Representation Archives

Dissimilarities

In previous posts the usage of features and pixels is discussed for representing objects in numerical ways. Pros and cons are sketched. Here, a third alternative will be considered: the direct use of dissimilarities. First, we summarize  the conclusions on the use of features and pixels. Features are well suited to represent objects by numbers…

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The pixel representation looses information

The pixel representation in its broadest sense samples the objects and uses them to build a vector space. If the sampling is sufficiently dense, it covers everything. How can we loose information? What is wrong? Let us take an image and sample it as on the left above. The pixels can now be ordered as…

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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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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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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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What is the core business of pattern recognition?

Around 2000 Fabio Roli raised the question “what is the core business of pattern recognition?”‘. Given very related areas like machine learning, statistical decision theory and neural networks it became natural, and even urgent to wonder about the identity of the field of pattern recognition. These fields are all dealing with learning from examples, with…

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