sphere-ser 0.1.0

SPHERE: Single-Pass Hierarchical Effort-Robust Estimator — psychoacoustically grounded feature scaler for Speech Emotion Recognition

sphere-ser

SPHERE — Single-Pass Hierarchical Effort-Robust Estimator

A psychoacoustically grounded, sklearn-compatible feature scaler for Speech Emotion Recognition (SER).

pip install sphere-ser

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Why SPHERE?

Existing scalers treat all frames and feature dimensions uniformly. Emotional speech breaks every assumption they make:

Problem	Existing scalers	SPHERE
High-energy emotion frames distort statistics	Ignored	Energy-weighted P² median
MFCC distributions are right/left-skewed	Symmetric	Asymmetric σ⁺ / σ⁻
All frequency bands treated equally	None	Bark-ERB perceptual gain γ_f
Outlier arousal peaks break StandardScaler	Breakdown ε*→0	ε* = ½ (centre)
Expensive rolling median	O(T log T)	O(1) per sample via P²

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Quick Start

import numpy as np
from sphere_ser import SPHERE

X_train = np.random.randn(200, 40)   # (T frames, F features)
X_test  = np.random.randn(50,  40)

scaler = SPHERE(sample_rate=22050)
X_train_scaled = scaler.fit_transform(X_train)
X_test_scaled  = scaler.transform(X_test)

sklearn Pipeline

from sklearn.pipeline import Pipeline
from sklearn.svm import SVC
from sphere_ser import SPHERE

pipe = Pipeline([
    ('sphere', SPHERE(sample_rate=22050)),
    ('clf',    SVC(kernel='rbf', class_weight='balanced')),
])
pipe.fit(X_train_feats, y_train)
preds = pipe.predict(X_test_feats)

Inspect fitted statistics

scaler = SPHERE().fit(X_train)
print(scaler.feature_summary())
# SPHERE fitted on 200 frames × 40 features
#   Median range  : [-0.31, 0.42]
#   σ⁺ range      : [0.08, 1.43]
#   σ⁻ range      : [0.07, 1.22]
#   Bark γ range  : [0.98, 1.27]
#   Asymmetry (ρ) : right=18  sym≈14  left=8

stats = scaler.get_statistics()
# Keys: medians, sigma_plus, sigma_minus, bark_gains, asymmetry_ratio,
#       n_features, n_samples

print("Right-skewed features:", (stats['asymmetry_ratio'] > 1.2).sum())

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Algorithm

Offline  │  Bark-ERB gain γ_f     O(F)    precomputed once
─────────┼───────────────────────────────────────────────────
Pass 1   │  P² streaming median   O(TF)   O(5F) memory
Pass 2   │  Centred TKEO ψ_c      O(TF)   O(F)  memory
         │  Asymmetric σ⁺, σ⁻    O(TF)
         │  SPHERE transform      O(TF)

Core transform for each sample (t, f):

x̃(t,f) = γ_f · (x(t,f) − m̂_f) / (σ̂_asym(t,f) + ε)

  σ̂_asym = σ̂⁺_ψ(f)  if x(t,f) > m̂_f
           σ̂⁻_ψ(f)  otherwise

Component	Purpose	Ref
P² median	O(1)-per-sample robust centre; ε* = ½	Jain & Chlamtac 1985
Centred TKEO	Effort-spread A²ω² per feature trajectory	Teager 1980
Asymmetric σ⁺/σ⁻	Adapts to skewness of emotional distributions	Novel
Bark-ERB gain γ_f	Cochlear frequency resolution weighting	Zwicker 1980

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Standalone Components

from sphere_ser import P2Quantile, BarkGain, TKEO, centred_tkeo, bark_gain

# P² streaming quantile
p2 = P2Quantile(n_features=40, p=0.5)
for frame in X:
    p2.update(frame)
medians = p2.estimate()          # (40,)

# Bark-ERB gain
bg = BarkGain(sample_rate=22050)
gains = bg.compute(n_features=40)               # (40,)
freqs = bg.centre_frequencies(n_features=40)    # Hz per coeff
bws   = bg.critical_bandwidths(n_features=40)   # Bark BW per coeff

# Centred TKEO
import numpy as np
psi_c = centred_tkeo(X, medians)                # (T-2, F)

# Asymmetric TKEO spread
op = TKEO(clip_factor=9.0)
psi        = op.centred(X, medians)
sig_p, sig_m = op.asymmetric_spread(X, medians, psi)

---

Parameters

Parameter	Default	Description
epsilon	1e-8	Numerical stability constant
sample_rate	22050	Sample rate (Hz) for Bark gain
use_bark_gain	True	Apply Bark-ERB perceptual gain
clip_tkeo	True	Clip TKEO at clip_factor × σ_pilot
clip_factor	9.0	TKEO clipping multiplier
min_frames_fallback	True	Fallback to mean/std for T < 5

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Theoretical Properties

Property	Value
Centre breakdown point	1/2 (optimal)
Scale breakdown point	1/3 (bounded contamination)
Location equivariance	Exact
Scale equivariance	Asymptotic (ε → 0)
Time complexity	O(TF)
Memory	O(F)

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Citation

@software{sphere_ser_2026,
  author = {{SPHERE Research Team}},
  title  = {{SPHERE}: Single-Pass Hierarchical Effort-Robust Estimator
            for Speech Emotion Recognition},
  year   = {2026},
  note   = {Proprietary Python software package}
}

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License

Proprietary software — see LICENSE for terms and conditions.