What is a Tensor
What is a Tensor is an often asked question whereby a short answer often used is that it is a multi-dimensional array used in big data analysis often today. In particular with deep learning using the Tensorflow Tool the word is more broadly used today. It is best understood when comparing it with vectors or matrices as shown in the illustration below. What many people already know is that data represented in two dimensions is called a matrix and there are a wide variety of application examples. In text analysis we might be interested in documents X terms while in survey data we are more interested in subjects X questions asked. Another simple example for a matrix used in electronic medical records are patients X diagnosis or patients X drugs.
A tensor represents a high dimensional dataset like for example three or more dimensional datasets that are often encoded as multi-dimensional arrays. Three dimensional examples can be often found in data analysis. One example is in environmental data analysis with sensor measurements using Location X Time X Variable of interest. Closely related is an example in process data analysis whereby the measurements can be a function of Batch X Variable X Time. Another example is in the Wine industry where the score of a wine can be represented as Wine Sample X Judge X Attribute. An example in text data analysis is the tensor authors X terms X time. Also very interesting are examples in social network data analysis using an adjacency matrix of users over time meaning User X User X time.
But also more dimensional tensors are possible that go beyond three dimensional. One example is in the field of spectroscopy whereby a tensor can be used like Wavelength X Retention X Sample X Time X Location. Therefore tensors should not be seen as only three dimensional since they are truly multi-dimensional datasets. For a more concrete example how tensors are used in machine learning we refer to our article on Tensor Machine Learning.
What is a Tensor exactly?
We recommend to have closer look to the following video: