[ \textFeature = \textVar\left( S_xx(t, t-w) \right) ] [ \textWeightedVar(S_xx) = \frac\sum w_i (S_xx^(i) - \barS_xx^(w))^2\sum w_i ] where ( w_i ) could be recency or confidence weights. c. Variance of Sxx across groups If data has groups ( g = 1 \dots G ), compute ( S_xx^(g) ) per group, then variance of these ( G ) values. d. Sxx variance ratio (deep feature for heteroskedasticity) [ R = \frac\textVar(S_xx^\text(left half))\textVar(S_xx^\text(right half)) ] e. Interaction with other variables For two variables ( x ) and ( y ): [ \textDeepFeature = \frac\textVar(S_xx)\textVar(S_yy) \times \textCov(x,y)^2 ] 2. If Sxx is Power Spectral Density (signal processing) In spectral analysis: [ S_xx(f) = \frac1F_s \left| \sum_n x(n) e^-j2\pi f n \right|^2 ] Variance of ( S_xx(f) ) across frequency is not typically used — instead, variance across time for a given frequency (spectrogram variance) is a deep feature. Deep feature: Temporal variance of spectral power For each frequency bin ( f_k ), over time frames ( t ): [ \textVar t[ S xx(f_k, t) ] ] Then aggregate across frequencies (e.g., mean, max, entropy of variances). Another deep feature: Spectral variance of Sxx [ \textVar f[ S xx(f) ] ] over the frequency axis — measures spectral flatness in variance terms. 3. General deep feature construction from Sxx variance If you want a learned deep feature (e.g., for a neural network), you can embed Sxx variance into a trainable form:
[ \textVar(x) = \fracS_xxn-1 \quad \text(sample variance) ] Sxx Variance Formula
= ( \textReLU(W_1 \cdot S_xx + W_2 \cdot v + b) ) or Use ( \log(v) ) and ( \log(m) ) as inputs to a dense layer. [ \textFeature = \textVar\left( S_xx(t, t-w) \right) ]
In many contexts, refers to the sum of squares of deviations for a variable ( x ), typically defined as: If Sxx is Power Spectral Density (signal processing)
[ S_xx = \sum_i=1^n (x_i - \barx)^2 ]
It sounds like you're asking for a — likely a derived feature for machine learning or signal processing — related to the Sxx variance formula .
For sequential data, apply an LSTM/Transformer to a sequence of ( S_xx ) values and compute the as a meta-feature. Summary Table of Deep Features for Sxx Variance | Interpretation | Deep Feature | Formula | |---|---|---| | Regression Sxx | Rolling window variance of Sxx | ( \textVar t(S xx(t-w:t)) ) | | Regression Sxx | Cross-group Sxx variance | ( \textVar g(S xx^(g)) ) | | Spectral Sxx(f) | Temporal variance of spectral power | ( \textVar t[S xx(f_k, t)] ) | | Spectral Sxx(f) | Variance across frequencies | ( \textVar f[S xx(f)] ) | | Generic | Nonlinear interaction | ( \sigma_S_xx^2 \cdot \mathbbE[S_xx^2] ) | If you clarify whether Sxx is from time-domain sums of squares or frequency-domain power spectrum , I can give you exact code (Python/NumPy) for extracting the deep feature.