{
  "title": "Independent Component Analysis Mastery: 100 MCQs",
  "description": "A comprehensive set of 100 multiple-choice questions to test and deepen your understanding of ICA, covering fundamentals, assumptions, applications, and practical scenarios.",
  "questions": [
    {
      "id": 1,
      "questionText": "What is the main goal of Independent Component Analysis (ICA)?",
      "options": [
        "To separate a multivariate signal into additive independent components",
        "To predict a continuous target variable",
        "To cluster similar data points",
        "To reduce the dimensionality of data"
      ],
      "correctAnswerIndex": 0,
      "explanation": "ICA aims to decompose mixed signals into statistically independent components, often used in blind source separation."
    },
    {
      "id": 2,
      "questionText": "Which assumption is crucial for ICA?",
      "options": [
        "All features are equally scaled",
        "Components are statistically independent and non-Gaussian",
        "Components are Gaussian",
        "Data has no missing values"
      ],
      "correctAnswerIndex": 1,
      "explanation": "ICA requires that the underlying sources be statistically independent and non-Gaussian to successfully separate them."
    },
    {
      "id": 3,
      "questionText": "ICA is commonly applied in:",
      "options": [
        "Predicting stock prices",
        "Image recognition only",
        "Dimensionality reduction only",
        "Blind source separation, like separating mixed audio signals"
      ],
      "correctAnswerIndex": 3,
      "explanation": "ICA is widely used for separating mixed signals, such as audio, EEG, and financial signals, where independence is assumed."
    },
    {
      "id": 4,
      "questionText": "Scenario: You mix two audio signals into two recordings. Applying ICA:",
      "options": [
        "Will reduce dimensions only",
        "Will cluster the recordings",
        "Cannot do anything without labels",
        "Can recover the original separate audio sources"
      ],
      "correctAnswerIndex": 3,
      "explanation": "ICA can separate mixed signals into the original independent sources, assuming statistical independence."
    },
    {
      "id": 5,
      "questionText": "Which property differentiates ICA from PCA?",
      "options": [
        "ICA finds independent components, PCA finds uncorrelated components",
        "ICA reduces dimensions, PCA does not",
        "ICA works only for Gaussian data",
        "PCA requires independence, ICA does not"
      ],
      "correctAnswerIndex": 0,
      "explanation": "PCA decorrelates data but does not ensure independence. ICA focuses on statistical independence of components."
    },
    {
      "id": 6,
      "questionText": "Scenario: You apply ICA on 3 mixed signals but get more than 3 components. Likely reason?",
      "options": [
        "Algorithm error or wrong number of components specified",
        "Random initialization causes extra components",
        "Mixing is linear, so components must increase",
        "ICA always produces more components"
      ],
      "correctAnswerIndex": 0,
      "explanation": "The number of extracted independent components should not exceed the number of observed mixtures."
    },
    {
      "id": 7,
      "questionText": "ICA assumes the mixing process is:",
      "options": [
        "Nonlinear only",
        "Non-invertible",
        "Randomly noisy",
        "Linear and invertible"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Standard ICA assumes the observed signals are linear mixtures of independent sources, which allows recovery."
    },
    {
      "id": 8,
      "questionText": "Scenario: You apply ICA on EEG data. Purpose?",
      "options": [
        "Remove artifacts like eye blinks",
        "Reduce dimensionality only",
        "Cluster subjects",
        "Predict disease directly"
      ],
      "correctAnswerIndex": 0,
      "explanation": "ICA can separate EEG components and isolate artifacts for cleaner signal analysis."
    },
    {
      "id": 9,
      "questionText": "Which metric is commonly used to measure independence in ICA?",
      "options": [
        "Euclidean distance",
        "Correlation coefficient",
        "Variance explained",
        "Kurtosis or mutual information"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Non-Gaussianity measures like kurtosis or mutual information are used to quantify statistical independence."
    },
    {
      "id": 10,
      "questionText": "Scenario: Two independent sources are Gaussian. Applying ICA?",
      "options": [
        "Separation will work perfectly",
        "ICA will automatically decorrelate",
        "Cannot separate them because Gaussian sources do not satisfy ICA assumptions",
        "PCA is better"
      ],
      "correctAnswerIndex": 2,
      "explanation": "ICA requires non-Gaussian sources; Gaussian independent sources cannot be separated due to rotational ambiguity."
    },
    {
      "id": 11,
      "questionText": "Scenario: You observe mixed signals from two microphones. ICA aims to:",
      "options": [
        "Cluster the microphone locations",
        "Predict the next sound sample",
        "Reduce noise only",
        "Separate the original sound sources"
      ],
      "correctAnswerIndex": 3,
      "explanation": "ICA separates mixed signals into their statistically independent source components."
    },
    {
      "id": 12,
      "questionText": "What type of data scaling is usually recommended before ICA?",
      "options": [
        "Normalization to [0,1]",
        "Centering and whitening",
        "Log transformation",
        "No scaling needed"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Centering (zero mean) and whitening (decorrelation) improve ICA performance."
    },
    {
      "id": 13,
      "questionText": "Scenario: ICA applied on two mixed images. Output?",
      "options": [
        "Generate random noise",
        "Compress the images",
        "Recover original independent images",
        "Reduce image resolution"
      ],
      "correctAnswerIndex": 2,
      "explanation": "ICA can separate mixed signals in images, like separating overlapping patterns."
    },
    {
      "id": 14,
      "questionText": "ICA works best when sources are:",
      "options": [
        "Gaussian",
        "Non-Gaussian and independent",
        "Highly correlated",
        "Categorical"
      ],
      "correctAnswerIndex": 1,
      "explanation": "ICA relies on non-Gaussianity and independence to separate components successfully."
    },
    {
      "id": 15,
      "questionText": "Scenario: Two audio signals mixed linearly, ICA extracts 2 components. Issue if you extract 3?",
      "options": [
        "Extra component is meaningless",
        "Algorithm improves accuracy",
        "Signals become correlated",
        "Automatically reduces to 2"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Number of extracted components should match observed mixtures; extra components do not correspond to real sources."
    },
    {
      "id": 16,
      "questionText": "ICA differs from PCA because:",
      "options": [
        "ICA reduces dimensions, PCA does not",
        "PCA finds independent components, ICA finds uncorrelated components",
        "PCA decorrelates, ICA seeks independence",
        "ICA is supervised"
      ],
      "correctAnswerIndex": 2,
      "explanation": "PCA removes correlation, ICA removes higher-order dependencies (statistical independence)."
    },
    {
      "id": 17,
      "questionText": "Scenario: You want to denoise images using ICA. How?",
      "options": [
        "Randomly remove pixels",
        "Apply PCA only",
        "Cluster similar images",
        "Separate noise components from signals and remove them"
      ],
      "correctAnswerIndex": 3,
      "explanation": "ICA can isolate noise as an independent component, enabling its removal."
    },
    {
      "id": 18,
      "questionText": "Scenario: Applying ICA on mixed financial time series. Goal?",
      "options": [
        "Reduce time resolution",
        "Predict exact future prices",
        "Extract independent latent factors affecting markets",
        "Cluster assets"
      ],
      "correctAnswerIndex": 2,
      "explanation": "ICA identifies underlying independent sources driving observed mixed signals."
    },
    {
      "id": 19,
      "questionText": "ICA requires which property of the mixing matrix?",
      "options": [
        "Diagonal",
        "Singular",
        "Invertible",
        "Random"
      ],
      "correctAnswerIndex": 2,
      "explanation": "The mixing matrix must be invertible to recover the original sources."
    },
    {
      "id": 20,
      "questionText": "Scenario: Two signals are perfectly Gaussian. ICA outcome?",
      "options": [
        "Separation works normally",
        "Cannot separate sources due to rotational ambiguity",
        "Algorithm produces errors",
        "Signals are automatically decorrelated"
      ],
      "correctAnswerIndex": 1,
      "explanation": "ICA cannot separate Gaussian sources as any orthogonal rotation preserves Gaussianity."
    },
    {
      "id": 21,
      "questionText": "ICA can be used in which biomedical application?",
      "options": [
        "Genetic sequencing",
        "X-ray imaging only",
        "Blood pressure measurement",
        "EEG artifact removal"
      ],
      "correctAnswerIndex": 3,
      "explanation": "ICA is commonly used to separate eye-blink and muscle artifacts from EEG recordings."
    },
    {
      "id": 22,
      "questionText": "Scenario: ICA on audio + noise mixture. Noise is independent. Outcome?",
      "options": [
        "Noise can be separated and removed",
        "Signals become correlated",
        "Noise remains mixed",
        "Cannot separate due to Gaussian assumption"
      ],
      "correctAnswerIndex": 0,
      "explanation": "ICA can isolate independent noise components for removal."
    },
    {
      "id": 23,
      "questionText": "Scenario: ICA applied to images with overlapping letters. Goal?",
      "options": [
        "Predict next letter",
        "Separate individual letter images",
        "Remove color information",
        "Compress the image"
      ],
      "correctAnswerIndex": 1,
      "explanation": "ICA separates mixed patterns into independent sources, such as letters overlapping in images."
    },
    {
      "id": 24,
      "questionText": "Which algorithm is commonly used for ICA?",
      "options": [
        "K-means",
        "SVM",
        "FastICA",
        "Decision Tree"
      ],
      "correctAnswerIndex": 2,
      "explanation": "FastICA is a popular algorithm that maximizes non-Gaussianity to find independent components."
    },
    {
      "id": 25,
      "questionText": "Scenario: You mix 3 audio signals. Observed signals = 3. How many ICs can you extract?",
      "options": [
        "More than 3",
        "1",
        "At most 3",
        "Cannot extract any"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Number of independent components cannot exceed number of observed mixtures."
    },
    {
      "id": 26,
      "questionText": "Scenario: ICA applied to sensor signals with outliers. Best practice?",
      "options": [
        "Increase dimensions",
        "Ignore outliers",
        "Preprocess or remove outliers before ICA",
        "Randomly mix signals"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Outliers distort estimated independent components; preprocessing improves performance."
    },
    {
      "id": 27,
      "questionText": "Scenario: ICA on financial returns data. Why non-Gaussianity is needed?",
      "options": [
        "Independence does not matter",
        "Gaussian sources are easier",
        "Gaussian data cannot be analyzed",
        "Non-Gaussianity ensures sources are uniquely recoverable"
      ],
      "correctAnswerIndex": 3,
      "explanation": "ICA leverages higher-order statistics of non-Gaussian sources for unique separation."
    },
    {
      "id": 28,
      "questionText": "Scenario: ICA applied on images of faces. Use case?",
      "options": [
        "Identify independent facial features",
        "Predict identity directly",
        "Compress images",
        "Cluster faces only"
      ],
      "correctAnswerIndex": 0,
      "explanation": "ICA can extract independent features like eyes, nose, mouth patterns for face recognition."
    },
    {
      "id": 29,
      "questionText": "Scenario: Whitening is done before ICA. Why?",
      "options": [
        "Random initialization",
        "Reduces dimensionality only",
        "Reduces correlation and simplifies component extraction",
        "Removes labels"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Whitening transforms data to uncorrelated components, improving ICA convergence."
    },
    {
      "id": 30,
      "questionText": "Scenario: ICA applied to music mixture. Output components are rotated. Why?",
      "options": [
        "Algorithm failed",
        "Features are missing",
        "ICA is unique up to scaling and permutation",
        "Data is Gaussian"
      ],
      "correctAnswerIndex": 2,
      "explanation": "ICA components are identifiable only up to scaling and order; rotation/permutation does not affect independence."
    },
    {
      "id": 31,
      "questionText": "Scenario: ICA applied to mixed EEG signals. You observe one component is dominated by eye-blink artifacts. Best action?",
      "options": [
        "Keep all components",
        "Apply PCA only",
        "Remove that component to clean EEG",
        "Randomly select another component"
      ],
      "correctAnswerIndex": 2,
      "explanation": "ICA separates independent sources; removing artifact-dominated components cleans the EEG signal."
    },
    {
      "id": 32,
      "questionText": "ICA assumes that the sources are:",
      "options": [
        "Correlated and Gaussian",
        "Non-Gaussian and statistically independent",
        "Categorical only",
        "Binary and independent"
      ],
      "correctAnswerIndex": 1,
      "explanation": "ICA relies on non-Gaussianity and independence to successfully separate mixed signals."
    },
    {
      "id": 33,
      "questionText": "Scenario: Two mixed audio signals, one is nearly Gaussian. Applying ICA?",
      "options": [
        "Algorithm automatically converts to non-Gaussian",
        "Separation works perfectly",
        "May not separate Gaussian source",
        "Ignore the Gaussian source"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Gaussian sources cannot be uniquely separated due to rotational ambiguity in ICA."
    },
    {
      "id": 34,
      "questionText": "Scenario: You apply ICA on financial time series. One extracted component shows sudden spikes. Likely reason?",
      "options": [
        "Independent shock or outlier in market data",
        "Gaussian assumption violated",
        "Algorithm failure",
        "Too few observations"
      ],
      "correctAnswerIndex": 0,
      "explanation": "ICA separates independent sources; sudden spikes may correspond to independent events or outliers."
    },
    {
      "id": 35,
      "questionText": "ICA can be combined with PCA. Why?",
      "options": [
        "PCA improves independence",
        "Reduce dimensionality and noise before applying ICA",
        "Only for visualization",
        "ICA replaces PCA"
      ],
      "correctAnswerIndex": 1,
      "explanation": "PCA whitening simplifies ICA computation and reduces noise in high-dimensional data."
    },
    {
      "id": 36,
      "questionText": "Scenario: ICA applied to two mixed audio signals. Number of sources = number of observations. What if more sources than observations?",
      "options": [
        "ICA works normally",
        "Cannot fully recover sources",
        "Ignore extra sources",
        "Extra sources merged automatically"
      ],
      "correctAnswerIndex": 1,
      "explanation": "ICA requires the number of observed mixtures ≥ number of sources for unique recovery."
    },
    {
      "id": 37,
      "questionText": "ICA maximizes:",
      "options": [
        "Variance explained",
        "Non-Gaussianity of components",
        "Correlation between signals",
        "Euclidean distance"
      ],
      "correctAnswerIndex": 1,
      "explanation": "ICA algorithms maximize non-Gaussianity (kurtosis, negentropy) to find independent components."
    },
    {
      "id": 38,
      "questionText": "Scenario: ICA on images with overlapping text. Extracted component is noisy. Solution?",
      "options": [
        "Apply PCA only",
        "Remove components randomly",
        "Preprocess images, apply filtering, then ICA",
        "Increase number of components"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Noise can be reduced by preprocessing before ICA for clearer separation."
    },
    {
      "id": 39,
      "questionText": "Scenario: You use ICA for blind source separation of mixed speech signals. One component is silent. Likely cause?",
      "options": [
        "Gaussian assumption violated",
        "Random initialization failed",
        "Algorithm error",
        "ICA extracted a component with very low contribution from sources"
      ],
      "correctAnswerIndex": 3,
      "explanation": "ICA may extract components with negligible variance, appearing silent but still independent."
    },
    {
      "id": 40,
      "questionText": "Scenario: ICA applied to EEG, but one channel shows mixture of multiple brain regions. Why?",
      "options": [
        "Algorithm failed",
        "Signal is mixed; ICA separates independent sources, but spatial resolution limited",
        "Data is Gaussian",
        "Channel is corrupted"
      ],
      "correctAnswerIndex": 1,
      "explanation": "ICA can separate sources, but physical sensor overlap may cause mixed contributions."
    },
    {
      "id": 41,
      "questionText": "Scenario: ICA applied on high-dimensional dataset. Observed singular matrix. Solution?",
      "options": [
        "Ignore issue",
        "Apply PCA for dimensionality reduction before ICA",
        "Increase output dimensions",
        "Remove random features"
      ],
      "correctAnswerIndex": 1,
      "explanation": "High-dimensional data can cause singular covariance; PCA reduces dimensions and stabilizes ICA."
    },
    {
      "id": 42,
      "questionText": "Scenario: ICA applied to audio signals with strong noise. Best approach?",
      "options": [
        "Reduce number of components",
        "Increase ICA iterations",
        "Preprocess to reduce noise or apply filtering",
        "Use raw signals"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Noise affects ICA separation; preprocessing improves quality."
    },
    {
      "id": 43,
      "questionText": "Scenario: ICA applied on two mixed images; one image is highly uniform. Effect?",
      "options": [
        "Algorithm automatically enhances it",
        "ICA may have difficulty separating low-variance components",
        "No effect",
        "Outputs random component"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Low-variance sources contribute little to the mixture, making separation challenging."
    },
    {
      "id": 44,
      "questionText": "Scenario: ICA applied to mixed sensor signals, some channels missing. Effect?",
      "options": [
        "Data automatically interpolated",
        "ICA works normally",
        "Algorithm generates random values",
        "Cannot fully recover sources"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Missing observations reduce information; ICA cannot recover all independent components."
    },
    {
      "id": 45,
      "questionText": "Scenario: ICA on audio and image data combined. Feasible?",
      "options": [
        "Only images can be separated",
        "No, ICA works only for audio",
        "Yes, if signals are mixed and independent",
        "Only if data is Gaussian"
      ],
      "correctAnswerIndex": 2,
      "explanation": "ICA separates independent components regardless of domain, provided assumptions hold."
    },
    {
      "id": 46,
      "questionText": "Scenario: ICA applied to EEG signals. A component contains mixed artifacts. Why?",
      "options": [
        "Artifacts may not be perfectly independent",
        "Gaussian assumption violated",
        "Number of components too high",
        "Algorithm error"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Non-perfect independence of sources may cause mixed artifact components."
    },
    {
      "id": 47,
      "questionText": "ICA vs PCA: Which captures higher-order statistics?",
      "options": [
        "PCA",
        "ICA",
        "Neither",
        "Both equally"
      ],
      "correctAnswerIndex": 1,
      "explanation": "ICA uses higher-order statistics (non-Gaussianity), while PCA relies only on covariance (second-order statistics)."
    },
    {
      "id": 48,
      "questionText": "Scenario: ICA applied on two mixed audio tracks. Output shows small artifacts. Best practice?",
      "options": [
        "Discard ICA result",
        "Randomly re-initialize algorithm",
        "Increase number of components",
        "Post-process with filtering or denoising"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Post-processing can clean residual artifacts after ICA separation."
    },
    {
      "id": 49,
      "questionText": "Scenario: ICA applied to financial signals. One component is highly skewed. Why?",
      "options": [
        "ICA extracts non-Gaussian independent components, skewed distributions are typical",
        "Noise corrupted data",
        "Algorithm failed",
        "Increase number of components"
      ],
      "correctAnswerIndex": 0,
      "explanation": "ICA maximizes non-Gaussianity; skewed components are expected and represent independent sources."
    },
    {
      "id": 50,
      "questionText": "Scenario: ICA applied on audio signals. Components randomly scaled. Why?",
      "options": [
        "Algorithm failed",
        "Number of components wrong",
        "Data is Gaussian",
        "ICA components are identifiable up to scaling and permutation"
      ],
      "correctAnswerIndex": 3,
      "explanation": "ICA cannot determine original amplitude; scaling ambiguity is inherent in ICA."
    },
    {
      "id": 51,
      "questionText": "Scenario: ICA applied to two mixed images, one component inverted. Reason?",
      "options": [
        "Gaussian assumption violated",
        "ICA components are determined up to sign (polarity) ambiguity",
        "Algorithm error",
        "Noise dominance"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Sign ambiguity is common in ICA; independent components may appear inverted but remain valid."
    },
    {
      "id": 52,
      "questionText": "Scenario: You want to reduce dimensionality but retain independent features. Strategy?",
      "options": [
        "Apply PCA only",
        "Combine PCA for whitening, then ICA",
        "Apply ICA only",
        "Randomly remove features"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Whitening via PCA reduces dimensionality and removes correlations, improving ICA performance."
    },
    {
      "id": 53,
      "questionText": "Scenario: ICA applied to mixed music recordings. Some components overlap in frequency. Effect?",
      "options": [
        "Algorithm fails entirely",
        "No effect",
        "Partial separation; ICA may not fully disentangle overlapping frequency bands",
        "Complete separation"
      ],
      "correctAnswerIndex": 2,
      "explanation": "ICA separates independent sources; overlapping frequency bands can reduce separation quality."
    },
    {
      "id": 54,
      "questionText": "Scenario: ICA applied to EEG with eye blink artifacts. Component shows partial overlap with brain signals. Action?",
      "options": [
        "Carefully remove or attenuate artifact component to avoid losing brain signal",
        "Keep all components",
        "Remove completely",
        "Apply PCA only"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Overlapping components may contain both artifact and signal; selective attenuation preserves information."
    },
    {
      "id": 55,
      "questionText": "Scenario: ICA applied on audio mixture; one speaker quiet. Component extracted is faint. Why?",
      "options": [
        "Algorithm failed",
        "Source contribution is low, reflected in component magnitude",
        "Gaussian assumption violated",
        "Random initialization"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Components magnitude reflects source contribution; faint signals indicate weak source presence."
    },
    {
      "id": 56,
      "questionText": "ICA is particularly useful when signals are:",
      "options": [
        "Nonlinear only",
        "Gaussian and correlated",
        "Linearly mixed and non-Gaussian",
        "Categorical"
      ],
      "correctAnswerIndex": 2,
      "explanation": "ICA assumes linear mixing and non-Gaussian independent sources for successful separation."
    },
    {
      "id": 57,
      "questionText": "Scenario: ICA on mixed images produces components rotated. Reason?",
      "options": [
        "Algorithm error",
        "Data too noisy",
        "ICA components are identifiable only up to rotation, scaling, and permutation",
        "Gaussian assumption violated"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Rotation ambiguity is inherent; components may appear rotated but remain valid independent sources."
    },
    {
      "id": 58,
      "questionText": "Scenario: ICA applied to noisy EEG signals. Preprocessing includes:",
      "options": [
        "Removing labels only",
        "Random sampling",
        "Centering, whitening, artifact filtering",
        "No preprocessing"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Preprocessing enhances ICA performance by decorrelating signals and reducing noise."
    },
    {
      "id": 59,
      "questionText": "Scenario: ICA applied to financial data. Extracted component shows extreme values occasionally. Reason?",
      "options": [
        "Gaussian assumption violated",
        "Algorithm error",
        "Data missing",
        "Represents independent market shocks or events"
      ],
      "correctAnswerIndex": 3,
      "explanation": "ICA isolates independent events; extreme values may correspond to real shocks in sources."
    },
    {
      "id": 60,
      "questionText": "Scenario: ICA applied to audio mixture, one component silent. Best approach?",
      "options": [
        "Check source contribution; low-energy components may appear silent",
        "Increase iterations",
        "Mix signals randomly",
        "Discard ICA result"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Low-contribution sources produce faint components; it is normal in ICA separation."
    },
    {
      "id": 61,
      "questionText": "ICA assumes that the number of sources is:",
      "options": [
        "Always greater than mixtures",
        "Less than or equal to the number of observed mixtures",
        "Irrelevant",
        "Equal to one"
      ],
      "correctAnswerIndex": 1,
      "explanation": "ICA cannot separate more sources than observed signals; otherwise, the problem is underdetermined."
    },
    {
      "id": 62,
      "questionText": "Scenario: ICA applied on images of overlapping objects. Components are partially mixed. Solution?",
      "options": [
        "Randomly rotate components",
        "Discard ICA",
        "Improve preprocessing, reduce noise, adjust number of components",
        "Increase output dimension"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Better preprocessing and correct component selection improve separation quality."
    },
    {
      "id": 63,
      "questionText": "Scenario: ICA applied to audio, separated component inverted. Why?",
      "options": [
        "Algorithm failed",
        "Gaussian assumption violated",
        "Sign ambiguity is inherent in ICA",
        "Noise dominates"
      ],
      "correctAnswerIndex": 2,
      "explanation": "ICA components may be scaled and inverted; this does not affect independence."
    },
    {
      "id": 64,
      "questionText": "Scenario: ICA applied to mixed audio signals, one component shows slight distortion. Likely cause?",
      "options": [
        "Sources are not perfectly independent or noise present",
        "Algorithm failure",
        "Gaussian assumption violated",
        "Too few iterations"
      ],
      "correctAnswerIndex": 0,
      "explanation": "ICA assumes independence; slight dependence or noise can cause minor distortions in separated components."
    },
    {
      "id": 65,
      "questionText": "Scenario: You apply ICA to multi-sensor EEG recordings. Some components show mixed brain regions. Reason?",
      "options": [
        "Physical sensors capture overlapping signals; ICA cannot fully separate",
        "Algorithm failed",
        "Data is Gaussian",
        "Number of components too high"
      ],
      "correctAnswerIndex": 0,
      "explanation": "ICA separates independent sources, but sensor overlap can mix contributions from multiple regions."
    },
    {
      "id": 66,
      "questionText": "Scenario: ICA applied to images; one extracted component is nearly zero. Likely cause?",
      "options": [
        "Algorithm error",
        "The source has very low variance or contribution",
        "Gaussian assumption violated",
        "Too many iterations"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Low-variance sources appear faint or nearly zero in ICA outputs; this is normal behavior."
    },
    {
      "id": 67,
      "questionText": "Scenario: ICA applied to EEG data, but noise dominates. Best approach?",
      "options": [
        "Ignore noise",
        "Increase number of components",
        "Preprocess signals to remove artifacts before ICA",
        "Apply random scaling"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Preprocessing to remove artifacts improves ICA performance and separation quality."
    },
    {
      "id": 68,
      "questionText": "Scenario: ICA applied on financial data. Extracted components show skewed distributions. Why?",
      "options": [
        "Algorithm failed",
        "ICA extracts non-Gaussian independent components; skewness is expected",
        "Gaussian assumption violated",
        "Data incomplete"
      ],
      "correctAnswerIndex": 1,
      "explanation": "ICA maximizes non-Gaussianity, so skewed components reflect true independent sources."
    },
    {
      "id": 69,
      "questionText": "Scenario: ICA applied to mixed audio; one component appears inverted. Reason?",
      "options": [
        "Algorithm error",
        "Noise dominates",
        "ICA components are identifiable only up to sign (polarity) ambiguity",
        "Gaussian assumption violated"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Sign ambiguity is inherent in ICA; inverted components are valid independent sources."
    },
    {
      "id": 70,
      "questionText": "Scenario: ICA applied to multi-channel EEG, some channels missing. Effect?",
      "options": [
        "Algorithm produces random components",
        "Cannot fully recover all independent sources",
        "Gaussian assumption fails",
        "ICA works normally"
      ],
      "correctAnswerIndex": 1,
      "explanation": "ICA requires enough observed signals; missing channels reduce information and prevent full source recovery."
    },
    {
      "id": 71,
      "questionText": "Scenario: You applied ICA on EEG data with 64 channels and extracted 64 components. Some components are mixtures of multiple brain signals. Likely reason?",
      "options": [
        "Algorithm failed",
        "Gaussian assumption violated",
        "Sources are not perfectly independent and sensors pick overlapping signals",
        "Noise dominates"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Even with sufficient components, overlapping signals and partial dependence can cause mixed components."
    },
    {
      "id": 72,
      "questionText": "Scenario: ICA applied to financial returns of multiple assets. Some components show extreme spikes. Interpretation?",
      "options": [
        "Algorithm failure",
        "Gaussian sources assumption violated",
        "Represents independent shocks in the market",
        "Data insufficient"
      ],
      "correctAnswerIndex": 2,
      "explanation": "ICA isolates independent sources; extreme spikes can correspond to sudden market events or shocks."
    },
    {
      "id": 73,
      "questionText": "Scenario: You mix three audio sources into two channels. Applying ICA?",
      "options": [
        "Cannot fully recover all sources; problem is underdetermined",
        "ICA works normally",
        "Extra components are generated automatically",
        "Components become Gaussian"
      ],
      "correctAnswerIndex": 0,
      "explanation": "ICA requires the number of observed mixtures ≥ number of sources; fewer mixtures make full recovery impossible."
    },
    {
      "id": 74,
      "questionText": "Scenario: ICA applied on multi-sensor EEG with strong noise. Some components dominated by noise. Recommended action?",
      "options": [
        "Ignore noise",
        "Reduce number of components",
        "Preprocess signals to reduce noise and artifacts before ICA",
        "Apply PCA only"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Noise can dominate ICA outputs; preprocessing ensures cleaner separation of meaningful sources."
    },
    {
      "id": 75,
      "questionText": "Scenario: ICA applied to images with overlapping handwritten letters. One extracted component is faint and noisy. Likely reason?",
      "options": [
        "Algorithm failed",
        "Gaussian assumption violated",
        "Low variance of source or high noise contribution",
        "Too many components extracted"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Low-contribution sources appear faint; preprocessing or filtering can improve component clarity."
    },
    {
      "id": 76,
      "questionText": "Scenario: ICA applied to mixed audio signals. Extracted components randomly scaled. Why?",
      "options": [
        "Gaussian assumption violated",
        "Algorithm error",
        "ICA components are identifiable up to scaling and permutation",
        "Data insufficient"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Scaling ambiguity is inherent in ICA; absolute amplitude cannot be determined."
    },
    {
      "id": 77,
      "questionText": "Scenario: ICA applied to multi-sensor EEG data; one component contains both eye-blink artifacts and brain signals. Best practice?",
      "options": [
        "Remove entire component",
        "Apply PCA only",
        "Ignore and keep all components",
        "Carefully attenuate artifact without removing valuable brain signals"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Overlapping components require careful processing to preserve meaningful information while reducing artifacts."
    },
    {
      "id": 78,
      "questionText": "Scenario: ICA applied on financial time series. One extracted component shows skewed returns distribution. Interpretation?",
      "options": [
        "Algorithm failed",
        "Reflects independent non-Gaussian factors driving the market",
        "Gaussian assumption violated",
        "Data insufficient"
      ],
      "correctAnswerIndex": 1,
      "explanation": "ICA extracts non-Gaussian independent components; skewness indicates independent market factors."
    },
    {
      "id": 79,
      "questionText": "Scenario: ICA applied to audio signals. One extracted component is nearly silent. Reason?",
      "options": [
        "Algorithm failed",
        "Source contribution to the mixture is very low",
        "Gaussian assumption violated",
        "Random initialization failed"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Faint components reflect sources with low variance or weak presence in the mixtures."
    },
    {
      "id": 80,
      "questionText": "Scenario: ICA applied on EEG with missing channels. Effect?",
      "options": [
        "Algorithm works normally",
        "Components are random",
        "Cannot fully recover all independent sources",
        "Gaussian assumption violated"
      ],
      "correctAnswerIndex": 2,
      "explanation": "ICA requires enough observed signals; missing channels reduce information and prevent full separation."
    },
    {
      "id": 81,
      "questionText": "Scenario: ICA applied to high-dimensional images. Some components are mixtures of multiple features. Recommended action?",
      "options": [
        "Increase number of components",
        "Randomly remove features",
        "Ignore and use ICA directly",
        "Apply PCA for dimensionality reduction and whitening before ICA"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Dimensionality reduction and whitening improve ICA stability and separation in high-dimensional data."
    },
    {
      "id": 82,
      "questionText": "Scenario: ICA applied on mixed audio, some frequency bands overlap. Outcome?",
      "options": [
        "Complete separation",
        "Algorithm fails entirely",
        "No effect",
        "Partial separation; overlapping frequencies reduce effectiveness"
      ],
      "correctAnswerIndex": 3,
      "explanation": "ICA assumes independence; overlapping frequency content may limit perfect separation."
    },
    {
      "id": 83,
      "questionText": "Scenario: ICA applied on EEG signals with eye-blink artifacts. Some components contain both artifacts and brain signals. Action?",
      "options": [
        "Keep all components",
        "Apply PCA only",
        "Remove entire component",
        "Selective attenuation to remove artifacts without losing brain activity"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Careful component processing preserves useful information while reducing artifacts."
    },
    {
      "id": 84,
      "questionText": "Scenario: ICA applied to two mixed images; extracted components inverted in polarity. Reason?",
      "options": [
        "Gaussian assumption violated",
        "Sign ambiguity is inherent in ICA",
        "Noise dominates",
        "Algorithm error"
      ],
      "correctAnswerIndex": 1,
      "explanation": "ICA components can have arbitrary sign; inversion does not affect independence."
    },
    {
      "id": 85,
      "questionText": "Scenario: ICA applied to multi-sensor EEG with strong artifacts. Components show partial mixing. Likely reason?",
      "options": [
        "Data insufficient",
        "Gaussian assumption violated",
        "Algorithm failed",
        "Sources are not perfectly independent or sensor overlap exists"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Partial dependence or overlapping sensor recordings can cause mixed components."
    },
    {
      "id": 86,
      "questionText": "Scenario: ICA applied to audio mixture; faint component extracted. Best interpretation?",
      "options": [
        "Algorithm failed",
        "Component corresponds to source with low contribution to mixture",
        "Gaussian assumption violated",
        "Too many iterations"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Low-energy sources produce faint components, which is normal in ICA."
    },
    {
      "id": 87,
      "questionText": "Scenario: ICA applied on EEG with 128 channels. Extracted components appear noisy. Recommended step?",
      "options": [
        "Discard ICA result",
        "Randomly mix channels",
        "Increase number of components",
        "Preprocess with filtering and artifact removal before ICA"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Preprocessing improves signal quality and ICA separation."
    },
    {
      "id": 88,
      "questionText": "Scenario: ICA applied to financial signals. Extracted component has extreme outliers. Likely interpretation?",
      "options": [
        "Algorithm failure",
        "Gaussian assumption violated",
        "Represents independent extreme market events",
        "Data missing"
      ],
      "correctAnswerIndex": 2,
      "explanation": "ICA isolates independent sources; extreme values may correspond to real shocks or events."
    },
    {
      "id": 89,
      "questionText": "Scenario: ICA applied on multi-sensor EEG; some components appear to be mixtures of several brain sources. Why?",
      "options": [
        "Algorithm failed",
        "Partial dependence or overlapping sensor recordings",
        "Gaussian assumption violated",
        "Number of components too high"
      ],
      "correctAnswerIndex": 1,
      "explanation": "ICA assumes independence; overlapping measurements can create mixed components."
    },
    {
      "id": 90,
      "questionText": "Scenario: ICA applied to mixed audio; one component appears silent. Action?",
      "options": [
        "Randomly re-initialize algorithm",
        "Discard ICA result",
        "Increase number of components",
        "Check source contribution; low-energy sources may appear silent"
      ],
      "correctAnswerIndex": 3,
      "explanation": "Silent components usually reflect sources with minimal contribution; not a failure."
    },
    {
      "id": 91,
      "questionText": "Scenario: ICA applied on EEG with missing channels. Solution?",
      "options": [
        "Collect more channels or use methods for missing data",
        "Ignore missing channels",
        "Randomly fill missing data",
        "Apply PCA only"
      ],
      "correctAnswerIndex": 0,
      "explanation": "ICA requires sufficient observed signals; missing channels prevent full source recovery."
    },
    {
      "id": 92,
      "questionText": "Scenario: ICA applied on mixed images; low-variance components faint. Best approach?",
      "options": [
        "Discard faint components",
        "Enhance preprocessing or use more observations",
        "Increase ICA iterations only",
        "Randomly mix images"
      ],
      "correctAnswerIndex": 1,
      "explanation": "Low-variance sources require preprocessing and sufficient data for effective separation."
    },
    {
      "id": 93,
      "questionText": "Scenario: ICA applied to EEG with eye-blink and muscle artifacts. Some components overlap. Action?",
      "options": [
        "Apply PCA only",
        "Keep all components",
        "Selective attenuation to remove artifacts without losing brain signal",
        "Remove all overlapping components"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Overlapping components require careful attenuation to preserve meaningful signals."
    },
    {
      "id": 94,
      "questionText": "Scenario: ICA applied on audio mixture; overlapping frequency content. Effect?",
      "options": [
        "Algorithm fails",
        "Partial separation; overlapping reduces effectiveness",
        "No effect",
        "Complete separation"
      ],
      "correctAnswerIndex": 1,
      "explanation": "ICA cannot perfectly separate overlapping frequencies; independence assumption is partially violated."
    },
    {
      "id": 95,
      "questionText": "Scenario: ICA applied to EEG with noisy channels. Recommended preprocessing?",
      "options": [
        "Filtering, artifact removal, centering, whitening",
        "Randomly remove channels",
        "Apply ICA directly",
        "Ignore preprocessing"
      ],
      "correctAnswerIndex": 0,
      "explanation": "Preprocessing improves signal quality and ICA separation."
    },
    {
      "id": 96,
      "questionText": "Scenario: ICA applied to financial data; extracted component shows heavy skew. Interpretation?",
      "options": [
        "Data missing",
        "Represents independent non-Gaussian market factor",
        "Algorithm failed",
        "Gaussian assumption violated"
      ],
      "correctAnswerIndex": 1,
      "explanation": "ICA identifies independent non-Gaussian factors; skewness reflects this property."
    },
    {
      "id": 97,
      "questionText": "Scenario: ICA applied to multi-channel EEG; some components inverted. Reason?",
      "options": [
        "Algorithm error",
        "Noise dominates",
        "Sign ambiguity inherent in ICA",
        "Gaussian assumption violated"
      ],
      "correctAnswerIndex": 2,
      "explanation": "ICA components may appear inverted due to sign ambiguity; still valid."
    },
    {
      "id": 98,
      "questionText": "Scenario: ICA applied to audio signals; faint or near-zero components. Best explanation?",
      "options": [
        "Algorithm failed",
        "Gaussian assumption violated",
        "Low-contribution sources produce faint components",
        "Random initialization failed"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Components magnitude reflects source contribution; faint components indicate weak sources."
    },
    {
      "id": 99,
      "questionText": "Scenario: ICA applied on EEG; extracted components partially mixed. Solution?",
      "options": [
        "Increase ICA iterations only",
        "Randomly mix channels",
        "Improve preprocessing, adjust number of components, and check sensor overlap",
        "Discard ICA result"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Proper preprocessing and component selection improve separation of partially mixed sources."
    },
    {
      "id": 100,
      "questionText": "Scenario: ICA applied on audio mixture; one component dominated by noise. Best practice?",
      "options": [
        "Increase number of components",
        "Apply PCA only",
        "Preprocess to remove noise before ICA",
        "Ignore noise"
      ],
      "correctAnswerIndex": 2,
      "explanation": "Noise can dominate ICA; preprocessing ensures meaningful source separation."
    }
  ]
}