I have some data which looks roughly periodic - is there a nice way to measure this?    This is an example I'm working on and I'd like a metric that I will be able to just threshold to give a decision of yes or no. I was thinking maybe looking into the Fourier domain or looking at correlation. Many thanks.
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This post is the continuation of another post related to a . Basically, at this point I'm interested in a robust way to discover the periodicity/seasonality of a generic time series affected by a lot of noise. From a developer point of view, I would like a simple interface such as:  unsigned int discover_period(vector&lt;double&gt; v);  Where v is the array containing the samples, and the return value is the period of the signal. The main point is that, again, I can't make any assumption regarding the analyzed signal. I already tried an approach based on the signal autocorrelation (detecting the peaks of a correlogram), but it's not robust as I would like.
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I am trying to determine the level of spatial autocorrelation in a point dataset.  The attribute I'm interested in is binary (presence/absence of a species), for which Moran's I is not appropriate.  On the other hand, Joint Count statistics, which are typically recommended for binary or categorical data, apparently are not appropriate for point data. What is an appropriate statistic to measure global and/or local spatial autocorrelation of points when the attribute of interest is binary?
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Equivalently, about variance?  I realize it measures the spread of a distribution, but many other metrics could do the same (e.g., the average absolute deviation). What is its deeper significance? Does it have    a particular geometric interpretation (in the sense, e.g., that the mean is the balancing point of a distribution)?  any other intuitive interpretation that differentiates it from other possible measures of spread?   What's so special about it that makes it act as a normalizing factor in all sorts of situations (for example, convert covariance to correlation)?
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I am not getting satisficatory explanation for this. Clearly $f(x+T) = f(x)$ for all values of $T$.  If we assume it is periodic, does this mean period =  $0$?
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Which is best plot, from statistical standpoint, to show a , which is typically being analyzed by chi-square test? Is it a dodged barplot, stacked barplot, heatmap, contour plot, jitterred scatterplot, multiple lines plot or something else? Should one show absolute values or percentages?  Edit: Or as @forecaster suggests in the comments, the table of numbers is itself a simple plot and should be sufficient.
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I'm more of a math guy than a physics guy so bear with me....  In fractal geometry, fractals are considered to have fractional dimension. For instance an object such as the Koch curve has a fractal dimension of around $1.2$. You can also define a concept called fractal extent (which is the experimental version of hausdorff measure). This extent is a measure of how large a fractal is. It's even been used to more accurately model the distribution of coastline bird nesting.   Even though fractals work as an interpretation of geometrical units, I don't think they would describe things such as $kg^{1/2}$ very well. In addition, I've heard about white Gaussian noise that has square root time units.   What is the physical meaning of fractional units such as the above? (Since it obviously has little geometric meaning)
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Given two histograms, how do we assess whether they are similar or not?  Is it sufficient to simply look at the two histograms? The simple one to one mapping has the problem that if a histogram is slightly different and slightly shifted then we'll not get the desired result.  Any suggestions?
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What is the physical significance of $\omega$ in a function like  $$ f(x) = A\sin(kx + \omega t). $$  The only place that I am familiar with angular frequency is when dealing with circular motion, but when it comes to waves I am not clear how the analogy holds. I am familiar with the idea of a reference circle when dealing with simple harmonic motion, I am still a bit unclear on how this extends to waves. What exactly is this quantity measuring, and why is it useful to write the function in this form rather than an alternative (but equivalent) fashion?
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I noticed that , given an operation like $\frac{n}{m},\;n,m \in N$ that result in a periodic decimal number, computes really fast the length of the period.  E.g. $\frac{3923}{6173}$ has a period of 3086: .  I was wondering how this computation is done: is there some method to do this (except the trivial one of executing the division and looking for a sequence repetition) ?
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If $f$ is a periodic function with $T = \pi$, does that mean that $F$ (a primitive of $f$) has the same period ? What about the inverse implication (periodic primitive implies periodic function) ?
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Just saw , and realized that  1/9801 = 0.(000102030405060708091011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465666768697071727374757677787980818283848586878889909192939495969799)(repeat)  Similar properties are also exhibited by numbers , , .. and so on. Edit: fixed periodic start and end It is not very obvious to me why this happens. Is there some simple explanation to this property?
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I am using Silhouette width to compute the best value for k in k-means. As I am performing document clustering, I am calculating the values of a and b as follows in Python:  a = distance(data[index], centroids[clusters[index]], metric=metric, p=p) b = min([distance(data[index], c) for i,c in enumerate(centroids) if i != currentindex]) score = float(b - a) / max(a, b) if max(a, b) &gt; 0 else 0.0   The original formula from the  is the following:    I am using a cosine similarity measure to compute the distances and was wondering if this formula needs to be changed or it can be left as is. In the above snippet of code, the function distance computes the cosine similarity metric.
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As title, is there anything like this? I know how to calculate CI for arithmetic mean, but how about geometric mean? Thanks.
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With the Taylor series representation of $\sin$ or $\cos$ as a starting point (and assuming no other knowledge about those functions), how can one:  a. prove they are periodic?  b. find the value of the period?
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This is an elementary question, but I wasn't able to find the answer.  I have two measurements: n1 events in time t1 and n2 events in time t2, both produced (say) by Poisson processes with possibly-different lambda values.  This is actually from a news article, which essentially claims that since $n_1/t_1\neq n_2/t_2$ that the two are different, but I'm not sure that the claim is valid.  Suppose that the time periods were not chosen maliciously (to maximize the events in one or the other).  Can I just do a t-test, or would that not be appropriate?  The number of events is too small for me to comfortably call the distributions approximately normal.
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I need an algorithm that can determine whether two images are 'similar' and recognizes similar patterns of color, brightness, shape etc.. I might need some pointers as to what parameters the human brain uses to 'categorize' images. ..   I have looked at hausdorff based matching but that seems mainly for matching transformed objects and patterns of shape.
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Any rank 2 tensor would do the same trick, right?  Then, which is the motivation for choosing the metric one?    Also, if you help me to prove that $g^{kp}g_{ip}=\delta^k_i$, I would be thankful too ^^