The accuracy and reliance increase and consequently reduction of uncertainty of spatial prediction maps of environmental hazards including landslides is one of the challenges facing with in such studies Therefore, the objective of this research is to introduce a hybrid model of data mining algorithm named Random Forest (RF) -Random Subspace (RF-RS) in order to enhance the accuracy of spatial prediction map of landslide prone areas around the city of Bijar, Kurdistan province, Iran. Firstly, 19 affecting factors on shallow landslides in the study area including slope degree, slope aspect, elevation, curvature, profile curvature, plan curvature, solar radiation, stream power index (SPI), topographic wetness index (TWI), length-angle of slope (LS), land use, normalized difference vegetation index (NDVI), litho logy, distance to fault, fault density, rainfall, distance to stream, stream density and distance to road were identified. Then based on Information Gain Ratio (IGR), twelve factors among them were selected to be used in modeling. The elative importance of each factor was assessed by Random Forest (RF) model as well as Random Forest-Random Subspace (RF-RS) hybrid model. Kappa, Precision, Recall, and AUROC indices were used to evaluate the models not only for training dataset but also for testing dataset. Shallow landslide susceptibility maps of the study area were prepared using both models. The results showed that slope aspect in the RF model and slope degree in the RF-RS hybrid model is the most important affecting factor on landslide occurrence in the area. The model evaluation results indicated that both models are reasonable in application for shallow landslide susceptibility mapping. The findings also indicated that the percentage of area under the curve of ROC (AUROC) was 0.729 and 0.784 for training dataset by RF and RF-RS hybrid model, respectively, while these values were 0.717 and 0.771 for testing dataset. In conclusion, it can be claimed that the new technique (RF-RS hybrid model) is able to increase the accuracy of spatial prediction map of shallow landslides in the study area. This accurate map will help decision-makers to protect infrastructures of an area, to develop better land-use planning programs and to more effectively control sediments.

Let $\mathcal{P}_q(n)$ be the set of all Subspaces in the vector space $\mathbb{F}_q^n$. There is a Subspace distance $d_S(U,V)$ between any two Subspaces $U$ and $V$. A Subspace code is also a subset of $\mathcal{P}_q(n)$. It is known that $d_S(U,V)\geq d_H(\nu(\pi U),\nu(\pi V))$, where $\pi\in S_n$, $\nu(U)$ denotes the pivot vector of $E(U)$ and $E(U)$ is the reduced row echelon form of the generator matrix of $U$. In this paper, we show that if $E(U)$ and $E(V)$ have at most one non-zero entry in each rows and each columns then the equality holds. Moreover, we introduce the sets $\mathcal{G}_{U,V}=\{\pi\in S_n\mid d_S(U,V)=d_H(\nu(\pi U),\nu(\pi V))\}$ for any $U,V\in\mathcal{P}_q(n)$ and examine them in the spaces $\mathcal{P}_2(4)$, $\mathcal{P}_2(5)$, $\mathcal{P}_2(6)$ and $\mathcal{P}_3(4)$. It is shown that the groups $1$, $\mathbb{Z}_2$, $\mathbb{Z}_2\times \mathbb{Z}_2$, $S_3$, $S_4$ and $1$, $\mathbb{Z}_2$, $\mathbb{Z}_2\times \mathbb{Z}_2$, $S_3$, $D_8$, $S_3\times \mathbb{Z}_2$, $S_4$, $S_5$ appears between these sets in $\mathcal{P}_2(4)$ and $\mathcal{P}_2(5)$, respectively. Moreover, the groups $1$, $\mathbb{Z}_2$, $\mathbb{Z}_2\times \mathbb{Z}_2$, $S_3$, $D_8$, $\mathbb{Z}_2\times \mathbb{Z}_2 \times \mathbb{Z}_2$, $S_3\times \mathbb{Z}_2$, $D_8\times \mathbb{Z}_2$, $S_4$, $S_3\times S_3$, $S_4\times \mathbb{Z}_2$, $(S_3\times S_3)$:$2$, $S_5$, $S_6$ and $1$, $\mathbb{Z}_2$, $\mathbb{Z}_2\times \mathbb{Z}_2$, $S_3$, $D_8$, $S_4$ appears between these sets in $\mathcal{P}_2(6)$ and $\mathcal{P}_3(4)$, respectively.

We give a general overview of the state-of-the-art in Subspace system identification methods. We have restricted ourselves to the most important ideas and developments since the methods appeared in the late eighties. First, the basis of linear Subspace identification are summarized. Different algorithms one finds in literature (Such as N4SID, MOESP, CVA) are discussed and put into a unifying framework. Further, a comparison between Subspace identification and prediction error methods is made on the basis of computational complexity and precision of methods by applying them to a glass tube manufacturing process.

In this paper, we introduce Subspace-frequently hypercyclic operators. We show that these operators are Subspace-hypercyclic and there are Subspace-hypercyclic  operators that are not Subspace-frequently hypercyclic. There is a criterion like to Subspace-hypercyclicity criterion that implies Subspace-frequent hypercyclicity and if an operator $T$ satisfies this criterion, then $T\oplus T$ is Subspace-frequently hypercyclic. Additionally, operators on finite spaces can not  be Subspace-frequently hypercyclic.