collinearity

简明释义

英[ˌkɑːlɪˈnɛərɪti]美[ˌkɑːlɪˈnɛərɪti]

n. [数] 共线性

英英释义

单词用法

同义词

反义词

例句

1.In solving the regression equations, collinearity in the design matrix can result in inaccurate parameter estimates.

在解回归方程时，设计矩阵中的共线性可能产生不精确的参数估计。

2.First, the counterparts of the points on image in camera coordinate system (CCS) are found by utilizing two properties, namely collinearity and Euclidean distance invariability.

首先，利用共线性和欧氏距离不变性这两个特性可以求得图像中的点在相机坐标系（CCS）中的坐标。

3.A collinearity equation based space resection adjustment model is presented under frame imaging pattern.

在框幅式成像模式下提出了基于共线方程的空间后方交会条件平差模型。

4.A new method of the linearization of collinearity equations is given in this thesis. It makes the process of the linearization of collinearity equations concise, convenient and easy to master.

给出一种新的共线条件方程线性化方法，使共线条件方程线性化过程简明易懂，便于掌握。

5.The rigorous geometric model based on the collinearity equations is the basic model for object positioning of high resolution remotely sensed imagery.

简要叙述高分辨率卫星遥感影像的严格几何模型，建立影像姿态角常差检校模型。

6.Results there is multi-collinearity bias in the result of the least square estimation trend-surface model, use the method of ridge regression can control the multi-collinearity bias.

结果趋势面分析往往存在共线性偏倚，利用岭回归趋势面分析可以在一定程度上控制共线性偏倚。

7.A collinearity equation of the calibration parameters was derived and linearized.

建立了关于校准参数的共线性方程，并对其进行线性化。

8.A new method of the linearization of collinearity equations is given in this thesis. It makes the process of the linearization of collinearity equations concise, convenient and easy to master.

给出一种新的共线条件方程线性化方法，使共线条件方程线性化过程简明易懂，便于掌握。

9.Collinearity Equation Model. Besides, the neural network can eliminate the influence of GCPs with gross error, and hence can better improve the efficiency.

网络模型能够自动抑制含较大误差控制点对模型纠正精度的影响，在实际应用中可以提高几何纠正效率。

10.Of all the methods for geometric rectification of remote sensing imagery, the Collinearity Equation Modelis usually considered to have the best accuracy.

在遥感影像几何校正方法中，通常认为精度最高的是共线方程模型。

11.In statistical analysis, we must check for collinearity 共线性 among the independent variables to avoid multicollinearity issues.

在统计分析中，我们必须检查自变量之间的collinearity 共线性以避免多重共线性问题。

12.The analysis revealed a significant collinearity 共线性 between the two factors affecting the outcome.

分析显示影响结果的两个因素之间存在显著的collinearity 共线性。

13.In geometry, three points are said to be in collinearity 共线性 if they lie on the same straight line.

在几何学中，如果三点位于同一条直线上，则称这三点具有collinearity 共线性。

14.To assess collinearity 共线性, we can calculate the Variance Inflation Factor (VIF) for each predictor.

为了评估collinearity 共线性，我们可以计算每个预测变量的方差膨胀因子（VIF）。

15.The presence of collinearity 共线性 can lead to unreliable coefficient estimates in regression models.

在回归模型中，collinearity 共线性的存在可能导致不可靠的系数估计。

作文

In the field of mathematics and geometry, the concept of collinearity plays a significant role in understanding the relationship between points in a plane. To describe collinearity, we refer to a situation where three or more points lie on a single straight line. This idea is fundamental in various branches of mathematics, including algebra, geometry, and even calculus. When we analyze geometric figures, determining whether points are collinear can help simplify complex problems and provide insights into the properties of shapes.For instance, consider three points A, B, and C on a coordinate plane. If we know the coordinates of these points, we can use the slope formula to check for collinearity. The slope between two points is calculated as the change in y divided by the change in x. If the slope between point A and point B is equal to the slope between point A and point C, then the three points are collinear. This method can be particularly useful when dealing with larger sets of points, as it allows us to quickly assess their arrangement.The importance of collinearity extends beyond pure mathematics; it has practical applications in fields such as physics, engineering, and computer graphics. For example, in physics, understanding the collinearity of forces acting on an object can determine the resultant force. If multiple forces are collinear, they can be summed directly, simplifying the analysis of motion and equilibrium.In engineering, ensuring that structural elements are collinear can affect the stability and integrity of buildings and bridges. Engineers often use principles of collinearity when designing frameworks to ensure that loads are distributed evenly, preventing potential failures. Similarly, in computer graphics, algorithms often rely on the concept of collinearity to render shapes and animations accurately. By determining whether points are collinear, graphic designers can optimize rendering processes and improve performance.Moreover, collinearity is also a critical concept in statistics, particularly in regression analysis. In this context, collinearity refers to a situation where two or more independent variables are highly correlated, which can complicate the interpretation of results. When variables are collinear, it becomes challenging to isolate the effect of each variable on the dependent variable. This phenomenon, known as multicollinearity, can lead to unreliable estimates and inflated standard errors, ultimately affecting the conclusions drawn from statistical models.In conclusion, the concept of collinearity is integral to various disciplines, providing a framework for understanding relationships between points and lines. Whether in mathematics, physics, engineering, computer graphics, or statistics, recognizing and applying the principles of collinearity can enhance our problem-solving capabilities and deepen our understanding of complex systems. Embracing the significance of collinearity not only enriches our mathematical knowledge but also equips us with valuable tools applicable in real-world scenarios.

在数学和几何学领域，共线性的概念在理解平面中点之间的关系时起着重要作用。我们所指的共线性是指三个或更多点位于同一条直线上的情况。这个概念在代数、几何甚至微积分等多个数学分支中都是基础。当我们分析几何图形时，确定点是否共线可以帮助简化复杂问题，并提供关于形状特性的见解。例如，考虑坐标平面上的三个点A、B和C。如果我们知道这些点的坐标，我们可以使用斜率公式来检查共线性。两个点之间的斜率计算为y的变化除以x的变化。如果点A和点B之间的斜率等于点A和点C之间的斜率，那么这三个点就是共线的。这种方法在处理更大点集时特别有用，因为它可以让我们快速评估它们的排列。共线性的重要性超越了纯数学，它在物理学、工程和计算机图形学等领域具有实际应用。例如，在物理学中，理解作用在物体上的力的共线性可以决定合力。如果多个力是共线的，它们可以直接相加，从而简化运动和平衡的分析。在工程中，确保结构元素是共线的可以影响建筑物和桥梁的稳定性和完整性。工程师在设计框架时经常使用共线性的原理，以确保负载均匀分布，防止潜在的失败。同样，在计算机图形学中，算法通常依赖于共线性的概念，以准确渲染形状和动画。通过确定点是否共线，图形设计师可以优化渲染过程并提高性能。此外，共线性在统计学中也是一个关键概念，尤其是在回归分析中。在这种情况下，共线性指的是两个或多个自变量高度相关的情况，这可能会使结果的解释变得复杂。当变量是共线的时，孤立每个变量对因变量的影响变得困难。这种现象被称为多重共线性，可能导致不可靠的估计和膨胀的标准误差，从而最终影响从统计模型中得出的结论。总之，共线性的概念对于各种学科来说都是不可或缺的，为理解点和线之间的关系提供了框架。无论是在数学、物理学、工程、计算机图形学还是统计学中，识别和应用共线性的原理都能增强我们的解决问题能力，加深我们对复杂系统的理解。接受共线性的重要性不仅丰富了我们的数学知识，还为我们提供了适用于现实世界场景的宝贵工具。