The Pixel Space

As image pixels are used for computing features, the pixel representation seems to be more general. This has the advantage limitations caused by that bad or missing features  can be overcome by a thorough  analysis of the pixel space. There is however a price to pay. Consider two face images represented by their pixels. In…

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Pixel Representation

Good representations enable the recognition of real world objects. They make it possible to compute differences between objects. If the differences between similar objects are always small, they constitute the basis for a generalization. This is the case for a continuous mapping of the original objects, what has been called a compact representation. It may,…

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True Representations

The significance of a proper representation has been discussed here in several ways. The scene is now ready to make a significant step which is not often discussed in the pattern recognition literature. Let us first summarize the observations made so far. Representation is the step in pattern recognition between real world objects or events…

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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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Representation and generalization

No two objects in the world are identical. They are all different. Even if they belong to the same class, even if they come from the same production process or when they are twins, they differ. It may take some inspection before we have found the difference. Nevertheless, in spite of the fact that all…

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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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Features need statistics as they reduce

Is statistics needed for learning? Well, it depends. A definite answer will be postponed for the time being. Here a first step will be made based on the traditional representation used for pattern recognition: the feature space. Objects belonging to different pattern classes differ. Otherwise it would not be possible to distinguish these classes. May…

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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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