Patterns and operators : the foundations of data representation

Cover......Page __sk_0000.djvu Copyright......Page __sk_0002.djvu Contents......Page __sk_0003.djvu Foreword......Page __sk_0007.djvu 1.1. Definitions......Page __sk_0011.djvu 1.1.1. Primitive recursive and partial recursive functions......Page __sk_0012.djvu 1.1.5. Theorem: identity of classes of functions......Page __sk_0013.djvu 1.2. Computational complexity: hierarchical order......Page __sk_0014.djvu 1.2.2. Complexity and usefulness of an algorithm......Page __sk_0015.djvu 1.2.4. Problems of intrinsically exponential or higher order complexity......Page __sk_0017.djvu 1.3.1. Example of an NP problem......Page __sk_0018.djvu 1.3.3. Problems in graph theory......Page __sk_0020.djvu 1.3.4. Problems concerning sets and partitions......Page __sk_0021.djvu 1.3.6. Problems concerning syntactical relations......Page __sk_0022.djvu 1.4. Polynomial problems......Page __sk_0023.djvu 1.4.3. Signal and image processing......Page __sk_0024.djvu 1.5. Overcoming exponential intractability......Page __sk_0025.djvu 1.5.1. Relaxing the conditions of a problem......Page __sk_0026.djvu 1.5.2. Making use of the semantics of the problem......Page __sk_0027.djvu 2.1. Signs: signifiers and signifieds......Page __sk_0029.djvu 2.2.1. Definitions......Page __sk_0030.djvu 2.2.2. The aims of pattern recognition......Page __sk_0032.djvu 2.2.3. Some further definitions......Page __sk_0033.djvu 2.2.4. The methods of pattern recognition......Page __sk_0034.djvu 2.3.1. Relations between the representations......Page __sk_0036.djvu 2.3.2. Object-concept distance; characteristic functions......Page __sk_0037.djvu 2.3.3. Finite set of representations......Page __sk_0039.djvu 2.3.4. Ordinal variables......Page __sk_0040.djvu 2.3.6. Euclidean vector space......Page __sk_0041.djvu 2.3.7. Invariant representations......Page __sk_0045.djvu 2.3.8. Influence of the interpretation on the properties of the representation......Page __sk_0046.djvu 2.4.1. Operators as signifiers......Page __sk_0048.djvu 2.4.2. Linear operators......Page __sk_0049.djvu 2.4.3. Logical, syntactic and linguistic operators......Page __sk_0051.djvu 2.4.4. Combinations of operators......Page __sk_0054.djvu 2.4.5. Semantics and pragmatics......Page __sk_0060.djvu 3.1.1. Linear filters......Page __sk_0067.djvu 3.1.2. Fourier transform......Page __sk_0069.djvu 3.1.3. Signals with bounded domain spectrum......Page __sk_0071.djvu 3.1.4. Fractals......Page __sk_0075.djvu 3.2. Periodic signals and Fourier series......Page __sk_0077.djvu 3.3. Fourier transforms in information science......Page __sk_0080.djvu 3.3.1. Discrete Fourier transform......Page __sk_0081.djvu 3.3.2. Fast Fourier transform......Page __sk_0082.djvu 3.4.1. Functions of a complex variable: recapitulation......Page __sk_0084.djvu 3.4.2. z-transform for linear filters......Page __sk_0085.djvu 3.4.3. Linear prediction......Page __sk_0086.djvu 3.5.1. Entropy and volume of information......Page __sk_0087.djvu 3.5.2. Use of unitary transforms......Page __sk_0092.djvu 3.5.3. Correlation matrix for an image......Page __sk_0097.djvu 3.5.4. Compression of multi-spectral images using the Karhunen-Loève algorithm......Page __sk_0099.djvu 3.5.5. Use of unitary transforms other than the Karhunen-Loève transform......Page __sk_0100.djvu 3.6.1. Vignes' permutation-perturbation method......Page __sk_0101.djvu 3.6.2. Practical application: software for Vignes' method......Page __sk_0102.djvu 4.1. Partitions of a finite set......Page __sk_0103.djvu 4.1.1. Enumeration of partitions Hierarchies......Page __sk_0104.djvu 4.3. Ultrametrics and clustering......Page __sk_0107.djvu 4.3.1. Ultrametric distance......Page __sk_0108.djvu 4.3.2. Ultrametric space......Page __sk_0109.djvu 4.3.3. Obtaining an ultrametric from a metric......Page __sk_0110.djvu 4.3.4. Distances and linkage effect......Page __sk_0112.djvu 4.3.5. Comments on the clustering methods......Page __sk_0113.djvu 4.4. Finite sets and the graph of distances......Page __sk_0114.djvu 4.4.1. Minimum length tree......Page __sk_0115.djvu 4.4.2. Algorithms for graphs of distances......Page __sk_0117.djvu 4.5.1. Relational data structures......Page __sk_0118.djvu 4.5.2. Comparison of descriptions......Page __sk_0119.djvu 4.5.3. Classification of descriptions......Page __sk_0123.djvu 4.5.4. Inference and expert systems......Page __sk_0126.djvu 4.6. Pattern matching......Page __sk_0131.djvu 4.6.1. String matching......Page __sk_0132.djvu 4.6.2. Searching for repeated patterns......Page __sk_0133.djvu 4.7. Distance between elements......Page __sk_0135.djvu 4.7.1. Quantitative variables......Page __sk_0136.djvu 4.7.2. Qualitative variables......Page __sk_0138.djvu 4.7.3. Distance between character strings......Page __sk_0140.djvu 4.7.4. Dynamic programming......Page __sk_0141.djvu 4.8. Measures of similarity between variables......Page __sk_0146.djvu 4.9. Distance measures for objects and concepts......Page __sk_0147.djvu 4.9.1. Comparison of object-concept distances......Page __sk_0149.djvu 4.10. Adaptive partitions......Page __sk_0151.djvu 4.10.1. Basic principles, and some history......Page __sk_0152.djvu 4.10.2. The dynamic cluster algorithm......Page __sk_0153.djvu 4.10.3. Some properties of R^n......Page __sk_0160.djvu 4.10.4. Initial tests for inhomogeneity......Page __sk_0161.djvu 5. Ordinal representation space......Page __sk_0163.djvu 5.1. Peano-Hilbert scan in an n-ordinal space......Page __sk_0164.djvu 5.1.1. Definition of the Peano-Hilbert scan......Page __sk_0165.djvu 5.1.2. Properties of the Peano-Hilbert scan......Page __sk_0167.djvu 5.1.3. Application of the Peano-Hilbert scan......Page __sk_0168.djvu 5.2. Intrinsic dimension of a data set......Page __sk_0172.djvu 5.3.1. Properties of the neighbourhood graph......Page __sk_0175.djvu 5.4. n-ordinal data structures......Page __sk_0180.djvu 5.4.1. Oriented binary search tree......Page __sk_0181.djvu 6.1. Linear separation......Page __sk_0183.djvu 6.1.1. The perceptron algorithm......Page __sk_0184.djvu 6.1.2. The Ho Kashyap algorithm......Page __sk_0185.djvu 6.1.3. Partitioning by hyperplanes into k classes......Page __sk_0186.djvu 6.2. Statistical pattern recognition......Page __sk_0187.djvu 6.2.1. Bayesian decision theory......Page __sk_0188.djvu 6.2.2. Parametric Bayesian learning......Page __sk_0191.djvu 6.2.3. Non-parametric learning......Page __sk_0193.djvu 6.2.4. The q nearest neighbours......Page __sk_0194.djvu Bibliography......Page __sk_0199.djvu Index......Page __sk_0215.djvu