Applications of Tensors

Tensors, with their multi-dimensional nature, find applications across a diverse range of data tasks. Their structure and shape are pivotal in determining how they represent and process data in various scenarios. Let's explore:

• Table Data: Often represented in 2D tensors, table data is reminiscent of matrices. Each row can represent a data entry, and each column might signify a feature or attribute of the data. For instance, a dataset with 1000 samples and 10 features would be encapsulated in a tensor of shape (1000, 10);

• Text Sequences: Sequences, such as a time series or text data, are typically mapped to 2D tensors. One dimension sequences through time or length, while the other denotes features at each timestep. A 200-word text processed with embeddings of size 50 would translate to a tensor of (200, 50);

  Note

  Embeddings in text processing are a way to convert words into numerical vectors, such that words with similar meanings have similar vector values. This allows computers to better understand and work with textual data by capturing semantic relationships between words. In this example, every word will be converted into a vector with a length of 50, meaning each word will be represented by 50 floating-point numbers.

• Numerical Sequences: In scenarios such as monitoring multiple system parameters over time, 2D tensors can be employed. Consider a control system where you're observing the behavior of 5 different parameters (e.g., temperature, pressure, humidity, voltage, and current) over a span of 10 hours. Each parameter has 40 data points recorded every hour. Over 10 hours, this aggregates to a tensor shape of (400, 5). In this format, the first dimension sequentially tracks the timeline (with 40 data points for each of the 10 hours, totaling 400), while the second dimension details the data for each of the 5 parameters at every data point;

• Image Processing: Images are predominantly represented as 3D tensors. The height and width of the image create the first two dimensions, while the depth (color channels like RGB) forms the third. A colored image of 256x256 pixels would have a tensor shape of (256, 256, 3);

  Note

  The last dimension has a length of 3 since each pixel in the RGB color palette is represented by three distinct values, corresponding to its color channels: Red, Green, and Blue.

• Video Processing: Videos, being sequences of images, are expressed using 4D tensors. Think of each frame as an image. So, a 60-second video, sampled at 1 frame per second, with each frame being a 256x256 colored image, would be represented as a tensor of (60, 256, 256, 3).

Note

For a video with 30 frames every second, we would have 30 * number of seconds total frames. So, for 60 seconds, that's 30 frames/second multiplied by 60 seconds, giving us 1800 frames. This would result in a tensor shape of (1800, 256, 256, 3).

Understanding these shapes and the logic behind them is fundamental. By ensuring the correct tensor dimensions, we align data appropriately, laying the groundwork for effective model training and inference.