In this article there is proposed a new two-parametrical variant of the gravitational classification method. We use the general idea of objects' behavior in a gravity field. Classification depends on a test object's motion in a gravity field of training points. To solve this motion problem, we use a simulation method. This classifier is compared to the 1NN method, because our method tends towards it for some parameter values. Experimental results on different data sets demonstrate an improvement in efficiency and that this approach outperforms the 1NN method by providing a significant reduction in the mean classification error rate.
The Linear Discriminant Analysis (LDA) technique is an important and well-developed area of classification, and to date many linear (and also nonlinear) discrimination methods have been put forward. A complication in applying LDA to real data occurs when the number of features exceeds that of observations. In this case, the covariance estimates do not have full rank, and thus cannot be inverted. There are a number of ways to deal with this problem. In this paper, we propose improving LDA in this area, and we present a new approach which uses a generalization of the Moore-Penrose pseudoinverse to remove this weakness. Our new approach, in addition to managing the problem of inverting the covariance matrix, significantly improves the quality of classification, also on data sets where we can invert the covariance matrix. Experimental results on various data sets demonstrate that our improvements to LDA are efficient and our approach outperforms LDA.
There is a growing need to analyze data sets characterized by several sets of variables observed on the same set of individuals. Such complex data structures are known as multiblock (or multiple-set) data sets. Multi-block data sets are encountered in diverse fields including bioinformatics, chemometrics, food analysis, etc. Generalized Canonical Correlation Analysis (GCCA) is a very powerful method to study this kind of relationships between blocks. It can also be viewed as a method for the integration of information from K > 2 distinct sources (Takane and Oshima-Takane 2002). In this paper, GCCA is considered in the context of multivariate functional data. Such data are treated as realizations of multivariate random processes. GCCA is a technique that allows the joint analysis of several sets of data through dimensionality reduction. The central problem of GCCA is to construct a series of components aiming to maximize the association among the multiple variable sets. This method will be presented for multivariate functional data. Finally, a practical example will be discussed.
The aim of this paper is to present a statistical methodology to assess patterns of cultivars' adaptive response to agricultural environments (agroecosystems) on the basis of complete Genotype x Crop Management x Location x Year (GxMxLxY) data obtained from 3-year multi-location twofactor trials conducted within the framework of the Polish post-registration trials (PDOiR), with an illustration of the application and usefulness of this methodology in analyzing winter wheat grain yield. Producing specific varieties for each subregion of a target region, from widely adapted varieties, may exploit positive genotype x location (GL) interactions to increase crop yields. Experiments designed to examine combinations of environment (E), management practices (M) and cultivars (G) also provide evidence of the relative importance of each of these factors for yield improvement. The evidence shows that variation due to E far outweighs the variation of grain yield that can be attributed to M or G, or the interactions between these factors, and between these factors and E (Anderson, 2010). This statistical method involves the use of functional PCA and cluster analysis. A total of 24 cultivars were evaluated over 3 years in 20 environments using randomized incomplete split-block designs with two replications per trial. The methodology proved an efficient tool for the reliable classification of 24 winter wheat cultivars, distinguishing cultivar groups that exhibited homogeneous adaptive response to environments. It enables the identification of cultivars displaying wide or specific adaptation. The remaining cultivars were locally adapted to some testing environments, or some of them were not relatively adapted to the environments because they always yielded substantially below the environmental means. Performing earlier specific selection, or adopting distinct genetic bases for each agro-ecosystem, may further increase the advantage of specific breeding.
Ground resonance is an unbalance of the helicopter main rotor rotation caused by its asymmetry. Whilst the helicopter is in contact with the ground this asymmetry generates a divergent and often destructive oscillations of the helicopter structure. These oscillations are self-excited. This paper present results of both theoretical and experimental investigations of this phenomenon. They were dedicated to the new polish UAV helicopter ILX-27. The theoretical analysis were done with commercial software ANSYS using Finite Element Method. The virtual model of the helicopter model accurately reproduced the geometry of all elements of the helicopter and was easy to modify to simulate various kinds of damages. Calculations were done for the following cases: C1 – the helicopter standing on the ground with zero thrust of the rotor, C2 = C1 + helicopter with additional support of the rotor mast, C3 = C2 + thrust of the rotor equal to the total mass of the helicopter, C4 = C2 + fixing the helicopter to the ground, C5 = C2 + helicopter with additional mass. At the beginning the modal analysis for all cases was done – natural frequencies and modes of the structure were identified. Next, for selected cases, harmonic analysis was performed – the structure of the helicopter was loaded with concentrated harmonic forces. Finally the dynamic analysis gave time courses of blades and the hub center motions in the case of structural damages. All phases of simulations were correlated with ground tests of the helicopter prototype. This allowed to compare results of theoretical investigations. These results also supported tests of the prototype.