Compression reduces the size of a representation of an object while preserving all or some of its information. Lossless compression loses no information and allows the original object to be reconstructed exactly, while lossy compression loses some. Information can only be compressed insofar as it has lawful regularities; noise, which has no regularities by definition, is incompressible.
ββββββββββββββ COMPRESSION TOPOLOGY ANALYZER ββββββββββββββββββ
β Information Density and Pattern Recognition β
ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
β β
β Lossless Compression: β
β βββββββββββββββββββββββββββββββββββββββββββββββββββ β
β β Original Compressed Reconstructed β β
β β AAABBBCCC β 3A3B3C β AAABBBCCC β β
β β Size: 9 Size: 6 Size: 9 β β
β β Info: 100% Info: 100% Info: 100% β β
β βββββββββββββββββββββββββββββββββββββββββββββββββββ β
β β
β Lossy Compression: β
β βββββββββββββββββββββββββββββββββββββββββββββββββββ β
β β Original Compressed Reconstructed β β
β β ββββββ β βββ β βββ β β
β β ββββββ βββ βββ β β
β β ββββββ βββ βββ β β
β β Size: 48 Size: 12 Size: 12 β β
β β Info: 100% Info: 85% Info: 85% β β
β βββββββββββββββββββββββββββββββββββββββββββββββββββ β
β β
β Pattern vs. Noise Compression: β
β βββββββββββββββββββββββββββββββββββββββββββββββββββ β
β β Pattern: 1010101010 β [10]Γ5 (60% smaller) β β
β β Noise: 1001011100 β 1001011100 (0% smaller)β β
β βββββββββββββββββββββββββββββββββββββββββββββββββββ β
β β
β Compression Ratio vs. Pattern Recognition: β
β βββββββββββββββββββββββββββββββββββββββββββββββββββ β
β βRatioβ β β
β β100% β βββ β β
β β 80% β β βββ β β
β β 60% β β βββ β β
β β 40% β β βββ β β
β β 20% ββ ββββ β β
β β 0% ββββββββββββββββββββββββββ> Pattern Strengthβ β
β βββββββββββββββββββββββββββββββββββββββββββββββββββ β
β β
β Information Theory Metrics: β
β β’ Shannon Entropy: H = -β p(x) logβ p(x) β
β β’ Compression Ratio = Compressed Size / Original Size β
β β’ Information Retention = Recovered Info / Original Info β
β β
β [Analyze Pattern] [Compress Data] [Calculate Entropy] β
βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ