Method for solving waveform sequence-matching problems using multidimensional attractor tokens
First Claim
1. A method of waveform comparison comprising:
- (a) mapping, through an attractor process, at least first and second waveform sequence source multisets, from an original representation space (ORS) into an attractor behavior space;
(i) each of said at least first and second waveform sequence source multisets being a plurality of subsets of a first and second waveform sequence and each subset having a plurality of waveform sequence elements;
(ii) said attractor process being an iterative process which causes first and second waveform sequences source multisets in the ORS to converge to at least two distinct behaviors in said attractor behavior space;
(iii) wherein each behavior in said attractor behavior space is assigned a distinct symbol from a symbol scheme, (iv) said mapping resulting in a first and second token string, each consisting of a series of said symbols, corresponding to said first and second waveform sequence source multisets respectively;
(b) mapping, through said attractor process and into said attractor behavior space, a plurality of first and second waveform subsequences source multisets of said first and second waveform sequences respectively, (i) said plurality of first and second waveform subsequence source multisets each being a plurality of subsets of a different one of a plurality of first and second waveform subsequence of said first and second waveform sequence and each having a number of waveform sequence elements;
(ii) said mapping resulting in a plurality of first and second subsequence token strings, each consisting of a series of said symbols, corresponding to said plurality of first and second waveform subsequence source multisets respectively; and
(c) comparing said first token string and said plurality of first subsequence token strings with said second token string and said plurality of second subsequence token strings to determine a match among said first and second waveform sequence source multisets and said plurality of first and second waveform subsequences source multisets.
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Abstract
An improved method is provided for solving waveform description, matching and comparison problems using attractor-based processes to extract identity tokens that indicate sequence and subsequence symbol content and order of the waveform or waveform segments. The waveform is described with a suitable alphabet to extract the ontology of the waveform, and syntactical rules are applied to direct pattern extraction using the alphabet. The patterns are extracted in a hierarchical, embedded manner according the global or local maximia and minimia so that the resulting statements are compatible with analysis in catastrophe theory. The attractor processes map the resulting waveform sequence from its original sequence representation space (OSRS) into a hierarchical multidimensional attractor space (HMAS). The HMAS can be configured to represent equivalent symbol distributions within two symbol sequences or perform exact symbol sequence matching. The mapping process results in each sequence being drawn to an attractor in the HMAS. Each attractor within the HMAS forms a unique token for a group of sequences with no overlap between the sequence groups represented by different attractors. The size of the sequence groups represented by a given attractor can be reduced from approximately half of all possible sequences to a much smaller subset of possible sequences. The mapping process is repeated for a given sequence so that tokens are created for the whole sequence and a series of subsequences created by repeatedly removing a symbol or group of symbols from the one end of sequence and then repeating the process from the other end. The resulting string of tokens represents the exact identity of the whole sequence and all its subsequences ordered from each end.
10 Citations
30 Claims
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1. A method of waveform comparison comprising:
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(a) mapping, through an attractor process, at least first and second waveform sequence source multisets, from an original representation space (ORS) into an attractor behavior space;
(i) each of said at least first and second waveform sequence source multisets being a plurality of subsets of a first and second waveform sequence and each subset having a plurality of waveform sequence elements;
(ii) said attractor process being an iterative process which causes first and second waveform sequences source multisets in the ORS to converge to at least two distinct behaviors in said attractor behavior space;
(iii) wherein each behavior in said attractor behavior space is assigned a distinct symbol from a symbol scheme, (iv) said mapping resulting in a first and second token string, each consisting of a series of said symbols, corresponding to said first and second waveform sequence source multisets respectively;
(b) mapping, through said attractor process and into said attractor behavior space, a plurality of first and second waveform subsequences source multisets of said first and second waveform sequences respectively, (i) said plurality of first and second waveform subsequence source multisets each being a plurality of subsets of a different one of a plurality of first and second waveform subsequence of said first and second waveform sequence and each having a number of waveform sequence elements;
(ii) said mapping resulting in a plurality of first and second subsequence token strings, each consisting of a series of said symbols, corresponding to said plurality of first and second waveform subsequence source multisets respectively; and
(c) comparing said first token string and said plurality of first subsequence token strings with said second token string and said plurality of second subsequence token strings to determine a match among said first and second waveform sequence source multisets and said plurality of first and second waveform subsequences source multisets. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22)
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23. A method of waveform comparison comprising:
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(a) mapping, through an attractor process, a first waveform sequence source multiset, from an original representation space (ORS) into an attractor behavior space;
(i) said first waveform sequence source multisets being a plurality of subsets of a first waveform sequence and each subset having a plurality of waveform sequence elements;
(ii) said attractor process being an iterative and contractive process which causes first waveform sequences source multisets in the ORS to converge to at least two distinct behaviors in said attractor behavior space;
(iii) wherein each behavior in said attractor behavior space is assigned a distinct symbol from a symbol scheme, (iv) said mapping resulting in a first token string consisting of a series of said symbols, corresponding to said first waveform sequence source multisets respectively;
(b) mapping, through said attractor process and into said attractor behavior space, a plurality of first waveform subsequences source multisets of said first waveform sequences respectively, (i) said plurality of first waveform subsequence source multisets being a plurality of subsets of a different one of a plurality of a first waveform subsequence of said first waveform sequence and each having a number of waveform sequence elements;
(ii) said mapping resulting in a plurality of first subsequence token strings, each consisting of a series of said symbols, corresponding to said plurality of first waveform subsequence source multisets respectively; and
(c) mapping, through an attractor process, a second waveform sequence source multiset, from an original representation space (ORS) into an attractor behavior space;
(i) said second waveform sequence source multisets being a plurality of subsets of a second waveform sequence and each subset having a plurality of waveform sequence elements;
(ii) said attractor process being an iterative and contractive process which causes second waveform sequences source multisets in the ORS to converge to at least two distinct behaviors in said attractor behavior space;
(iii) wherein each behavior in said attractor behavior space is assigned a distinct symbol from said symbol scheme, (iv) said mapping resulting in a second token string consisting of a series of said symbols, corresponding to said second waveform sequence source multisets respectively;
(d) mapping, through said attractor process and into said attractor behavior space, a plurality of second waveform subsequences source multisets of said second waveform sequences respectively, (i) said plurality of second waveform subsequence source multisets being a plurality of subsets of a different one of a plurality of a second waveform subsequence of said second waveform sequence and each having a number of waveform sequence elements;
(ii) said mapping resulting in a plurality of second subsequence token strings, each consisting of a series of said symbols, corresponding to said plurality of second waveform subsequence source multisets respectively; and
(e) comparing said first token string and said plurality of first subsequence token strings with said second token string and said plurality of second subsequence token strings respectively to determine a match among said first and second waveform sequence source multisets and said plurality of first and second waveform subsequences source multisets.
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24. A method of waveform comparison comprising:
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(a) representing a first waveform as a first series of discrete points, each point having a value, a first waveform sequence source multiset being at least a portion of said first series of discrete points and a plurality of subsets of said portion of said first series of discrete points, and each subset having a plurality of said discrete points as waveform sequence elements;
(i) mapping, through an iterative and contractive process, said first waveform sequence source multiset into an attractor behavior space having at least two distinct behaviors with each behavior assigned a distinct symbol;
(ii) said mapping resulting in a first token string consisting of a series of said symbols, corresponding to said first waveform sequence source multisets;
(b) representing a second waveform as a second series of discrete points, each point having a value, a second waveform sequence source multiset being at least a portion of said second series of discrete points and a plurality of subsets of said portion of said second series of discrete points, and each subset having a plurality of said discrete points as waveform sequence elements;
(i) mapping, through said iterative and contractive process, said second waveform sequence source multiset into said attractor behavior space;
(ii) said mapping resulting in a second token string consisting of a series of said symbols, corresponding to said second waveform sequence source multisets;
(c) comparing said first token string and with said second token string to determine a match among said first and second waveform sequence source multisets. - View Dependent Claims (25, 26, 27, 28)
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29. A method of comparing at least a first and second waveform comprising the steps of:
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(a) representing the first waveform as a series of discrete points;
(b) setting k initially equal to “
first”
where k is an ordinal number;
(c) selecting a k plurality of points based on a k resolution examination of said series of discrete points;
(d) assigning symbols from an alphabet of symbols to represent the k plurality of points at said k resolution examination;
(e) incrementing k such that k=k+1;
(f) repeating steps (c) and (d) at least once;
(g) forming a sequence of symbols by combining the assigned symbols formed in steps (d);
(h) mapping said sequence with an iterative, contractive process which causes said sequence to converge on one of at least two different behaviors, and assigning a first token indicative of said behavior;
(i) representing the second waveform as a series of discrete points;
(j) setting m initially equal to “
first”
where m is an ordinal number;
(k) selecting a m plurality of points based on a m resolution examination of said series of discrete points;
(l) assigning symbols from said alphabet of symbols to represent the m plurality of points at said m resolution examination;
(m) incrementing m such that m=m+1;
(n) repeating steps (k) and (l) at least once;
(o) forming a sequence of symbols by combining the assigned symbols formed in steps (l);
(p) mapping said sequence with an iterative, contractive process which causes said sequence to converge on one of at least two different behaviors, and assigning a second token indicative of said behavior;
(q) comparing said first and second waveforms by comparing the first and second tokens. - View Dependent Claims (30)
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Specification