scholarly journals Adaptive interpolation based on optimization of the decision rule in a multidimensional feature space

2020 ◽  
Vol 44 (1) ◽  
pp. 101-108
Author(s):  
M.V. Gashnikov
Keyword(s):  
Decision Tree ◽  
Decision Rule ◽  
Feature Space ◽  
Computational Experiments ◽  
Arbitrary Form ◽  
Multidimensional Signals ◽  
Adaptive Interpolation ◽  
Multidimensional Signal ◽  
Adaptive Interpolator

An adaptive multidimensional signal interpolator is proposed, which selects an interpolating function at each signal point by means of the decision rule optimized in a multidimensional feature space using a decision tree. The search for the dividing boundary when splitting the decision tree vertices is carried out by a recurrence procedure that allows, in addition to the search for the boundary, selecting the best pair of interpolating functions from a predetermined set of functions of an arbitrary form. Results of computational experiments in nature multidimensional signals are presented, confirming the effectiveness of the adaptive interpolator.

scholarly journals Parameter space dimension reduction of an adaptive interpolator during multidimensional signal differential compression

2019 ◽  
pp. 23-30
Author(s):  
A I Maksimov ◽  
M V Gashnikov
Keyword(s):  
Dimension Reduction ◽  
Parameter Space ◽  
Compression Ratio ◽  
Space Dimension ◽  
Computational Experiments ◽  
Parameter Range ◽  
Compression Method ◽  
Multidimensional Signals ◽  
Multidimensional Signal ◽  
Adaptive Interpolator

We propose a new adaptive multidimensional signal interpolator for differential compression tasks. To increase the efficiency of interpolation, we optimize its parameters space by the minimum absolute interpolation error criterion. To reduce the complexity of interpolation optimization, we reduce the dimension of its parameter range. The correspondence between signal samples in a local neighbourhood is parameterized. Besides, we compare several methods for such parameterization. The developed adaptive interpolator is embedded in the differential compression method. Computational experiments on real multidimensional signals confirm that the use of the proposed interpolator can increase the compression ratio.

scholarly journals Adaptive interpolation of multidimensional signals for compression on board an aircraft

2019 ◽  
pp. 97-102
Author(s):  
N I Glumov ◽  
M V Gashnikov
Keyword(s):  
Compression Ratio ◽  
Real World ◽  
Adaptive Algorithm ◽  
Computational Experiments ◽  
Interpolation Algorithm ◽  
Compression Method ◽  
Multidimensional Signals ◽  
Adaptive Interpolation ◽  
Hierarchical Compression ◽  
Adaptive Interpolator

We consider the compression of multidimensional signals on the aircraft board. We describe the data of such signals as a hypercube, which is "rotated" in a special way. To compress this hypercube, we use a hierarchical compression method. As one of the stages of this method, we use an adaptive interpolation algorithm. The adaptive algorithm automatically switches between different interpolating functions at each signal point. We perform computational experiments in real-world multidimensional signals. Computational experiments confirm that the use of proposed adaptive interpolator allows increasing (up to 31%) the compression ratio of the “rotated” hypercube corresponding to multidimensional hyperspectral signals.

scholarly journals Interpolation of multidimensional signals using the reduction of the dimension of parametric spaces of decision rules

2019 ◽  
pp. 31-40
Author(s):  
M V Gashnikov
Keyword(s):  
Decision Rule ◽  
Optimization Problem ◽  
Decision Rules ◽  
Compression Method ◽  
Parametric Space ◽  
Archive File ◽  
Multidimensional Signals ◽  
Reduced Dimension ◽  
Hierarchical Compression ◽  
Adaptive Interpolator

In this paper, we consider the interpolation of multidimensional signals problem. We develop adaptive interpolators that select the most appropriate interpolating function at each signal point. Parameterized decision rule selects the interpolating function based on local features at each signal point. We optimize the adaptive interpolator in the parameter space of this decision rule. For solving this optimization problem, we reduce the dimension of the parametric space of the decision rule. Dimension reduction is based on the parameterization of the ratio between local differences at each signal point. Then we optimize the adaptive interpolator in parametric space of reduced dimension. Computational experiments to investigate the effectiveness of an adaptive interpolator are conducted using real-world multidimensional signals. The proposed adaptive interpolator used as a part of the hierarchical compression method showed a gain of up to 51% in the size of the archive file compared to the smoothing interpolator.

scholarly journals A branch & bound algorithm to determine optimal bivariate splits for oblique decision tree induction

2021 ◽  
Author(s):  
Ferdinand Bollwein ◽  
Stephan Westphal
Keyword(s):  
Decision Tree ◽  
Feature Space ◽  
Classification Problems ◽  
Decision Tree Induction ◽  
Single Attribute ◽  
Global Optimal ◽  
The Individual ◽  
Tree Building ◽  
Very High ◽  
Multiclass Classification Problems

AbstractUnivariate decision tree induction methods for multiclass classification problems such as CART, C4.5 and ID3 continue to be very popular in the context of machine learning due to their major benefit of being easy to interpret. However, as these trees only consider a single attribute per node, they often get quite large which lowers their explanatory value. Oblique decision tree building algorithms, which divide the feature space by multidimensional hyperplanes, often produce much smaller trees but the individual splits are hard to interpret. Moreover, the effort of finding optimal oblique splits is very high such that heuristics have to be applied to determine local optimal solutions. In this work, we introduce an effective branch and bound procedure to determine global optimal bivariate oblique splits for concave impurity measures. Decision trees based on these bivariate oblique splits remain fairly interpretable due to the restriction to two attributes per split. The resulting trees are significantly smaller and more accurate than their univariate counterparts due to their ability of adapting better to the underlying data and capturing interactions of attribute pairs. Moreover, our evaluation shows that our algorithm even outperforms algorithms based on heuristically obtained multivariate oblique splits despite the fact that we are focusing on two attributes only.

scholarly journals treeheatr: an R package for interpretable decision tree visualizations

2020 ◽  
Author(s):  
Trang T. Le ◽  
Jason H. Moore
Keyword(s):  
Machine Learning ◽  
Decision Tree ◽  
Feature Space ◽  
R Package ◽  
Tree Structure ◽  
Decision Tree Model ◽  
Teaching Tool ◽  
Tree Model ◽  
Machine Learning Methods ◽  
Link Type

AbstractSummarytreeheatr is an R package for creating interpretable decision tree visualizations with the data represented as a heatmap at the tree’s leaf nodes. The integrated presentation of the tree structure along with an overview of the data efficiently illustrates how the tree nodes split up the feature space and how well the tree model performs. This visualization can also be examined in depth to uncover the correlation structure in the data and importance of each feature in predicting the outcome. Implemented in an easily installed package with a detailed vignette, treeheatr can be a useful teaching tool to enhance students’ understanding of a simple decision tree model before diving into more complex tree-based machine learning methods.AvailabilityThe treeheatr package is freely available under the permissive MIT license at https://trang1618.github.io/treeheatr and https://cran.r-project.org/package=treeheatr. It comes with a detailed vignette that is automatically built with GitHub Actions continuous [email protected]

scholarly journals Optimization of the multidimensional signal interpolator in a lower dimensional space

2019 ◽  
Vol 43 (4) ◽  
pp. 653-660 ◽  
Author(s):  
M.V. Gashnikov
Keyword(s):  
Experimental Study ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Multidimensional Signals ◽  
Multidimensional Signal ◽  
Signal Sample ◽  
Lower Dimensional Space ◽  
Lower Dimensional ◽  
Selection Of

Adaptive multidimensional signal interpolators are developed. These interpolators take into account the presence and direction of boundaries of flat signal regions in each local neighborhood based on the automatic selection of the interpolating function for each signal sample. The selection of the interpolating function is performed by a parameterized rule, which is optimized in a parametric lower dimensional space. The dimension reduction is performed using rank filtering of local differences in the neighborhood of each signal sample. The interpolating functions of adaptive interpolators are written for the multidimensional, three-dimensional and two-dimensional cases. The use of adaptive interpolators in the problem of compression of multidimensional signals is also considered. Results of an experimental study of adaptive interpolators for real multidimensional signals of various types are presented.

scholarly journals A Novel Multiway Splits Decision Tree for Multiple Types of Data

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Zhenyu Liu ◽  
Tao Wen ◽  
Wei Sun ◽  
Qilong Zhang
Keyword(s):  
Decision Tree ◽  
Decision Trees ◽  
Feature Space ◽  
Feature Weighting ◽  
Boundary Structure ◽  
Linear Combinations ◽  
Mixed Features ◽  
Axis Parallel ◽  
Classical Decision ◽  
Generalization Accuracy

Classical decision trees such as C4.5 and CART partition the feature space using axis-parallel splits. Oblique decision trees use the oblique splits based on linear combinations of features to potentially simplify the boundary structure. Although oblique decision trees have higher generalization accuracy, most oblique split methods are not directly conducive to the categorical data and are computationally expensive. In this paper, we propose a multiway splits decision tree (MSDT) algorithm, which adopts feature weighting and clustering. This method can combine multiple numerical features, multiple categorical features, or multiple mixed features. Experimental results show that MSDT has excellent performance for multiple types of data.

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