dimensionality

dimensionality 的音标是 [ˌdiːmɪˈnænɪtɪ]，基本翻译是“维度”。要记住这个单词，可以将其分解为“dimension”（维度）和“ity”（性质或状态）两部分，这样有助于联想到维度这个概念。同时，可以尝试将其与其它相关词汇一起记忆，例如“dimensionality reduction”（降维），这样更有助于整体记忆。

英文单词“dimensionality”来源于拉丁语词素，意为“维度”。其变化形式主要有复数形式“dimensionalities”和过去式和过去分词形式“dimensionalized”。

相关单词：

1. “dimension” - 同样来源于拉丁语，意为“维度”，与“dimensionality”有密切关联。

2. “multidimensional” - 意为“多维度的”，常用于描述具有多个维度的对象或现象。

3. “subdimension” - 意为“次维度”，通常用于数学和物理学中。

4. “hyperdimension” - 意为“超维度”，用于描述高于普通三维的维度。

5. “fractal dimension” - 分形维度，用于描述具有分形结构的对象的复杂程度。

6. “dimensionality reduction” - 意为“维度降低”，用于处理高维度数据的问题，使其更易于处理和分析。

7. “dimensionality analysis” - 维度分析，一种统计学方法，用于分析数据集的维度和结构。

8. “dimensionality reduction algorithm” - 维度降低算法，用于实现维度降低的算法和技术。

9. “dimensionality reduction technique” - 维度降低技术，泛指用于处理高维度数据的各种技术和方法。

10. “dimensionality explosion” - 意为“维度爆炸”，常用于描述高维度数据的问题和挑战。

以上单词都与“dimensionality”有着密切的关联，涵盖了不同维度的概念、表示、分析、算法和技术等方面。

常用短语：

1. dimensionality reduction

2. high-dimensional space

3. multidimensional array

4. multidimensional data

5. multidimensional modeling

6. multidimensional analysis

7. multidimensional processing

例句：

1. The dataset is highly dimensional, making traditional machine learning algorithms difficult to apply.

2. The algorithm successfully performed dimensionality reduction on the high-dimensional data.

3. The market data is in a highly dimensional space, making it difficult to analyze.

4. The multidimensional array contains information about each customer"s behavior across multiple dimensions.

5. The multidimensional modeling approach was effective in explaining the data"s patterns.

6. The analysis of the multidimensional data identified several key trends.

7. The multidimensional processing task required careful consideration of all dimensions simultaneously.

英文小作文：

High-Dimensional Data: Challenges and Possibilities

High-dimensional data is becoming increasingly common in many fields, from machine learning to healthcare analytics. This type of data involves numerous variables or dimensions, making it difficult to analyze and process effectively. However, with the right tools and techniques, high-dimensional data can provide valuable insights and unlock new opportunities.

One of the main challenges of high-dimensional data is the computational burden it poses. Traditional algorithms and methods are not designed to handle such large amounts of data efficiently, resulting in slow processing times and potential inaccuracies. To address this issue, dimensionality reduction techniques can be used to reduce the number of dimensions while maintaining the essential information in the data. This allows for faster processing and better accuracy when analyzing high-dimensional data.

Another challenge of high-dimensional data is the difficulty in visualizing and interpreting the results. Multidimensional visualization techniques can be used to present the data in a way that is easier to understand, allowing for a more comprehensive analysis of the data patterns and trends. By using these techniques, it is possible to gain a deeper understanding of the data and identify potential opportunities and risks that may be hidden within the high-dimensional data.

Finally, high-dimensional data can provide a rich source of information for developing advanced machine learning models. By incorporating multiple dimensions into the model, it is possible to capture more complex patterns and relationships in the data, resulting in more accurate predictions and better decision-making processes.

In conclusion, high-dimensional data presents both challenges and opportunities. By using appropriate tools and techniques, such as dimensionality reduction and multidimensional visualization techniques, it is possible to overcome these challenges and unlock the potential value of high-dimensional data for a wide range of applications.