Setting the Axis Scaling in Matlab: Accurate Proportions Lead to More Reliable Data Interpretation

# Overview of Coordinate Axis Scale Limitations

Coordinate axis scale limitations are a technique to control the range of axes, enhancing the clarity and accuracy of data visualization. By setting minimum and maximum values for the axes, one can limit the range of data points displayed, thereby highlighting specific data characteristics or eliminating the impact of extreme values. Coordinate axis scale limitations are widely applied across various fields, including scientific research, engineering design, and data analysis.

# Theoretical Foundation of Coordinate Axis Scale Limitations

### 2.1 Types and Functions of Coordinate Axis Scales

Coordinate axis scale limitations refer to restricting the range of data values on the axes to optimize data visualization. Coordinate axis scales are mainly divided into two types:

- **Linear scale:** Data values are distributed at equal intervals on the coordinate axis, with equal unit spacing. This scale is suitable for uniformly or approximately uniformly distributed data.
- **Logarithmic scale:** Data values are distributed on the coordinate axis according to a logarithmic scale, with unit intervals increasing exponentially. This scale is suitable for data with a wide distribution range or exhibiting exponential growth/decay characteristics.

The functions of coordinate axis scale limitations include:

- **Optimizing Data Visualization:** By limiting the scale range, data values can be distributed within a more appropriate range, thereby improving data visualization.
- **Highlighting Key Information:** Limiting the scale range can highlight key information in the data, such as trends, outliers, or specific value ranges.
- **Avoiding Misguidance:** Inappropriate scale limitations may lead to data distortion or misleading interpretations; thus, selecting an appropriate scale range based on data characteristics is necessary.

### 2.2 Mathematical Principles of Coordinate Axis Scale Limitations

The mathematical principles of coordinate axis scale limitations are based on linear and logarithmic transformations.

**Linear Transformation:**

y = mx + b

Where:

- `y` is the transformed data value
- `x` is the original data value
- `m` is the scaling factor
- `b` is the offset

Linear transformations map data values to a new scale range. The scaling factor `m` determines the degree of scaling of the data values, while the offset `b` determines the translation of the data values.

**Logarithmic Transformation:**

y = log(x)

Where:

- `y` is the logarithmically transformed data value
- `x` is the original data value

Logarithmic transformations convert data values to a logarithmic scale, compressing the range of data distribution. This transformation is suitable for data with a wide distribution range or exponential growth/decay characteristics