competence of classifiers with respect to each entry of the classification system
methods of combining solutions based on the use of neural networks .
Competence area method
The idea of collective classification based on areas of competence is that each basic classifier can work well in a certain area of the feature space (area of competence), exceeding in this area the remaining classifiers in accuracy and reliability of decisions. The area of competence of each basic classifier should be assessed somehow. The corresponding program is called the referee . The task of classification is solved in such a way that each algorithm is used only in the area of its competence, i.e. where it gives the best results in comparison with other classifiers. In this case, the decision of only one classifier is taken into account in each region. However, it is necessary to have some kind of algorithm, which for any input determines which of the classifiers is the most competent.
One approach assumes that a special algorithm (referee) is used with each classifier, which is designed to assess the competence of the classifier. Under the competence of the classifier in this area of the space of representation of objects of classification is understood its accuracy, i.e probability of correct classification of objects whose description belongs to this area.
The general scheme of learning collective recognition based on the assessment of competence consists of 2 steps (Fig. 1). At the 1st step, the training and testing of each specific basic classifier is performed. This step is no different from conventional learning patterns. In the next step, after testing each classifier, the training sample that was used at the testing stage for a classifier is divided into two subsets, L + and L− . At the same time, the first subset includes those instances of the original test sample, which were correctly classified during testing. The second subset includes the remaining test sample instances, i.e. those that were classified erroneously. Considering these data sets as areas of competence and incompetence of the classifier, respectively, they can be used as training data for training the “referee” algorithm. When classifying new data, the referee's task is to determine for each input example whether it belongs to the competence area of the algorithm or not, and if it belongs, what is the probability of correct classification of this example. After this, the referee instructs the most competent classifier to solve the classification problem. 
Neural network approaches.
Neural network approaches of collective classification are divided into methods that use the unification of classifiers using a neural network, ensembles of networks ( ensembles of neural networks ) and those that use neural networks built from modules.
Neural network for combining classifiers
One of the approaches considers the use of a neural network for combining the solutions of basic classifiers (Fig. 2). 
The output of each basic classifier is a decision vector (a vector containing soft labels as values), the values of the elements of which belong to a certain numerical interval [a, b] . These values are fed to the input of the neural network (it must be trained to integrate the decisions of the basic level classifiers), the output of which is a decision in favor of one or another class. The output of the network can also be a vector, the dimension of which is equal to the number of classes of recognizable objects, which at each position has a value of some measure of confidence in favor of one or another class. In this case, the class with the maximum value of such a measure can be chosen as a solution.
The system of combining solutions functions as follows:
- many basic classifiers are selected and trained;
- Meta-data are prepared for neural network training. For this, the basic classifiers are tested using an interpreted data sample and, for each test example, the decision vector of the basic classifiers is formed, to which the component is added, to which the name of the true class of the tested example is entered
- A sample of meta-data is used to train a neural network that performs the integration of solutions.
Modular Neural Network Method
For modular neural networks, it is proposed to use the so-called gateway network (“gating network”), a neural network to assess the competence of classifiers for a particular input vector of data presented to classifiers. This option considers the neural network paradigm for combining decisions based on competency assessments. The corresponding theory here is called a mixture of experts . Each classifier is assigned a “referee” program, which predicts the degree of its competence in relation to a particular input supplied to the input of many basic level classifiers (Fig. 3). 
Depending on the input vector X, the solutions of various classifiers can be selected and used to make a joint decision. The number of inputs of the predictive network is equal to the dimension of the input feature space vector. The number of network outputs equals the number of classifiers, i.e. L. A predictive neural network is trained to predict the measure of competence of each classifier upon presentation of a specific input vector to it, i.e. assessment of the fact that the classifier produces the correct solution. The degree of competence is estimated by the number of the interval [0,1] .
Neural Network Ensembles
Also, the proposed architecture of the system of integration solutions, which consists of several experts (neural networks). Combining the knowledge of neural networks in an ensemble has proven its effectiveness by demonstrating the promise of using collective recognition technologies in overcoming the problem of " fragility ."
An ensemble of neural networks is a set of neural network models that makes a decision by averaging the results of the work of individual models. Depending on how the ensemble is constructed, its use allows to solve one of two problems: the tendency of the basic neural network architecture to under-train (this problem is solved by the meta-algorithm of boosting ), or the tendency of the basic architecture to be re-trained (the meta-algorithm bagging ).
There are various universal voting schemes for which the class is the winner:
- maximum - with the maximum response of members of the ensemble;
- averaging - with the highest average response of the members of the ensemble;
- majority - with the largest number of votes of members of the ensemble.
Some other methods
There are also such ensemble machine learning algorithms as:
- Random forest (consisting in the use of a committee (ensemble) of decisive trees)
- Adaboost (algorithm for strengthening classifiers, by combining them into a committee proposed by Yoav Freund)
My question
The question is which collective recognition scheme is better to use for character / digit recognition / autonumbers. The data sources from which I took information about various group classification schemes are dated 2006 and I am afraid that some methods might become outdated. Which scheme will be more rational to use in terms of the relevance of any method.
I have mentioned the following schemes:
- on the basis of areas of competence
- based on the use of a single neural network to combine classifiers
- based on the use of modular neural network
- based on neural network ensembles
- committee methods Random forest and Adaboost
Which of the approaches in the potential can give the best indicators of accuracy and performance in the field of character recognition / numbers / autonumbers. Perhaps some of the methods are outdated or have shown their inconsistency in certain areas. Perhaps there are other more effective and relevant methods of collective recognition (group classification).
Sources with a detailed description (from there I took information about the methods of collective recognition):
Methods and algorithms for collective recognition: Overview (V.I. Gorodetsky, 2006, pdf)
