Foundation Archives

Non-Euclidean and non-metric dissimilarities

Dissimilarities measures may be defined as distances in an Euclidean space or such that they can be interpreted as the Euclidean distances. The Euclidean distances satisfy the triangle inequality: the direct distance between two points is smaller than any detour. They are thereby metric. Euclidean Assume we are given a set of pairwise dissimilarities between…

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PRTools: building blocks for pattern recognition

In science knowledge grows from new observations. Pattern recognition aims to contribute to this process in a systematic way. How is this organized in PRTools? What are the building blocks and how are they glued together? Do they constitute a sprawl or an interesting castle?           The most simple place where…

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Are classes open or closed sets?

The field of pattern recognition is a rich landscape offering large sets of tools and approaches. The traveler who enters this field for the first time may feel confused and will not find his way easily. He will be puzzled in understanding the tools that are offered to him and, after that, to find out…

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Compactness

Around 1965 the the concept of compactness was discussed in the Russian pattern recognition literature [1]. It has been almost entirely neglected by the authors of the textbooks published in the West. There is however a strong relation with the careful creation of a good representation as advocated by us. Here we will describe the…

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The recognition task

What do we want to recognize? What are the objects to be classified? What are our examples? What will be our observations? What are the classes we want to distinguish? Are they human defined or are we searching for some truth that might be hidden in the observations but not clearly defined? Many choices to…

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Distances and densities

What is the ground for classifying a new object if we just have some some examples? How to we determine a proper class given a training set? We may find an identical copy in the examples if we are lucky. If there are more identical copies and they belong to different classes we are in…

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Machine learning and pattern recognition

Are Machine Learning (ML) and Pattern Recognition (PR) refering to the same field? Elsewhere we discussed the difference between Artificial Intelligence (AI) and PR. We tried to characterize them in their origin as the Platonic and Aristotelian ways of gaining knowledge:  starting from the concepts or starting from the observations. But where do we have…

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Artificial Intelligence and Pattern Recognition

What is the difference between Artificial Intelligence (AI) and Pattern Recognition (PR)? Is one a subfield of the other or do they stand next to each other? Historically these two fields are strongly connected. Meetings in the 50’s and 60’s attracted researchers from both domains and for many the interest was so broad or not…

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Statistical pattern recognition

Statistical pattern recognition is to use statistics to learn from examples. It means to collect observations, study and digest them in order to infer general rules or concepts that can be applied to new, unseen observations. How should this be done in an automatic way? What tools are needed? Previous discussions on prior knowledge and…

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Plato and Aristotle

It is an exaggeration to say that Plato and Aristotle are recognized as the founding fathers of pattern recognition. There are hardly references to them in the text books and review papers. Nevertheless, it is my strong opinion that understanding the basis of their philosophical discussion is a big help in understanding the scientific basis…

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