Error Rate Word
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lies in the fact that the recognized word sequence can have a different length from the reference word sequence (supposedly the correct one). The WER is derived word error mswrd632 wpc from the Levenshtein distance, working at the word level instead of the
Bit Error Rate
phoneme level. The WER is a valuable tool for comparing different systems as well as for evaluating improvements within word error rate algorithm one system. This kind of measurement, however, provides no details on the nature of translation errors and further work is therefore required to identify the main source(s) of error and to word error rate example focus any research effort. This problem is solved by first aligning the recognized word sequence with the reference (spoken) word sequence using dynamic string alignment. Examination of this issue is seen through a theory called the power law that states the correlation between perplexity and word error rate.[1] Word error rate can then be computed as: W E R = S + D
Word Error Rate Python
+ I N = S + D + I S + D + C {\displaystyle {\mathit {WER}}={\frac {S+D+I}{N}}={\frac {S+D+I}{S+D+C}}} where S is the number of substitutions, D is the number of deletions, I is the number of insertions, C is the number of the corrects, N is the number of words in the reference (N=S+D+C) The intuition behind 'deletion' and 'insertion' is how to get from the reference to the hypothesis. So if we have the reference "This is wikipedia" and hypothesis "This _ wikipedia", we call it a deletion. When reporting the performance of a speech recognition system, sometimes word accuracy (WAcc) is used instead: W A c c = 1 − W E R = N − S − D − I N = H − I N {\displaystyle {\mathit {WAcc}}=1-{\mathit {WER}}={\frac {N-S-D-I}{N}}={\frac {H-I}{N}}} where H is N-(S+D), the number of correctly recognized words. IF I=0 then WAcc will be equivalent to Recall (information retrieval) a ratio of correctly recognized words 'H' to Total number of words in reference 'N'. Note that since N is the number of words in the reference, the w
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Error Rate Running Record
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an hypothesis and is defined like this: $$\mathit{WER} = \frac{S+D+I}{N}$$ where S is the number of substitutions, D is the number of deletions, I is the number of insertions and N is the number of words in the reference https://martin-thoma.com/word-error-rate-calculation/ Examples REF: What a bright day HYP: What a day In this case, a deletion happened. "Bright" was deleted by the ASR. REF: What a day HYP: What a bright day In this case, an insertion https://www.mathworks.com/matlabcentral/fileexchange/55825-word-error-rate happened. "Bright" was inserted by the ASR. REF: What a bright day HYP: What a light day In this case, an substitution happened. "Bright" was substituted by "light" by the ASR. Range of values As only error rate addition and division with non-negative numbers happen, WER cannot get negativ. It is 0 exactly when the hypothesis is the same as the reference. WER can get arbitrary large, because the ASR can insert an arbitrary amount of words. Calculation Interestingly, the WER is just the Levenshtein distance for words. I've understood it after I saw this on the German Wikipedia: \begin{align} m &= |r|\\ n &= |h|\\ \end{align} \begin{align} D_{0, 0} word error rate &= 0\\ D_{i, 0} &= i, 1 \leq i \leq m\\ D_{0, j} &= j, 1 \leq j \leq n \end{align} $$ \text{For } 1 \leq i\leq m, 1\leq j \leq n\\ D_{i, j} = \min \begin{cases} D_{i - 1, j - 1}&+ 0 \ {\rm if}\ u_i = v_j\\ D_{i - 1, j - 1}&+ 1 \ {\rm(Replacement)} \\ D_{i, j - 1}&+ 1 \ {\rm(Insertion)} \\ D_{i - 1, j}&+ 1 \ {\rm(Deletion)} \end{cases} $$ But I have written a piece of pseudocode to make it even easier to code this algorithm: WER calculation Python #!/usr/bin/env python def wer(r, h): """ Calculation of WER with Levenshtein distance. Works only for iterables up to 254 elements (uint8). O(nm) time ans space complexity. Parameters ---------- r : list h : list Returns ------- int Examples -------- >>> wer("who is there".split(), "is there".split()) 1 >>> wer("who is there".split(), "".split()) 3 >>> wer("".split(), "who is there".split()) 3 """ # initialisation import numpy d = numpy.zeros((len(r)+1)*(len(h)+1), dtype=numpy.uint8) d = d.reshape((len(r)+1, len(h)+1)) for i in range(len(r)+1): for j in range(len(h)+1): if i == 0: d[0][j] = j elif j == 0: d[i][0] = i # computation for i in range(1, len(r)+1): for j in range(1, len(h)+1): if r[i-1] == h[j-1]: d[i][j] = d[i-1][j-1] else: substitution = d[i-1][j-1] +
toolboxes, and other File Exchange content using Add-On Explorer in MATLAB. » Watch video Highlights from Word Error Rate WORD ERROR RATE WER(h,r,varargin)The function is intended for calculation of word error rate (WER) View all files Join the 15-year community celebration. Play games and win prizes! » Learn more Be the first to rate this file! 5 Downloads (last 30 days) File Size: 8.67 KB File ID: #55825 Version: 1.0 Word Error Rate by Eduard Polityko Eduard Polityko (view profile) 8 files 71 downloads 4.5 07 Mar 2016 The function calculates WER between word sequences H (hypothesis) and R (reference). | Watch this File File Information Description Word error rate (WER) is a measure (metric) of the performance of an automatic speech recognition, machine translation etc. The function is intended for calculation of WER between word sequence H (hypothesis) and word sequence R (reference). For calculation we use Levenshtein distance on word level. Levenshtein distance is a minimal quantity of insertions, deletions and substitutions of words for conversion of a hypothesis to a reference. WER=D(H,R)/N, where D(H,R) is a Levenshtein distance between H and R and N is the number of words in the reference R. H and R are cell arrays of words (for example after using TEXTSCAN) or cells with word sequences or strings. Types H and R may be different. MATLAB release MATLAB 8.5 (R2015a) MATLAB Search Path / /html Tags for This File Please login to tag files. error ratestringsutilities Cancel Please login to add a comment or rating. Contact us MathWorks Accelerating the pace of engineering and science MathWorks is the leading developer of mathematical computing software for engineers and scientists. Discover... Explore Products MATLAB Simulink Student Software Hardware Support File Exchange Try or Buy Downloads Trial Software Contact Sales Pricing and Licensing Learn to Use Documentation Tutorials Examples Videos and Webinars Training Get Support Installation Help Answers Consulting License Center About MathWorks Careers Company Overview Newsroom Social Mission © 1994-2016 The MathWorks, Inc. Patents Trademarks Privacy Policy Preventing Piracy Terms of Use RSS Google+ Facebook Twitter