Abstract. The paper proposes a new approach to building models of statistical recognition algorithms, taking into account high dimensional feature space (HDFS). The construction of the model was performed within the framework of recognition algorithms based on the method for making statistical decisions. A distinctive feature of the proposed model of algorithms is the determination of a suitable set of two-dimensional threshold functions (TTF) when constructing an extremal recognition algorithm. The purpose of this article is to develop a model of statistical recognition algorithms based on the construction of the TTF. The main advantage of the proposed recognition algorithms is to reduce the volume of computational operations in the recognition of unknown objects. At the same time, the reduction in the volume of computational operations is ensured as a result of the application of the following basic computational procedures: selection of representative features; building a TTF; determination of a set of reference TTFs; determination of basic TTFs and calculation of a probability assessment of the membership of objects. These algorithms can be used in preparing various software systems focused on solving applied recognition problems under conditions of HDFS.