dimensionality

简明释义

英[dɪˌmenʃə'nælɪtɪ]美[dɪˌmenʃə'nælətɪ]

n. 维度；幅员；广延

英英释义

单词用法

同义词

反义词

例句

1.Such technique pursues, through the study of the eigenvalues, the reduction of the dimensionality in the representation space.

这种方法是通过对特征值的研究，追求表征空间的维数压缩。

2.The challenge of data mining is dealing with the dimensionality of the data and the volume of it.

数据挖掘所面临的挑战在于数据的维数及其容量。

3.Philosophy of education is the most unique and novel dimensionality of Dewey's thought.

教育哲学是杜威思想中最为独特和新颖的维度。

4.High dimensionality is the main difficulty of similarity search over time-series data.

数据的高维度是造成时序数据相似性搜索困难的主要原因。

5.The trick is to find an arrangement of springs that "flattens" the data set, or in other words, reduces its dimensionality.

而诀窍就是找到一个弹性阵列，能够将非单调的数据集“变成单调数据集”，或者换言之，就是降维。

6.He credits such success to “the blessing of dimensionality.”

他把这一切归功于“来自高维度的恩赐”。

7.That's why it's called the blessing of dimensionality.

这就是我说的来自高维度的恩赐。

8.It is also strong in image clarity and three dimensionality.

这也是强大的图像清晰度和三个维度。

9.In physics, the dimensionality 维度 of a system can affect its properties and behaviors.

在物理学中，系统的dimensionality 维度可以影响其属性和行为。

10.Reducing the dimensionality 维度 of a dataset can help in visualizing the data more effectively.

减少数据集的dimensionality 维度可以帮助更有效地可视化数据。

11.In machine learning, increasing the dimensionality 维度 of the data can sometimes improve the model's performance.

在机器学习中，增加数据的dimensionality 维度有时可以提高模型的性能。

12.The artist experimented with the dimensionality 维度 of her sculptures to create a sense of depth.

这位艺术家通过实验她雕塑的dimensionality 维度来创造出一种深度感。

13.The concept of dimensionality 维度 is crucial in understanding how data is structured in a multi-dimensional space.

理解数据在多维空间中如何结构化的过程中，dimensionality 维度的概念是至关重要的。

作文

In the realm of mathematics and physics, the concept of dimensionality plays a crucial role in understanding the nature of space and objects within it. At its core, dimensionality refers to the number of dimensions an object possesses. For instance, a point is considered to have zero dimensionality, a line has one dimensionality, a plane has two, and a solid object in three-dimensional space has three dimensionality. This classification helps us comprehend how different objects interact with one another and how they can be represented in various mathematical models.The study of dimensionality extends beyond simple geometric shapes; it also encompasses complex phenomena in higher dimensions. In theoretical physics, for example, string theory proposes that the universe consists of multiple dimensions beyond the familiar three. These additional dimensions, often compactified or curled up, suggest a rich tapestry of interactions and forces that govern the fundamental aspects of reality. Understanding these higher dimensionalities allows scientists to explore concepts such as gravity and quantum mechanics in new and innovative ways.Moreover, in data science and machine learning, dimensionality takes on a different but equally significant meaning. Here, it refers to the number of features or variables in a dataset. High dimensionality can lead to challenges known as the "curse of dimensionality," where the volume of the space increases so much that the available data becomes sparse. This sparsity makes it difficult for algorithms to find patterns and relationships within the data. To combat this issue, techniques such as dimensionality reduction are employed, allowing researchers to simplify their datasets without losing essential information.Dimensionality reduction methods, such as Principal Component Analysis (PCA) or t-Distributed Stochastic Neighbor Embedding (t-SNE), help reduce the number of features while retaining the most important aspects of the data. By doing so, analysts can visualize complex data structures in two or three dimensions, making it easier to interpret and draw conclusions from the data. This process highlights the importance of understanding dimensionality in both theoretical and applied contexts.Furthermore, the idea of dimensionality can be applied metaphorically in our everyday lives. For instance, when we talk about the dimensionality of a person's character or personality, we often refer to the various facets that make them unique. Just as a geometric shape can be described by its dimensions, a person can be understood through their experiences, emotions, and relationships. Recognizing the multi-faceted dimensionality of individuals encourages empathy and deeper connections among people.In conclusion, the concept of dimensionality is integral to various fields, from mathematics and physics to data science and personal relationships. By exploring the different meanings and implications of dimensionality, we gain a more comprehensive understanding of the world around us. Whether we are analyzing the physical universe, tackling complex datasets, or navigating human interactions, appreciating the layers of dimensionality enriches our perspective and enhances our ability to engage with complex systems. As we continue to delve into the intricacies of dimensionality, we open ourselves to new insights and discoveries that can shape our understanding of reality itself.

在数学和物理的领域中，维度概念在理解空间及其内物体的本质方面发挥着至关重要的作用。其核心是，维度指的是一个物体所拥有的维度数量。例如，一个点被认为具有零维度，一条线具有一维度，一个平面具有二维度，而三维空间中的固体物体具有三维度。这种分类帮助我们理解不同物体之间的相互作用，以及它们如何在各种数学模型中表示。维度的研究不仅限于简单的几何形状；它还包含高维空间中的复杂现象。例如，在理论物理中，弦理论提出宇宙由多个维度构成，超出了我们熟悉的三维。这些额外的维度常常是紧凑化或卷曲的，暗示着支配现实基本方面的丰富交互和力量。理解这些更高的维度使科学家能够以新的创新方式探索重力和量子力学等概念。此外，在数据科学和机器学习中，维度又有不同但同样重要的意义。在这里，它指的是数据集中变量或特征的数量。高维度可能导致称为“维度诅咒”的挑战，其中空间的体积增加得如此之多，以至于可用的数据变得稀疏。这种稀疏性使算法难以发现数据中的模式和关系。为了解决这个问题，采用了诸如降维等技术，使研究人员能够简化数据集而不丢失重要信息。降维方法，如主成分分析（PCA）或t-分布随机邻居嵌入（t-SNE），帮助减少特征数量，同时保留数据中最重要的方面。通过这样做，分析师可以在二维或三维中可视化复杂数据结构，从而更容易解释和得出结论。这个过程突显了在理论和应用背景下理解维度的重要性。此外，维度的概念在我们的日常生活中也可以隐喻地应用。例如，当我们谈论一个人的性格或个性的维度时，我们通常指的是使他们独特的各种方面。就像几何形状可以通过其维度来描述一样，一个人可以通过他们的经历、情感和关系来理解。认识到个体的多面维度鼓励同理心和更深的联系。总之，维度的概念在各个领域中都是不可或缺的，从数学和物理到数据科学和人际关系。通过探索维度的不同含义和影响，我们获得了对周围世界更全面的理解。无论我们是在分析物理宇宙、处理复杂数据集，还是在与人类互动中，欣赏维度的层次丰富了我们的视角，并增强了我们与复杂系统互动的能力。当我们继续深入探讨维度的复杂性时，我们为新见解和发现打开了大门，这些发现可以塑造我们对现实本身的理解。