Indexing of matrixes by a form of a surface.
Exact/fuzzy search and recognition of
matrixes by a form of a surface.

Matrixes are NBIT-primitives.

Each matrix should be defined as two-dimensional array of its values.

Search of matrixes in NBITSearch uses normalized form of their surfaces in accordance with search criterion and inaccuracy given by the user.

Adjusting of search inaccuracy can be realized by means of interface like similar adjusting is realized in standard oscillograph by means of spinning knobs.

Fig.1. Samples forms of matrix surfaces

The surfaces of matrixes can be visualized by mapping them to the sites with appropriate tints. This technique is used in the images drawn in Fig.2.

Fig.2. Search of matrixes by the normalized shape of their surface
(see Video).

Fig.2: Search of matrixes by the normalized shape of their surface. In each row the first matrix is a search pattern, and the other three are the results similar to the pattern.

It is clear that it is a very difficult task to discover the patterns shown in Fig.2 by merely looking at a matrix of numbers. If the matrix are large or if array of matrixes are large, then to see any patterns in the numbers is totally impossible.

NBITSearch is designed to provide fast solution for such search tasks.

To index and search, it is not only the source matrix M that can be transferred to NBITSearch, but any of their transformations T(M), which are also matrixes.

For example, depending on the specific task, the transformations T of the source matrixes M can be represented by their expansions into Fourier series, integrals, derivatives, logarithms, different spectra, etc.

Such a method of mapping the source matrixes to their arbitrary transformations can be easily programmed by a user.

Transformations T must not be necessarily stored on a hard disk. It is sufficient to implement these transformations so that they are automatically executed in the computer RAM before sending them directly to NBITSearch instead of M.

Therefore, researchers are able to carry out the following types of searches with the help of NBITSearch:

– search of matrixes by the normalized shape of their surfaces with controlled inaccuracy,
– search of matrixes by the normalized shape of the surface of their transformations with controlled inaccuracy.

Indexing not the matrixes themselves, but their transformations allows the following types of searches to be done:

– search of matrixes by the area of their surface with controlled inaccuracy,
– search of matrixes by a volume limited by them with controlled inaccuracy,
– search of matrixes by their spectra with controlled inaccuracy.

NBITSearch allows to create indexes, each of which supports an efficient (high-speed) search of billions of source matrixes M or their transformations T(M).

These features allow researchers to search more efficiently for hidden patterns in large arrays and matrixes of objects represented by matrixes.

Small-Angle Scattering (SAS) methods make it possible to identify a structure of microscopic patterns and objects, such as micro particles and proteins by a form of a functional curve.

NBITSearch allows to compare the same structures by the form of matrixes more accurately, since the matrix describing the objects contains de facto significantly more information than the functional curves, which describe the same objects.

NBITSearch is indispensable in studies of various arrays of matrixes associated with their analysis and identification by the form of their surface.

The need for such an analysis and identification occurs, for example, in many cases.

– in dynamic object management solutions,
– in process management solutions,
– in experimental studies of micro world and nano world.

Apart from these applications there is a large number of other ones, for which NBITSearch tool is an indispensable instrument.

Search Technology developed with support from FASIE
foundation formed by the Government of Russian Federation
Novosib-BIT LLC 2004 - 2017